From f46ed208c3db53538809a55a05ed5f1702bf1af7 Mon Sep 17 00:00:00 2001 From: Terencio Agozzino Date: Wed, 25 May 2022 10:11:17 +0200 Subject: [PATCH] major: public master thesis --- Makefile | 71 ++ bibli.bib | 1077 +++++++++++++++++ data/embedders/max-depth/bert.csv | 4 + data/embedders/max-depth/fasttext.csv | 4 + data/embedders/max-depth/word2vec.csv | 4 + data/embedders/max-walks/bert.csv | 5 + data/embedders/max-walks/fasttext.csv | 5 + data/embedders/max-walks/word2vec.csv | 5 + .../max-depth/2/objfreq-inv-split.csv | 4 + data/samplers/max-depth/2/objfreq-inv.csv | 4 + data/samplers/max-depth/2/objfreq.csv | 4 + data/samplers/max-depth/2/objpredfreq-inv.csv | 4 + data/samplers/max-depth/2/objpredfreq.csv | 4 + .../max-depth/2/pagerank-inv-split.csv | 4 + data/samplers/max-depth/2/pagerank-inv.csv | 4 + data/samplers/max-depth/2/pagerank-split.csv | 4 + data/samplers/max-depth/2/pagerank.csv | 4 + data/samplers/max-depth/2/predfreq-inv.csv | 4 + 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.../scaled-dot-product-attention.pdf | Bin 0 -> 22019 bytes master-thesis.pdf | Bin 0 -> 2158798 bytes master-thesis.tex | 153 +++ res/internship_master-thesis.pdf | Bin 0 -> 1920469 bytes res/specs.pdf | Bin 0 -> 77404 bytes src/abstract.tex | 32 + src/acknowledgments.tex | 63 + src/background.tex | 32 + src/background/attention.tex | 304 +++++ src/background/graphs.tex | 147 +++ src/background/ml.tex | 264 ++++ src/background/nlp.tex | 154 +++ src/background/transformers.tex | 207 ++++ src/benchmarks.tex | 42 + src/benchmarks/embedders.tex | 237 ++++ src/benchmarks/samplers.tex | 470 +++++++ src/benchmarks/walkers.tex | 236 ++++ src/conclusion.tex | 116 ++ src/discussion.tex | 156 +++ src/embedders.tex | 15 + src/embedders/bert.tex | 244 ++++ src/embedders/fasttext.tex | 146 +++ src/embedders/word2vec.tex | 467 +++++++ src/flyleaf.tex | 82 ++ src/introduction.tex | 122 ++ src/objectives.tex | 118 ++ src/rdf2vec.tex | 225 ++++ src/references.tex | 7 + src/related-work.tex | 122 ++ 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+LANG_ASPELL=en + +IMG_DIR=img +SRC_DIR=src + +MISC=Makefile + +MAJOR_VERSION=0 +MINOR_VERSION=1 +VERSION=$(MAJOR_VERSION).$(MINOR_VERSION) + +UNAME=$(shell uname) + +BIBTEX=bibtex +TEX=xelatex +TEX_FILES=$(wildcard $(SRC_DIR)/*.tex) +TEX_FLAGS=--shell-escape --synctex=1 + +all: $(NAME) + +$(NAME): + @echo "** Compiling the \"$(NAME)\" file." + $(TEX) $(TEX_FLAGS) $(NAME) + +check: $(addsuffix .spchk,$(basename $(TEX_FILES))) + +%.spchk: %.tex + aspell -x -l $(LANG_ASPELL) -t -c $< + +clean: + @echo "** Removing subsidiary TeX files." + $(RM) $(NAME).{aux,bbl,blg,lof,log,lom,lot,out,snm,tex.backup,nav,toc} + +help: + @echo "make COMMAND" + @echo + @echo "COMMAND:" + @echo " all compile the \"$(NAME)\" file" + @echo " check check spelling of TeX files" + @echo " clean remove subsidiary TeX files" + @echo " help display available commands" + @echo " full compile the \"$(NAME)\" file and the bibliography" + @echo " open open the \"$(NAME)\" fileq" + @echo " tar create a tar archive" + +full: + @echo "** Compiling the \"$(NAME)\" file and the bibliography." + $(TEX) $(TEX_FLAGS) $(NAME) + $(BIBTEX) $(NAME) + $(TEX) $(TEX_FLAGS) $(NAME) + $(TEX) $(TEX_FLAGS) $(NAME) + +open: +ifeq ($(UNAME), Linux) + @echo "** Opening the \"$(NAME)\" file with evince." + evince $(NAME).pdf & +endif +ifeq ($(UNAME), Darwin) + @echo "** Opening the \"$(NAME)\" file with preview." + open $(NAME).pdf & +endif + +tar: + @echo "** Creating the tar archive." + @mkdir -p $(NAME)-$(VERSION) + @cp -r $(SRC_DIR) $(IMG_DIR) $(MISC) $(NAME).tex $(NAME)-$(VERSION) + tar czvf $(NAME)-$(VERSION).tar.gz $(NAME)-$(VERSION) + $(RM) -r $(NAME)-$(VERSION) + +.PHONY: all check clean help full open tar $(NAME) diff --git a/bibli.bib b/bibli.bib new file mode 100644 index 0000000..108c130 --- /dev/null +++ b/bibli.bib @@ -0,0 +1,1077 @@ +@article{DBLP:journals/tacl/BojanowskiGJM17, + author = {Piotr Bojanowski and + Edouard Grave and + Armand Joulin and + Tom{\'{a}}s Mikolov}, + title = {Enriching Word Vectors with Subword Information}, + journal = {Trans. Assoc. Comput. Linguistics}, + volume = {5}, + pages = {135--146}, + year = {2017}, + url = {https://transacl.org/ojs/index.php/tacl/article/view/999}, + timestamp = {Wed, 17 Feb 2021 21:55:26 +0100}, + biburl = {https://dblp.org/rec/journals/tacl/BojanowskiGJM17.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@inproceedings{DBLP:conf/emnlp/LuongPM15, + author = {Thang Luong and + Hieu Pham and + Christopher D. Manning}, + editor = {Llu{\'{\i}}s M{\`{a}}rquez and + Chris Callison{-}Burch and + Jian Su and + Daniele Pighin and + Yuval Marton}, + title = {Effective Approaches to Attention-based Neural Machine Translation}, + booktitle = {Proceedings of the 2015 Conference on Empirical Methods in Natural + Language Processing, {EMNLP} 2015, Lisbon, Portugal, September 17-21, + 2015}, + pages = {1412--1421}, + publisher = {The Association for Computational Linguistics}, + year = {2015}, + url = {https://doi.org/10.18653/v1/d15-1166}, + doi = {10.18653/v1/d15-1166}, + timestamp = {Tue, 28 Jan 2020 10:28:39 +0100}, + biburl = {https://dblp.org/rec/conf/emnlp/LuongPM15.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@inproceedings{DBLP:conf/acl/HendrycksLWDKS20, + author = {Dan Hendrycks and + Xiaoyuan Liu and + Eric Wallace and + Adam Dziedzic and + Rishabh Krishnan and + Dawn Song}, + editor = {Dan Jurafsky and + Joyce Chai and + Natalie Schluter and + Joel R. Tetreault}, + title = {Pretrained Transformers Improve Out-of-Distribution Robustness}, + booktitle = {Proceedings of the 58th Annual Meeting of the Association for Computational + Linguistics, {ACL} 2020, Online, July 5-10, 2020}, + pages = {2744--2751}, + publisher = {Association for Computational Linguistics}, + year = {2020}, + url = {https://doi.org/10.18653/v1/2020.acl-main.244}, + doi = {10.18653/v1/2020.acl-main.244}, + timestamp = {Fri, 08 Jan 2021 21:20:23 +0100}, + biburl = {https://dblp.org/rec/conf/acl/HendrycksLWDKS20.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@article{article:beseiso, +author = {Beseiso, Majdi and Alzahrani, Saleh}, +year = {2020}, +month = {11}, +pages = {204-210}, +title = {An Empirical Analysis of BERT Embedding for Automated Essay Scoring}, +volume = {11}, +journal = {International Journal of Advanced Computer Science and Applications}, +doi = {10.14569/IJACSA.2020.0111027} +} + +@inproceedings{DBLP:conf/embc/SahaLG20, + author = {Budhaditya Saha and + Sanal Lisboa and + Shameek Ghosh}, + title = {Understanding patient complaint characteristics using contextual clinical + {BERT} embeddings}, + booktitle = {42nd Annual International Conference of the {IEEE} Engineering in + Medicine {\&} Biology Society, {EMBC} 2020, Montreal, QC, Canada, + July 20-24, 2020}, + pages = {5847--5850}, + publisher = {{IEEE}}, + year = {2020}, + url = {https://doi.org/10.1109/EMBC44109.2020.9175577}, + doi = {10.1109/EMBC44109.2020.9175577}, + timestamp = {Fri, 25 Dec 2020 01:14:44 +0100}, + biburl = {https://dblp.org/rec/conf/embc/SahaLG20.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + + +@article{DBLP:journals/jodsn/CeravoloAACCDMK18, + author = {Paolo Ceravolo and + Antonia Azzini and + Marco Angelini and + Tiziana Catarci and + Philippe Cudr{\'{e}}{-}Mauroux and + Ernesto Damiani and + Alexandra Mazak and + Maurice van Keulen and + Mustafa Jarrar and + Giuseppe Santucci and + Kai{-}Uwe Sattler and + Monica Scannapieco and + Manuel Wimmer and + Robert Wrembel and + Fadi A. Zaraket}, + title = {Big Data Semantics}, + journal = {J. Data Semant.}, + volume = {7}, + number = {2}, + pages = {65--85}, + year = {2018}, + url = {https://doi.org/10.1007/s13740-018-0086-2}, + doi = {10.1007/s13740-018-0086-2}, + timestamp = {Tue, 08 Sep 2020 13:32:22 +0200}, + biburl = {https://dblp.org/rec/journals/jodsn/CeravoloAACCDMK18.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@misc{singhal_2012, +title={Introducing the Knowledge Graph: things, not strings}, +url={https://www.blog.google/products/search/introducing-knowledge-graph-things-not}, +journal={Google}, +publisher={Google}, +author={Singhal, Amit}, +year={2012}, +month={May}, +note={Accessed: May 2021} +} + +@article{article:genese, + author = {Genet Asefa Gesese and + Russa Biswas and + Mehwish Alam and + Harald Sack}, + title = {A Survey on Knowledge Graph Embeddings with Literals: Which model + links better Literal-ly?}, + journal = {CoRR}, + volume = {abs/1910.12507}, + year = {2019}, + url = {http://arxiv.org/abs/1910.12507}, + archivePrefix = {arXiv}, + eprint = {1910.12507}, + timestamp = {Thu, 31 Oct 2019 14:02:26 +0100}, + biburl = {https://dblp.org/rec/journals/corr/abs-1910-12507.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@article{article:vandewiele, + author = {Gilles Vandewiele and + Bram Steenwinckel and + Pieter Bonte and + Michael Weyns and + Heiko Paulheim and + Petar Ristoski and + Filip De Turck and + Femke Ongenae}, + title = {{Walk Extraction Strategies for Node Embeddings with RDF2Vec in Knowledge + Graphs}}, + journal = {CoRR}, + volume = {abs/2009.04404}, + year = {2020}, + url = {https://arxiv.org/abs/2009.04404}, + archivePrefix = {arXiv}, + eprint = {2009.04404}, + timestamp = {Thu, 17 Sep 2020 12:49:52 +0200}, + biburl = {https://dblp.org/rec/journals/corr/abs-2009-04404.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@inproceedings{inproceedings:kristiadi, + author = {Agustinus Kristiadi and + Mohammad Asif Khan and + Denis Lukovnikov and + Jens Lehmann and + Asja Fischer}, + editor = {Chiara Ghidini and + Olaf Hartig and + Maria Maleshkova and + Vojtech Sv{\'{a}}tek and + Isabel F. Cruz and + Aidan Hogan and + Jie Song and + Maxime Lefran{\c{c}}ois and + Fabien Gandon}, + title = {Incorporating Literals into Knowledge Graph Embeddings}, + booktitle = {The Semantic Web - {ISWC} 2019 - 18th International Semantic Web Conference, + Auckland, New Zealand, October 26-30, 2019, Proceedings, Part {I}}, + series = {Lecture Notes in Computer Science}, + volume = {11778}, + pages = {347--363}, + publisher = {Springer}, + year = {2019}, + url = {https://doi.org/10.1007/978-3-030-30793-6\_20}, + doi = {10.1007/978-3-030-30793-6\_20}, + timestamp = {Sat, 30 May 2020 20:05:29 +0200}, + biburl = {https://dblp.org/rec/conf/semweb/KristiadiKL0F19.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@inproceedings{vaswani:attention, + author = {Ashish Vaswani and + Noam Shazeer and + Niki Parmar and + Jakob Uszkoreit and + Llion Jones and + Aidan N. Gomez and + Lukasz Kaiser and + Illia Polosukhin}, + editor = {Isabelle Guyon and + Ulrike von Luxburg and + Samy Bengio and + Hanna M. Wallach and + Rob Fergus and + S. V. N. Vishwanathan and + Roman Garnett}, + title = {Attention is All you Need}, + booktitle = {Advances in Neural Information Processing Systems 30: Annual Conference + on Neural Information Processing Systems 2017, December 4-9, 2017, + Long Beach, CA, {USA}}, + pages = {5998--6008}, + year = {2017}, + url = {https://proceedings.neurips.cc/paper/2017/hash/3f5ee243547dee91fbd053c1c4a845aa-Abstract.html}, + timestamp = {Thu, 21 Jan 2021 15:15:21 +0100}, + biburl = {https://dblp.org/rec/conf/nips/VaswaniSPUJGKP17.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@article{vaswani, + author = {Cheng{-}Zhi Anna Huang and + Ashish Vaswani and + Jakob Uszkoreit and + Noam Shazeer and + Curtis Hawthorne and + Andrew M. Dai and + Matthew D. Hoffman and + Douglas Eck}, + title = {An Improved Relative Self-Attention Mechanism for Transformer with + Application to Music Generation}, + journal = {CoRR}, + volume = {abs/1809.04281}, + year = {2018}, + url = {http://arxiv.org/abs/1809.04281}, + archivePrefix = {arXiv}, + eprint = {1809.04281}, + timestamp = {Fri, 05 Oct 2018 11:34:52 +0200}, + biburl = {https://dblp.org/rec/journals/corr/abs-1809-04281.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@inproceedings{bahdanau, + author = {Jan Chorowski and + Dzmitry Bahdanau and + Dmitriy Serdyuk and + Kyunghyun Cho and + Yoshua Bengio}, + editor = {Corinna Cortes and + Neil D. Lawrence and + Daniel D. Lee and + Masashi Sugiyama and + Roman Garnett}, + title = {Attention-Based Models for Speech Recognition}, + booktitle = {Advances in Neural Information Processing Systems 28: Annual Conference + on Neural Information Processing Systems 2015, December 7-12, 2015, + Montreal, Quebec, Canada}, + pages = {577--585}, + year = {2015}, + url = {http://papers.nips.cc/paper/5847-attention-based-models-for-speech-recognition}, + timestamp = {Fri, 06 Mar 2020 16:57:49 +0100}, + biburl = {https://dblp.org/rec/conf/nips/ChorowskiBSCB15.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@inproceedings{cheng, + author = {Jianpeng Cheng and + Li Dong and + Mirella Lapata}, + editor = {Jian Su and + Xavier Carreras and + Kevin Duh}, + title = {Long Short-Term Memory-Networks for Machine Reading}, + booktitle = {Proceedings of the 2016 Conference on Empirical Methods in Natural + Language Processing, {EMNLP} 2016, Austin, Texas, USA, November 1-4, + 2016}, + pages = {551--561}, + publisher = {The Association for Computational Linguistics}, + year = 2016, + url = {https://doi.org/10.18653/v1/d16-1053}, + doi = {10.18653/v1/d16-1053}, + timestamp = {Tue, 28 Jan 2020 10:28:37 +0100}, + biburl = {https://dblp.org/rec/conf/emnlp/0001DL16.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +% RELATED WORK + +@inproceedings{khatri, + author = {Akshay Khatri and + Pranav P}, + editor = {Beata Beigman Klebanov and + Ekaterina Shutova and + Patricia Lichtenstein and + Smaranda Muresan and + Chee Wee Leong and + Anna Feldman and + Debanjan Ghosh}, + title = {Sarcasm Detection in Tweets with {BERT} and GloVe Embeddings}, + booktitle = {Proceedings of the Second Workshop on Figurative Language Processing, + Fig-Lang@ACL 2020, Online, July 9, 2020}, + pages = {56--60}, + publisher = {Association for Computational Linguistics}, + year = {2020}, + url = {https://www.aclweb.org/anthology/2020.figlang-1.7/}, + timestamp = {Fri, 14 Aug 2020 11:51:21 +0200}, + biburl = {https://dblp.org/rec/conf/acl-figlang/KhatriP20.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@inproceedings{peng, + author = {Yifan Peng and + Shankai Yan and + Zhiyong Lu}, + editor = {Dina Demner{-}Fushman and + Kevin Bretonnel Cohen and + Sophia Ananiadou and + Junichi Tsujii}, + title = {Transfer Learning in Biomedical Natural Language Processing: An Evaluation + of {BERT} and ELMo on Ten Benchmarking Datasets}, + booktitle = {Proceedings of the 18th BioNLP Workshop and Shared Task, BioNLP@ACL + 2019, Florence, Italy, August 1, 2019}, + pages = {58--65}, + publisher = {Association for Computational Linguistics}, + year = {2019}, + url = {https://doi.org/10.18653/v1/w19-5006}, + doi = {10.18653/v1/w19-5006}, + timestamp = {Tue, 28 Jan 2020 10:29:22 +0100}, + biburl = {https://dblp.org/rec/conf/bionlp/PengYL19.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@article{DBLP:journals/semweb/RistoskiRNLP19, + author = {Petar Ristoski and + Jessica Rosati and + Tommaso Di Noia and + Renato De Leone and + Heiko Paulheim}, + title = {RDF2Vec: {RDF} graph embeddings and their applications}, + journal = {Semantic Web}, + volume = {10}, + number = {4}, + pages = {721--752}, + year = {2019}, + url = {https://doi.org/10.3233/SW-180317}, + doi = {10.3233/SW-180317}, + timestamp = {Wed, 25 Sep 2019 17:53:41 +0200}, + biburl = {https://dblp.org/rec/journals/semweb/RistoskiRNLP19.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@inproceedings{inproceedings:mikolov, + author = {Tomas Mikolov and + Kai Chen and + Greg Corrado and + Jeffrey Dean}, + editor = {Yoshua Bengio and + Yann LeCun}, + title = {Efficient Estimation of Word Representations in Vector Space}, + booktitle = {1st International Conference on Learning Representations, {ICLR} 2013, + Scottsdale, Arizona, USA, May 2-4, 2013, Workshop Track Proceedings}, + year = {2013}, + url = {http://arxiv.org/abs/1301.3781}, + timestamp = {Thu, 25 Jul 2019 14:25:36 +0200}, + biburl = {https://dblp.org/rec/journals/corr/abs-1301-3781.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@inproceedings{ethayarajh, + author = {Kawin Ethayarajh}, + editor = {Kentaro Inui and + Jing Jiang and + Vincent Ng and + Xiaojun Wan}, + title = {How Contextual are Contextualized Word Representations? Comparing + the Geometry of BERT, ELMo, and {GPT-2} Embeddings}, + booktitle = {Proceedings of the 2019 Conference on Empirical Methods in Natural + Language Processing and the 9th International Joint Conference on + Natural Language Processing, {EMNLP-IJCNLP} 2019, Hong Kong, China, + November 3-7, 2019}, + pages = {55--65}, + publisher = {Association for Computational Linguistics}, + year = {2019}, + url = {https://doi.org/10.18653/v1/D19-1006}, + doi = {10.18653/v1/D19-1006}, + timestamp = {Thu, 12 Dec 2019 13:23:49 +0100}, + biburl = {https://dblp.org/rec/conf/emnlp/Ethayarajh19.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@article{distilbert, + author = {Victor Sanh and + Lysandre Debut and + Julien Chaumond and + Thomas Wolf}, + title = {DistilBERT, a distilled version of {BERT:} smaller, faster, cheaper + and lighter}, + journal = {CoRR}, + volume = {abs/1910.01108}, + year = {2019}, + url = {http://arxiv.org/abs/1910.01108}, + archivePrefix = {arXiv}, + eprint = {1910.01108}, + timestamp = {Tue, 02 Jun 2020 12:48:59 +0200}, + biburl = {https://dblp.org/rec/journals/corr/abs-1910-01108.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@article{zhang, + author = {Jiawei Zhang and + Haopeng Zhang and + Congying Xia and + Li Sun}, + title = {Graph-Bert: Only Attention is Needed for Learning Graph Representations}, + journal = {CoRR}, + volume = {abs/2001.05140}, + year = {2020}, + url = {https://arxiv.org/abs/2001.05140}, + archivePrefix = {arXiv}, + eprint = {2001.05140}, + timestamp = {Thu, 12 Nov 2020 15:00:59 +0100}, + biburl = {https://dblp.org/rec/journals/corr/abs-2001-05140.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@article{article:mukherjee, + author = {Sourav Mukherjee and + Tim Oates and + Ryan Wright}, + title = {{Graph Node Embeddings using Domain-Aware Biased Random Walks}}, + journal = {CoRR}, + volume = {abs/1908.02947}, + year = 2019, + url = {http://arxiv.org/abs/1908.02947}, + archivePrefix = {arXiv}, + eprint = {1908.02947}, + timestamp = {Fri, 09 Aug 2019 12:15:56 +0200}, + biburl = {https://dblp.org/rec/journals/corr/abs-1908-02947.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@article{article:hamilton, + author = {William L. Hamilton and + Rex Ying and + Jure Leskovec}, + title = {Representation Learning on Graphs: Methods and Applications}, + journal = {{IEEE} Data Eng. 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Web Semant.}, + volume = {36}, + pages = {1--22}, + year = {2016}, + url = {https://doi.org/10.1016/j.websem.2016.01.001}, + doi = {10.1016/j.websem.2016.01.001}, + timestamp = {Tue, 29 Jan 2019 12:27:04 +0100}, + biburl = {https://dblp.org/rec/journals/ws/RistoskiP16.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@article{article:taweel, + author = {Ahmad Al Taweel and + Heiko Paulheim}, + title = {{Towards Exploiting Implicit Human Feedback for Improving RDF2vec Embeddings}}, + journal = {CoRR}, + volume = {abs/2004.04423}, + year = {2020}, + url = {https://arxiv.org/abs/2004.04423}, + archivePrefix = {arXiv}, + eprint = {2004.04423}, + timestamp = {Tue, 14 Apr 2020 01:00:00 +0200}, + biburl = {https://dblp.org/rec/journals/corr/abs-2004-04423.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@article{article:vries, + author = {Gerben Klaas Dirk de Vries and + Steven de Rooij}, + title = {Substructure counting graph kernels for machine learning from {RDF} + data}, + journal = {J. Web Semant.}, + volume = {35}, + pages = {71--84}, + year = {2015}, + url = {https://doi.org/10.1016/j.websem.2015.08.002}, + doi = {10.1016/j.websem.2015.08.002}, + timestamp = {Tue, 29 Jan 2019 12:27:03 +0100}, + biburl = {https://dblp.org/rec/journals/ws/VriesR15.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@inproceedings{inproceedings:cochez, + author = {Michael Cochez and + Petar Ristoski and + Simone Paolo Ponzetto and + Heiko Paulheim}, + editor = {Rajendra Akerkar and + Alfredo Cuzzocrea and + Jannong Cao and + Mohand{-}Said Hacid}, + title = {Biased graph walks for {RDF} graph embeddings}, + booktitle = {Proceedings of the 7th International Conference on Web Intelligence, + Mining and Semantics, {WIMS} 2017, Amantea, Italy, June 19-22, 2017}, + pages = {21:1--21:12}, + publisher = {{ACM}}, + year = 2017, + url = {https://doi.org/10.1145/3102254.3102279}, + doi = {10.1145/3102254.3102279}, + timestamp = {Fri, 27 Mar 2020 08:55:29 +0100}, + biburl = {https://dblp.org/rec/conf/wims/CochezRPP17.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@misc{mccormick, +author = {Chris McCormick}, +title={{\textit{Word2Vec Tutorial Part 2 - Negative Sampling}}}, +url={http://mccormickml.com/2017/01/11/word2vec-tutorial-part-2-negative-sampling/}, +journal={Word2Vec Tutorial Part 2 - Negative Sampling}, +year={2017}, +month={Jan}, +note={Accessed: April 2021} +} + +@inproceedings{inproceedings:ristoski:strategies, + author = {Petar Ristoski and + Heiko Paulheim}, + editor = {Ilaria Tiddi and + Mathieu d'Aquin and + Nicolas Jay}, + title = {A Comparison of Propositionalization Strategies for Creating Features + from Linked Open Data}, + booktitle = {Proceedings of the 1st Workshop on Linked Data for Knowledge Discovery + co-located with European Conference on Machine Learning and Principles + and Practice of Knowledge Discovery in Databases {(ECML} {PKDD} 2014), + Nancy, France, September 19th, 2014}, + series = {{CEUR} Workshop Proceedings}, + volume = {1232}, + publisher = {CEUR-WS.org}, + year = {2014}, + url = {http://ceur-ws.org/Vol-1232/paper1.pdf}, + timestamp = {Wed, 12 Feb 2020 16:44:28 +0100}, + biburl = {https://dblp.org/rec/conf/pkdd/RistoskiP14.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@misc{website:fourkind, +author={Max Pagels}, +title={{\textit{What is Online Machine Learning?}}}, +url={https://medium.com/value-stream-design/online-machine-learning-515556ff72c5}, +journal={Medium}, +publisher={The Hands-on Advisors}, +year={2020}, +month={Feb}, +note={Accessed: March 2021} +} + +@misc{website:deepai:unsupervised:learning, +author={Thomas Wood}, +title={{\textit{Unsupervised Learning}}}, +howpublished={\href{https://deepai.org/machine-learning-glossary-and-terms/unsupervised-learning} +{https://deepai.org/machine-learning-glossary-and-terms/unsupervised-learning}}, +journal={DeepAI}, +year={2020}, +month={Aug}, +note={Accessed: March 2021} +} + +@misc{website:deepai:softmax, +author={Thomas Wood}, +title={{\textit{Softmax Function}}}, +howpublished={\href{https://deepai.org/machine-learning-glossary-and-terms/softmax-layer} +{https://deepai.org/machine-learning-glossary-and-terms/softmax-layer}}, +journal={DeepAI}, +year=2019, +month={May}, +note={Accessed: April 2021} +} + +@misc{website:deepai:one:hot:encoding, +author={DeepAI}, +title={{\textit{One Hot Encoding}}}, +howpublished={\href{https://deepai.org/machine-learning-glossary-and-terms/one-hot-encoding}}, +url={https://deepai.org/machine-learning-glossary-and-terms/one-hot-encoding}, +journal={DeepAI}, +publisher={DeepAI}, +year={2019}, +month={May}, +note={Accessed: April 2021} +} + +@misc{website:deepai:cosine:similarity, +author={{DeepAI}}, +title={{\textit{Cosine Similarity}}}, +url={https://deepai.org/machine-learning-glossary-and-terms/cosine-similarity}, +journal={DeepAI}, +year={2019}, +month={May}, +note={Accessed: March 2021} +} + +@misc{website:medium:embedding:matrix, +author={Ashwin Prasad}, +title={{\textit{Word Embeddings Explained}}}, +howpublished={\href{https://medium.com/analytics-vidhya/word-embeddings-explained-62c046f7c79e}}, +url={https://medium.com/analytics-vidhya/word-embeddings-explained-62c046f7c79e}, +journal={Medium}, +publisher={Analytics Vidhya}, +year={2020}, +month={Sep}, +note={Accessed: April 2021} +} + + +@misc{website:deepai:distributed:representation, +author={{DeepAI}}, +title={{\textit{Distributed Representations}}}, +url={https://deepai.org/machine-learning-glossary-and-terms/distributed-representation}, +journal={DeepAI}, +year={2019}, +month={May}, +note={Accessed: March 2021} +} + +@misc{website:kamakoti, +author={Balaji Kamakoti}, +title={{\textit{Introduction to Knowledge Graph Embedding with DGL-KE}}}, +url={https://towardsdatascience.com/introduction-to-knowledge-graph-embedding-with-dgl-ke-77ace6fb60ef}, +journal={Medium}, +publisher={Towards Data Science}, +year={2020}, +month={Jun}, +note={Accessed: April 2021} +} + +@inproceedings{inproceddings:oza, + author = {Nikunj C. Oza}, + title = {Online bagging and boosting}, + booktitle = {Proceedings of the {IEEE} International Conference on Systems, Man + and Cybernetics, Waikoloa, Hawaii, USA, October 10-12, 2005}, + pages = {2340--2345}, + publisher = {{IEEE}}, + year = {2005}, + url = {https://doi.org/10.1109/ICSMC.2005.1571498}, + doi = {10.1109/ICSMC.2005.1571498}, + timestamp = {Wed, 16 Oct 2019 14:14:51 +0200}, + biburl = {https://dblp.org/rec/conf/smc/Oza05.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@article{article:hoi, + author = {Steven C. H. Hoi and + Doyen Sahoo and + Jing Lu and + Peilin Zhao}, + title = {Online Learning: {A} Comprehensive Survey}, + journal = {CoRR}, + volume = {abs/1802.02871}, + year = {2018}, + url = {http://arxiv.org/abs/1802.02871}, + archivePrefix = {arXiv}, + eprint = {1802.02871}, + timestamp = {Mon, 13 Aug 2018 16:47:30 +0200}, + biburl = {https://dblp.org/rec/journals/corr/abs-1802-02871.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@inproceedings{DBLP:conf/nips/MikolovSCCD13, + author = {Tom{\'{a}}s Mikolov and + Ilya Sutskever and + Kai Chen and + Gregory S. Corrado and + Jeffrey Dean}, + editor = {Christopher J. C. Burges and + L{\'{e}}on Bottou and + Zoubin Ghahramani and + Kilian Q. Weinberger}, + title = {Distributed Representations of Words and Phrases and their Compositionality}, + booktitle = {Advances in Neural Information Processing Systems 26: 27th Annual + Conference on Neural Information Processing Systems 2013. 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Cowell and + Zoubin Ghahramani}, + title = {Hierarchical Probabilistic Neural Network Language Model}, + booktitle = {Proceedings of the Tenth International Workshop on Artificial Intelligence + and Statistics, {AISTATS} 2005, Bridgetown, Barbados, January 6-8, + 2005}, + publisher = {Society for Artificial Intelligence and Statistics}, + year = {2005}, + url = {http://www.gatsby.ucl.ac.uk/aistats/fullpapers/208.pdf}, + timestamp = {Wed, 06 May 2015 20:37:32 +0200}, + biburl = {https://dblp.org/rec/conf/aistats/MorinB05.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@inproceedings{DBLP:journals/jmlr/GutmannH10, + author = {Michael Gutmann and + Aapo Hyv{\"{a}}rinen}, + editor = {Yee Whye Teh and + D. Mike Titterington}, + title = {Noise-contrastive estimation: {A} new estimation principle for unnormalized + statistical models}, + booktitle = {Proceedings of the Thirteenth International Conference on Artificial + Intelligence and Statistics, {AISTATS} 2010, Chia Laguna Resort, Sardinia, + Italy, May 13-15, 2010}, + series = {{JMLR} Proceedings}, + volume = {9}, + pages = {297--304}, + publisher = {JMLR.org}, + year = {2010}, + url = {http://proceedings.mlr.press/v9/gutmann10a.html}, + timestamp = {Wed, 29 May 2019 08:41:47 +0200}, + biburl = {https://dblp.org/rec/journals/jmlr/GutmannH10.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@misc{weng_2017, +author={Lilian Weng}, +title={{\textit{Learning Word Embedding}}}, +url={https://lilianweng.github.io/lil-log/2017/10/15/learning-word-embedding.html}, +journal={Lil'Log}, +year={2017}, +month={Oct}, +note={Accessed: April 2021} +} + +@misc{sijun_he, +author={Sijun He}, +title={{\textit{Word Embeddings}}}, +url={https://sijunhe.github.io/blog/2018/09/12/word-embeddings/}, +journal={Blog | Sijun He}, +year={2018}, +month={Sep}, +note={Accessed: April 2021} +} + +@inproceedings{DBLP:conf/paclic/FanZCZ14, + author = {Miao Fan and + Qiang Zhou and + Emily Chang and + Thomas Fang Zheng}, + editor = {Wirote Aroonmanakun and + Prachya Boonkwan and + Thepchai Supnithi}, + title = {Transition-based Knowledge Graph Embedding with Relational Mapping + Properties}, + booktitle = {Proceedings of the 28th Pacific Asia Conference on Language, Information + and Computation, {PACLIC} 28, Cape Panwa Hotel, Phuket, Thailand, + December 12-14, 2014}, + pages = {328--337}, + publisher = {The {PACLIC} 28 Organizing Committee and {PACLIC} Steering Committee + / {ACL} / Department of Linguistics, Faculty of Arts, Chulalongkorn + University}, + year = {2014}, + url = {https://www.aclweb.org/anthology/Y14-1039/}, + timestamp = {Mon, 16 Sep 2019 17:08:53 +0200}, + biburl = {https://dblp.org/rec/conf/paclic/FanZCZ14.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@inproceedings{inproceedings:devlin, + author = {Jacob Devlin and + Ming{-}Wei Chang and + Kenton Lee and + Kristina Toutanova}, + editor = {Jill Burstein and + Christy Doran and + Thamar Solorio}, + title = {{BERT:} Pre-training of Deep Bidirectional Transformers for Language + Understanding}, + booktitle = {Proceedings of the 2019 Conference of the North American Chapter of + the Association for Computational Linguistics: Human Language Technologies, + {NAACL-HLT} 2019, Minneapolis, MN, USA, June 2-7, 2019, Volume 1 (Long + and Short Papers)}, + pages = {4171--4186}, + publisher = {Association for Computational Linguistics}, + year = {2019}, + url = {https://doi.org/10.18653/v1/n19-1423}, + doi = {10.18653/v1/n19-1423}, + timestamp = {Tue, 28 Jan 2020 10:30:29 +0100}, + biburl = {https://dblp.org/rec/conf/naacl/DevlinCLT19.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@inproceedings{DBLP:conf/nips/BordesUGWY13, + author = {Antoine Bordes and + Nicolas Usunier and + Alberto Garc{\'{\i}}a{-}Dur{\'{a}}n and + Jason Weston and + Oksana Yakhnenko}, + editor = {Christopher J. C. Burges and + L{\'{e}}on Bottou and + Zoubin Ghahramani and + Kilian Q. Weinberger}, + title = {Translating Embeddings for Modeling Multi-relational Data}, + booktitle = {Advances in Neural Information Processing Systems 26: 27th Annual + Conference on Neural Information Processing Systems 2013. Proceedings + of a meeting held December 5-8, 2013, Lake Tahoe, Nevada, United States}, + pages = {2787--2795}, + year = {2013}, + url = {https://proceedings.neurips.cc/paper/2013/hash/1cecc7a77928ca8133fa24680a88d2f9-Abstract.html}, + timestamp = {Thu, 21 Jan 2021 15:15:23 +0100}, + biburl = {https://dblp.org/rec/conf/nips/BordesUGWY13.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@inproceedings{DBLP:conf/esws/SchlichtkrullKB18, + author = {Michael Sejr Schlichtkrull and + Thomas N. Kipf and + Peter Bloem and + Rianne van den Berg and + Ivan Titov and + Max Welling}, + editor = {Aldo Gangemi and + Roberto Navigli and + Maria{-}Esther Vidal and + Pascal Hitzler and + Rapha{\"{e}}l Troncy and + Laura Hollink and + Anna Tordai and + Mehwish Alam}, + title = {Modeling Relational Data with Graph Convolutional Networks}, + booktitle = {The Semantic Web - 15th International Conference, {ESWC} 2018, Heraklion, + Crete, Greece, June 3-7, 2018, Proceedings}, + series = {Lecture Notes in Computer Science}, + volume = {10843}, + pages = {593--607}, + publisher = {Springer}, + year = {2018}, + url = {https://doi.org/10.1007/978-3-319-93417-4\_38}, + doi = {10.1007/978-3-319-93417-4\_38}, + timestamp = {Tue, 14 May 2019 10:00:44 +0200}, + biburl = {https://dblp.org/rec/conf/esws/SchlichtkrullKB18.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@inproceedings{DBLP:conf/esws/GeseseBS19, + author = {Genet Asefa Gesese and + Russa Biswas and + Harald Sack}, + editor = {Mehwish Alam and + Davide Buscaldi and + Michael Cochez and + Francesco Osborne and + Diego Reforgiato Recupero and + Harald Sack}, + title = {A Comprehensive Survey of Knowledge Graph Embeddings with Literals: + Techniques and Applications}, + booktitle = {Proceedings of the Workshop on Deep Learning for Knowledge Graphs + {(DL4KG2019)} Co-located with the 16th Extended Semantic Web Conference + 2019 {(ESWC} 2019), Portoroz, Slovenia, June 2, 2019}, + series = {{CEUR} Workshop Proceedings}, + volume = {2377}, + pages = {31--40}, + publisher = {CEUR-WS.org}, + year = {2019}, + url = {http://ceur-ws.org/Vol-2377/paper\_4.pdf}, + timestamp = {Wed, 12 Feb 2020 16:45:11 +0100}, + biburl = {https://dblp.org/rec/conf/esws/GeseseBS19.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@misc{alammar, +title={The Illustrated Transformer}, +url={http://jalammar.github.io/illustrated-transformer/}, +journal={The Illustrated Transformer – Jay Alammar – Visualizing machine learning one concept at a time.}, +author={Jay Alammar}, +year={2018}, +month={Jun}, +note={Accessed: May 2021} +} + +@inproceedings{gehring, + author = {Jonas Gehring and + Michael Auli and + David Grangier and + Denis Yarats and + Yann N. Dauphin}, + editor = {Doina Precup and + Yee Whye Teh}, + title = {Convolutional Sequence to Sequence Learning}, + booktitle = {Proceedings of the 34th International Conference on Machine Learning, + {ICML} 2017, Sydney, NSW, Australia, 6-11 August 2017}, + series = {Proceedings of Machine Learning Research}, + volume = {70}, + pages = {1243--1252}, + publisher = {{PMLR}}, + year = {2017}, + url = {http://proceedings.mlr.press/v70/gehring17a.html}, + timestamp = {Wed, 29 May 2019 08:41:45 +0200}, + biburl = {https://dblp.org/rec/conf/icml/GehringAGYD17.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@misc{alammar-seq2seq, +title={Visualizing A Neural Machine Translation Model (Mechanics of Seq2seq Models With Attention)}, +url={https://jalammar.github.io/visualizing-neural-machine-translation-mechanics-of-seq2seq-models-with-attention/}, journal={Visualizing A Neural Machine Translation Model (Mechanics of Seq2seq Models With Attention) – Jay Alammar – Visualizing machine learning one concept at a time.}, +author={Jay Alammar}, +year={2018}, +month={May}, +note={Accessed: May 2021} +} + +@inproceedings{DBLP:conf/ijcai/Tang0C00L20, + author = {Xiaobin Tang and + Jing Zhang and + Bo Chen and + Yang Yang and + Hong Chen and + Cuiping Li}, + editor = {Christian Bessiere}, + title = {{BERT-INT:} {A} BERT-based Interaction Model For Knowledge Graph Alignment}, + booktitle = {Proceedings of the Twenty-Ninth International Joint Conference on + Artificial Intelligence, {IJCAI} 2020}, + pages = {3174--3180}, + publisher = {ijcai.org}, + year = {2020}, + url = {https://doi.org/10.24963/ijcai.2020/439}, + doi = {10.24963/ijcai.2020/439}, + timestamp = {Mon, 20 Jul 2020 12:38:52 +0200}, + biburl = {https://dblp.org/rec/conf/ijcai/Tang0C00L20.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@article{DBLP:journals/corr/abs-1909-03193, + author = {Liang Yao and + Chengsheng Mao and + Yuan Luo}, + title = {{KG-BERT:} {BERT} for Knowledge Graph Completion}, + journal = {CoRR}, + volume = {abs/1909.03193}, + year = {2019}, + url = {http://arxiv.org/abs/1909.03193}, + archivePrefix = {arXiv}, + eprint = {1909.03193}, + timestamp = {Tue, 17 Sep 2019 11:23:44 +0200}, + biburl = {https://dblp.org/rec/journals/corr/abs-1909-03193.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@inproceedings{DBLP:conf/aaai/LiuZ0WJD020, + author = {Weijie Liu and + Peng Zhou and + Zhe Zhao and + Zhiruo Wang and + Qi Ju and + Haotang Deng and + Ping Wang}, + title = {{K-BERT:} Enabling Language Representation with Knowledge Graph}, + booktitle = {The Thirty-Fourth {AAAI} Conference on Artificial Intelligence, {AAAI} + 2020, The Thirty-Second Innovative Applications of Artificial Intelligence + Conference, {IAAI} 2020, The Tenth {AAAI} Symposium on Educational + Advances in Artificial Intelligence, {EAAI} 2020, New York, NY, USA, + February 7-12, 2020}, + pages = {2901--2908}, + publisher = {{AAAI} Press}, + year = {2020}, + url = {https://aaai.org/ojs/index.php/AAAI/article/view/5681}, + timestamp = {Tue, 02 Feb 2021 08:00:48 +0100}, + biburl = {https://dblp.org/rec/conf/aaai/LiuZ0WJD020.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@inproceedings{DBLP:conf/aics/VegupattiNC20, + author = {Mani Vegupatti and + Matthias Nickles and + Bharathi Raja Chakravarthi}, + editor = {Luca Longo and + Lucas Rizzo and + Elizabeth Hunter and + Arjun Pakrashi}, + title = {Simple Question Answering Over a Domain-Specific Knowledge Graph using + {BERT} by Transfer Learning}, + booktitle = {Proceedings of The 28th Irish Conference on Artificial Intelligence + and Cognitive Science, Dublin, Republic of Ireland, December 7-8, + 2020}, + series = {{CEUR} Workshop Proceedings}, + volume = {2771}, + pages = {289--300}, + publisher = {CEUR-WS.org}, + year = {2020}, + url = {http://ceur-ws.org/Vol-2771/AICS2020\_paper\_42.pdf}, + timestamp = {Tue, 22 Dec 2020 14:06:50 +0100}, + biburl = {https://dblp.org/rec/conf/aics/VegupattiNC20.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@misc{maison, +title={Python: How To Reduce Memory Consumption By Half By Adding Just One Line Of Code?}, +url={https://www.digitalminds.io/blog/python-how-to-reduce-memory-consumption-by-half-by-adding-just-one-line-of-code}, +journal={digitalminds.io Blog}, +author={Alex Maison}, +year={2019}, +month={Oct} +} + +@inproceedings{pyrdf2vec, + author = {Gilles Vandewiele and Bram Steenwinckel and Terencio Agozzino + and Michael Weyns and Pieter Bonte and Femke Ongenae + and Filip De Turck}, + title = {{pyRDF2Vec: Python Implementation and Extension of RDF2Vec}}, + organization = {IDLab}, + year = {2020}, + url = {https://github.com/IBCNServices/pyRDF2Vec} +} \ No newline at end of file diff --git a/data/embedders/max-depth/bert.csv b/data/embedders/max-depth/bert.csv new file mode 100644 index 0000000..d6469c2 --- /dev/null +++ b/data/embedders/max-depth/bert.csv @@ -0,0 +1,4 @@ +max_depth,accuracy +2,70.59 +4,74.26 +6,76.32 diff --git a/data/embedders/max-depth/fasttext.csv b/data/embedders/max-depth/fasttext.csv new file mode 100644 index 0000000..1491a16 --- /dev/null +++ b/data/embedders/max-depth/fasttext.csv @@ -0,0 +1,4 @@ +max_depth,accuracy +2,79.71 +4,77.06 +6,82.35 diff --git a/data/embedders/max-depth/word2vec.csv b/data/embedders/max-depth/word2vec.csv new file mode 100644 index 0000000..d7a4516 --- /dev/null +++ b/data/embedders/max-depth/word2vec.csv @@ -0,0 +1,4 @@ +max_depth,accuracy +2,76.76 +4,75.00 +6,74.71 diff --git a/data/embedders/max-walks/bert.csv b/data/embedders/max-walks/bert.csv new file mode 100644 index 0000000..e662df9 --- /dev/null +++ b/data/embedders/max-walks/bert.csv @@ -0,0 +1,5 @@ +max_walk,accuracy +100,69.43 +250,73.54 +500,75.24 +1000,76.58 diff --git a/data/embedders/max-walks/fasttext.csv b/data/embedders/max-walks/fasttext.csv new file mode 100644 index 0000000..b5320ac --- /dev/null +++ b/data/embedders/max-walks/fasttext.csv @@ -0,0 +1,5 @@ +max_walk,accuracy +100,77.94 +250,77.35 +500,76.18 +1000,77.35 diff --git a/data/embedders/max-walks/word2vec.csv b/data/embedders/max-walks/word2vec.csv new file mode 100644 index 0000000..7180b6d --- /dev/null +++ b/data/embedders/max-walks/word2vec.csv @@ -0,0 +1,5 @@ +max_walk,accuracy +100,71.47 +250,74.71 +500,73.53 +1000,74.41 diff --git a/data/samplers/max-depth/2/objfreq-inv-split.csv b/data/samplers/max-depth/2/objfreq-inv-split.csv new file mode 100644 index 0000000..95d44f9 --- /dev/null +++ b/data/samplers/max-depth/2/objfreq-inv-split.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,75.88 +250,75.88 +500,74.71 diff --git a/data/samplers/max-depth/2/objfreq-inv.csv b/data/samplers/max-depth/2/objfreq-inv.csv new file mode 100644 index 0000000..9423ed8 --- /dev/null +++ b/data/samplers/max-depth/2/objfreq-inv.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,73.53 +250,75.59 +500,72.65 diff --git a/data/samplers/max-depth/2/objfreq.csv b/data/samplers/max-depth/2/objfreq.csv new file mode 100644 index 0000000..d98eaed --- /dev/null +++ b/data/samplers/max-depth/2/objfreq.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,77.94 +250,75.59 +500,75.29 diff --git a/data/samplers/max-depth/2/objpredfreq-inv.csv b/data/samplers/max-depth/2/objpredfreq-inv.csv new file mode 100644 index 0000000..363e3a2 --- /dev/null +++ b/data/samplers/max-depth/2/objpredfreq-inv.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,76.76 +250,75.29 +500,73.82 diff --git a/data/samplers/max-depth/2/objpredfreq.csv b/data/samplers/max-depth/2/objpredfreq.csv new file mode 100644 index 0000000..44bb2de --- /dev/null +++ b/data/samplers/max-depth/2/objpredfreq.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,78.82 +250,75.29 +500,73.53 diff --git a/data/samplers/max-depth/2/pagerank-inv-split.csv b/data/samplers/max-depth/2/pagerank-inv-split.csv new file mode 100644 index 0000000..035adae --- /dev/null +++ b/data/samplers/max-depth/2/pagerank-inv-split.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,76.18 +250,75.88 +500,73.82 diff --git a/data/samplers/max-depth/2/pagerank-inv.csv b/data/samplers/max-depth/2/pagerank-inv.csv new file mode 100644 index 0000000..30511d2 --- /dev/null +++ b/data/samplers/max-depth/2/pagerank-inv.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,74.41 +250,75.00 +500,74.12 diff --git a/data/samplers/max-depth/2/pagerank-split.csv b/data/samplers/max-depth/2/pagerank-split.csv new file mode 100644 index 0000000..bc41d17 --- /dev/null +++ b/data/samplers/max-depth/2/pagerank-split.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,74.71 +250,75.88 +500,73.82 diff --git a/data/samplers/max-depth/2/pagerank.csv b/data/samplers/max-depth/2/pagerank.csv new file mode 100644 index 0000000..7451495 --- /dev/null +++ b/data/samplers/max-depth/2/pagerank.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,76.47 +250,74.12 +500,75.00 diff --git a/data/samplers/max-depth/2/predfreq-inv.csv b/data/samplers/max-depth/2/predfreq-inv.csv new file mode 100644 index 0000000..07231f4 --- /dev/null +++ b/data/samplers/max-depth/2/predfreq-inv.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,77.65 +250,73.82 +500,72.35 diff --git a/data/samplers/max-depth/2/predfreq.csv b/data/samplers/max-depth/2/predfreq.csv new file mode 100644 index 0000000..a7e8220 --- /dev/null +++ b/data/samplers/max-depth/2/predfreq.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,76.76 +250,76.18 +500,72.65 diff --git a/data/samplers/max-depth/2/uniform.csv b/data/samplers/max-depth/2/uniform.csv new file mode 100644 index 0000000..ba8e8b7 --- /dev/null +++ b/data/samplers/max-depth/2/uniform.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,76.18 +250,75.29 +500,73.53 diff --git a/data/samplers/max-depth/2/widesampler.csv b/data/samplers/max-depth/2/widesampler.csv new file mode 100644 index 0000000..93bf285 --- /dev/null +++ b/data/samplers/max-depth/2/widesampler.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,76.76 +250,77.35 +500,74.71 diff --git a/data/samplers/max-depth/4/objfreq-inv-split.csv b/data/samplers/max-depth/4/objfreq-inv-split.csv new file mode 100644 index 0000000..7559a6c --- /dev/null +++ b/data/samplers/max-depth/4/objfreq-inv-split.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,72.65 +250,75.59 +500,75.29 diff --git a/data/samplers/max-depth/4/objfreq-inv.csv b/data/samplers/max-depth/4/objfreq-inv.csv new file mode 100644 index 0000000..56bd8e0 --- /dev/null +++ b/data/samplers/max-depth/4/objfreq-inv.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,73.82 +250,76.18 +500,76.18 diff --git a/data/samplers/max-depth/4/objfreq.csv b/data/samplers/max-depth/4/objfreq.csv new file mode 100644 index 0000000..072309b --- /dev/null +++ b/data/samplers/max-depth/4/objfreq.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,69.12 +250,78.53 +500,74.41 diff --git a/data/samplers/max-depth/4/objpredfreq-inv.csv b/data/samplers/max-depth/4/objpredfreq-inv.csv new file mode 100644 index 0000000..1ee576b --- /dev/null +++ b/data/samplers/max-depth/4/objpredfreq-inv.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,73.82 +250,70.41 +500,77.94 diff --git a/data/samplers/max-depth/4/objpredfreq.csv b/data/samplers/max-depth/4/objpredfreq.csv new file mode 100644 index 0000000..b469b0d --- /dev/null +++ b/data/samplers/max-depth/4/objpredfreq.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,75.29 +250,68.82 +500,74.41 diff --git a/data/samplers/max-depth/4/pagerank-inv-split.csv b/data/samplers/max-depth/4/pagerank-inv-split.csv new file mode 100644 index 0000000..7559a6c --- /dev/null +++ b/data/samplers/max-depth/4/pagerank-inv-split.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,72.65 +250,75.59 +500,75.29 diff --git a/data/samplers/max-depth/4/pagerank-inv.csv b/data/samplers/max-depth/4/pagerank-inv.csv new file mode 100644 index 0000000..3ce42a2 --- /dev/null +++ b/data/samplers/max-depth/4/pagerank-inv.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,75.00 +250,74.71 +500,75.29 diff --git a/data/samplers/max-depth/4/pagerank-split.csv b/data/samplers/max-depth/4/pagerank-split.csv new file mode 100644 index 0000000..b0607fa --- /dev/null +++ b/data/samplers/max-depth/4/pagerank-split.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,74.12 +250,71.18 +500,77.35 diff --git a/data/samplers/max-depth/4/pagerank.csv b/data/samplers/max-depth/4/pagerank.csv new file mode 100644 index 0000000..e5fee73 --- /dev/null +++ b/data/samplers/max-depth/4/pagerank.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,72.65 +250,73.53 +500,75.59 diff --git a/data/samplers/max-depth/4/predfreq-inv.csv b/data/samplers/max-depth/4/predfreq-inv.csv new file mode 100644 index 0000000..7bc0f92 --- /dev/null +++ b/data/samplers/max-depth/4/predfreq-inv.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,78.24 +250,74.71 +500,74.12 diff --git a/data/samplers/max-depth/4/predfreq.csv b/data/samplers/max-depth/4/predfreq.csv new file mode 100644 index 0000000..7c0cd85 --- /dev/null +++ b/data/samplers/max-depth/4/predfreq.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,73.82 +250,74.41 +500,75.59 diff --git a/data/samplers/max-depth/4/uniform.csv b/data/samplers/max-depth/4/uniform.csv new file mode 100644 index 0000000..279433d --- /dev/null +++ b/data/samplers/max-depth/4/uniform.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,73.24 +250,74.41 +500,77.35 diff --git a/data/samplers/max-depth/4/widesampler.csv b/data/samplers/max-depth/4/widesampler.csv new file mode 100644 index 0000000..c0742f2 --- /dev/null +++ b/data/samplers/max-depth/4/widesampler.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,78.82 +250,75.00 +500,74.41 diff --git a/data/samplers/max-depth/6/objfreq-inv-split.csv b/data/samplers/max-depth/6/objfreq-inv-split.csv new file mode 100644 index 0000000..0c48821 --- /dev/null +++ b/data/samplers/max-depth/6/objfreq-inv-split.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,74.12 +250,78.53 +500,75.88 diff --git a/data/samplers/max-depth/6/objfreq-inv.csv b/data/samplers/max-depth/6/objfreq-inv.csv new file mode 100644 index 0000000..f4f2f08 --- /dev/null +++ b/data/samplers/max-depth/6/objfreq-inv.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,76.76 +250,76.18 +500,78.82 diff --git a/data/samplers/max-depth/6/objfreq.csv b/data/samplers/max-depth/6/objfreq.csv new file mode 100644 index 0000000..9ec0528 --- /dev/null +++ b/data/samplers/max-depth/6/objfreq.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,75.59 +250,75 +500,78.24 diff --git a/data/samplers/max-depth/6/objpredfreq-inv.csv b/data/samplers/max-depth/6/objpredfreq-inv.csv new file mode 100644 index 0000000..24fa0e3 --- /dev/null +++ b/data/samplers/max-depth/6/objpredfreq-inv.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,75.59 +250,78.24 +500,75.59 diff --git a/data/samplers/max-depth/6/objpredfreq.csv b/data/samplers/max-depth/6/objpredfreq.csv new file mode 100644 index 0000000..cdbe67e --- /dev/null +++ b/data/samplers/max-depth/6/objpredfreq.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,70.88 +250,73.24 +500,77.06 diff --git a/data/samplers/max-depth/6/pagerank-inv-split.csv b/data/samplers/max-depth/6/pagerank-inv-split.csv new file mode 100644 index 0000000..e8bb1c6 --- /dev/null +++ b/data/samplers/max-depth/6/pagerank-inv-split.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,75.29 +250,76.18 +500,77.94 diff --git a/data/samplers/max-depth/6/pagerank-inv.csv b/data/samplers/max-depth/6/pagerank-inv.csv new file mode 100644 index 0000000..a9f734a --- /dev/null +++ b/data/samplers/max-depth/6/pagerank-inv.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,76.76 +250,80 +500,77.35 diff --git a/data/samplers/max-depth/6/pagerank-split.csv b/data/samplers/max-depth/6/pagerank-split.csv new file mode 100644 index 0000000..5abd252 --- /dev/null +++ b/data/samplers/max-depth/6/pagerank-split.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,77.06 +250,72.65 +500,76.76 diff --git a/data/samplers/max-depth/6/pagerank.csv b/data/samplers/max-depth/6/pagerank.csv new file mode 100644 index 0000000..679b1d2 --- /dev/null +++ b/data/samplers/max-depth/6/pagerank.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,73.53 +250,77.35 +500,77.35 diff --git a/data/samplers/max-depth/6/predfreq-inv.csv b/data/samplers/max-depth/6/predfreq-inv.csv new file mode 100644 index 0000000..0072daa --- /dev/null +++ b/data/samplers/max-depth/6/predfreq-inv.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,75.29 +250,78.24 +500,77.35 diff --git a/data/samplers/max-depth/6/predfreq.csv b/data/samplers/max-depth/6/predfreq.csv new file mode 100644 index 0000000..3ad2e0f --- /dev/null +++ b/data/samplers/max-depth/6/predfreq.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,79.41 +250,75.59 +500,79.40 diff --git a/data/samplers/max-depth/6/uniform.csv b/data/samplers/max-depth/6/uniform.csv new file mode 100644 index 0000000..9eaa4f1 --- /dev/null +++ b/data/samplers/max-depth/6/uniform.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,73.24 +250,75.59 +500,77.94 diff --git a/data/samplers/max-depth/6/widesampler.csv b/data/samplers/max-depth/6/widesampler.csv new file mode 100644 index 0000000..1ce59be --- /dev/null +++ b/data/samplers/max-depth/6/widesampler.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,76.76 +250,75 +500,78.53 diff --git a/data/walkers/max-depth/anonymous.csv b/data/walkers/max-depth/anonymous.csv new file mode 100644 index 0000000..40d2a68 --- /dev/null +++ b/data/walkers/max-depth/anonymous.csv @@ -0,0 +1,4 @@ +max_depth,accuracy +2,65.29 +4,66.47 +6,67.65 diff --git a/data/walkers/max-depth/halk.csv b/data/walkers/max-depth/halk.csv new file mode 100644 index 0000000..8c9d561 --- /dev/null +++ b/data/walkers/max-depth/halk.csv @@ -0,0 +1,4 @@ +max_depth,accuracy +2,75.59 +4,78.82 +6,81.18 diff --git a/data/walkers/max-depth/ngram.csv b/data/walkers/max-depth/ngram.csv new file mode 100644 index 0000000..30308be --- /dev/null +++ b/data/walkers/max-depth/ngram.csv @@ -0,0 +1,4 @@ +max_depth,accuracy +2,76.47 +4,75.88 +6,77.65 diff --git a/data/walkers/max-depth/random.csv b/data/walkers/max-depth/random.csv new file mode 100644 index 0000000..55ecc98 --- /dev/null +++ b/data/walkers/max-depth/random.csv @@ -0,0 +1,4 @@ +max_depth,accuracy +2,77.94 +4,76.76 +6,75.29 diff --git a/data/walkers/max-depth/split.csv b/data/walkers/max-depth/split.csv new file mode 100644 index 0000000..e971843 --- /dev/null +++ b/data/walkers/max-depth/split.csv @@ -0,0 +1,4 @@ +max_depth,accuracy +2,74.71 +4,77.35 +6,79.71 diff --git a/data/walkers/max-depth/walklet.csv b/data/walkers/max-depth/walklet.csv new file mode 100644 index 0000000..26c2b4f --- /dev/null +++ b/data/walkers/max-depth/walklet.csv @@ -0,0 +1,4 @@ +max_depth,accuracy +2,72.06 +4,73.82 +6,71.76 diff --git a/data/walkers/max-walks/anonymous.csv b/data/walkers/max-walks/anonymous.csv new file mode 100644 index 0000000..69c40ec --- /dev/null +++ b/data/walkers/max-walks/anonymous.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,65.59 +250,66.76 +500,65.80 diff --git a/data/walkers/max-walks/halk.csv b/data/walkers/max-walks/halk.csv new file mode 100644 index 0000000..b6a5d71 --- /dev/null +++ b/data/walkers/max-walks/halk.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,77.65 +250,76.76 +500,79.12 diff --git a/data/walkers/max-walks/ngram.csv b/data/walkers/max-walks/ngram.csv new file mode 100644 index 0000000..c9b3bec --- /dev/null +++ b/data/walkers/max-walks/ngram.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,68.82 +250,73.24 +500,71.76 diff --git a/data/walkers/max-walks/random.csv b/data/walkers/max-walks/random.csv new file mode 100644 index 0000000..cca9987 --- /dev/null +++ b/data/walkers/max-walks/random.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,72.35 +250,76.18 +500,72.06 diff --git a/data/walkers/max-walks/split.csv b/data/walkers/max-walks/split.csv new file mode 100644 index 0000000..f35ddeb --- /dev/null +++ b/data/walkers/max-walks/split.csv @@ -0,0 +1,4 @@ +max_walk,accuracy +100,79.12 +250,77.35 +500,77.35 diff --git 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\draw[->] (w\step.north) -> (h\step.south); + \draw[->] (h\step.north) -> (o\step.south); + } + + \foreach \step/\next in {1/2,2/3,3/4,4/5,5/6,6/7} + \draw[->] (h\step.east) -> (h\next.west) node[above,midway] {$h_\step$}; + + \node[label,below=of w1,yshift=30pt] {hello}; + \node[label,below=of w2,yshift=28pt] {my}; + \node[label,below=of w3,yshift=30pt] {dear}; + \node[label,below=of w4,yshift=28pt] {\texttt{}}; + \node[label,below=of w5,yshift=30pt] {bonjour}; + \node[label,below=of w6,yshift=28pt] {ma}; + \node[label,below=of w7,yshift=30pt] {chère}; + + \node[label,above=of h1.north,yshift=13pt] {$o_1$}; + \node[label,above=of h2.north,yshift=13pt] {$o_2$}; + \node[label,above=of h3.north,yshift=13pt] {$o_3$}; + \node[label,above=of h4.north,yshift=13pt] {bonjour}; + \node[label,above=of h5.north,yshift=15pt] {ma}; + \node[label,above=of h6.north,yshift=15pt] {chère}; + \node[label,above=of h7.north,yshift=15pt] {\texttt{}}; + + \draw[loosely dashed, thick] (8.75,3) -- (8.75,1); + \draw[loosely dashed, thick] (8.75,-0.5) -- (8.75,-2.5); + + \node[label,above=of h2.north,yshift=35pt] {\textbf{ENCODER}}; + \node[label,above=of h5.north,yshift=35pt,xshift=30pt] {\textbf{DECODER}}; + \end{tikzpicture} + \caption{Sequence-to-Sequence Learning With RNNs.} + \label{fig:rnn} +\end{figure} + +In Figure \ref{fig:rnn}, a Sequence to Sequence (Seq2Seq) model translates an +English sentence into French using RNN encoders and decoders. Each time step has +an RNN unit containing an activation function that takes a word embedding and a +hidden state as input for both encoding and decoding. This hidden state serves +as a memory to save the entire previous context. Specifically, the hidden state +at the $t$ time step is computed based on the hidden state at the $t − 1$ time +step and the current word embedding. Once one RNN encoder reaches the first +End-Of-Sentence (\texttt{}), the RNN decoder receives a context vector +containing the last generated hidden state, namely $h_3$. Finally, each RNN +decoder unit translates a word based on this context until to reach once more +the \texttt{} token. + +Although RNNs are effective for small sequences, this is not the case for more +extensive sequences. This mechanism uses a fixed size context vector and +generates the encoder's hidden states based on the previous hidden +state. Consequently, the last words of an input sequence have a greater weight +than the first ones. From this unbalanced weight, processing a long sequence by +a model comes at the cost of forgetting the earlier parts of that sequence, +resulting in a loss model's accuracy. RNN variants emerged to reduce this waste +of information, such as Long Short-Term Memory (LSTM) and Gated Recurrent Units +(GRU). These variants helped to improve the model's accuracy, but the Attention +mechanism came up with an interesting idea. + +\subsection{Mechanism} +\label{subsec:attention:mechanism} + +The basic idea of the Attention mechanism is not only to pay attention to each +input word in the context vector but also to give a relative importance to each +of them~\citep{bahdanau}. In other words, the Attention mechanism focuses on +matching input and output elements. After its publication, this mechanism became +one of the design choices in many NLP and Computer Vision tasks. Computer Vision +is a field of Artificial Intelligence where the computer learns digital images +or video content. This mechanism has received other +variants~\citep{DBLP:conf/emnlp/LuongPM15}, which increased the model's accuracy +in most of the benchmarks that have been performed. Finally, due to the +popularity of the Attention mechanism, the use of RNNs has been questioned many +times. However, RNNs are still present in everyday life through various voice +assistance applications such as Apple's Siri, Amazon Alexa, and Google Home. + +With the Attention mechanism, the context vector includes each encoder's hidden +state. In addition, each decoder's hidden state processes some additional +calculation to achieve a better model's accuracy compared to the use of RNNs +without Attention~\citep{alammar-seq2seq}. This mechanism mainly solved the +previous issues related to the lack of parallelization and forgetting previous +word contexts for long sequences. + + +\newpage + +Visually, the mechanism works as follows: +\begin{figure}[!ht] + \centering + \begin{tikzpicture}[ + hid/.style 2 args={rectangle split, rectangle split horizontal, draw=#2, + rectangle split parts=#1, fill=#2!20, outer sep=1mm}, + label/.style={font=\small}] + \tikzset{>=stealth',every on chain/.append style={join}, + every join/.style={->}} + + \foreach \step in {1,2,3} { + \node[label,rectangle, draw=grey, fill=grey!20, + minimum height=0.22cm,minimum width=1.35cm] (w\step) at (2.5*\step, -1.5) {\scriptsize{RNN}}; + \node[hid={3}{blue},below=of w\step,yshift=20pt] (e\step) {}; + \draw[->] (e\step) -> (w\step); + } + + + \node[label,rectangle, draw=grey, fill=grey!20, + minimum height=0.22cm,minimum width=1.35cm] (w4) at (12.25,-1.5) {\scriptsize{RNN}}; + \node[label,rectangle, draw=grey, fill=grey!20, + minimum height=0.22cm,minimum width=1.35cm] (w5) at (14.75,-1.5) {\scriptsize{RNN}}; + + \node[right=of w5,xshift=-20pt] (dots) {$\dotso$}; + + \node[hid={3}{blue},below=of w4,yshift=20pt] (e4) {}; + \node[hid={3}{red},below=of w5,yshift=20pt,opacity=0.4] (e5) {}; + \draw[->] (e4) -> (w4); + \draw[->] (e5) -> (w5); + + \foreach \step/\next in {1/2,2/3} + \draw[->] (w\step.east) -> (w\next.west) node[above,midway] (h\step) {$h_\step$}; + + \draw[->] (w3.east) -> ([xshift=30pt]w3.east) node[above,midway] (h3) {$h_3$}; + \draw[->] ([xshift=-50pt]w4.west) -> (w4.west) node[above,midway] (c) {$h_1,h_2,h_3$}; + \draw[->] (w4) -> (w5) node[above,midway] (h4) {$h_4$}; + + \foreach \step in {1,2,3}{ + \node[circle,fill=green!20,draw=green,outer sep=1mm,minimum + size=0.8cm,scale=0.8,above=of h\step] (dot\step) {.}; + \draw[->] (h\step.north) -> (dot\step.south); + } + + \node[circle,fill=red!30,draw=red,outer sep=0.1mm,above=of dot1,minimum size=0.8cm,scale=0.85] (s1) {\scriptsize{$9.7$}}; + \node[circle,fill=red!20,draw=red,outer sep=0.1mm,above=of dot2,minimum size=0.8cm,scale=0.85] (s2) {\scriptsize{$2.1$}}; + \node[circle,fill=red!10,draw=red,outer sep=0.1mm,above=of dot3,minimum size=0.8cm,scale=0.85] (s3) {\scriptsize{$1.2$}}; + + \node[rectangle,draw,above=of s1,minimum width=6cm,minimum height=1cm,xshift=72.5pt] (r) {}; + \node[rectangle,draw=mygreen,above=of s1,fill=mygreen,minimum height=0.7cm,yshift=0.9pt] (r1) {}; + \node[rectangle,draw=mygreen,above=of s2,fill=mygreen,minimum height=0.2cm,yshift=0.9pt] (r2) {}; + \node[rectangle,draw=mygreen,above=of s3,fill=mygreen,minimum height=0.1cm,yshift=0.9pt] (r3) {}; + + \node[label,below=of e1,yshift=30pt] {hello}; + \node[label,below=of e2,yshift=28pt] (my) {my}; + \node[label,below=of e3,yshift=30pt] {dear}; + \node[label,below=of e4,yshift=28pt] (eos) {\texttt{}}; + \node[label,below=of e5,yshift=30pt,opacity=0.7] (bonjour) {bonjour}; + + \draw[arrow] ([xshift=-20pt]dot3.west) |- (dot2.east); + \draw[arrow] ([xshift=-20pt]dot2.west) |- (dot1.east); + + \draw ([xshift=-20pt]dot3.west) |- ([xshift=-20pt,yshift=-25pt]dot3.west); + \draw ([xshift=-20pt]dot2.west) |- ([xshift=-20pt,yshift=-30pt]dot2.west); + + \draw[arrow] ([xshift=5pt]h4.north) |- (dot3.east); + \draw (h4) |- ([xshift=-20pt,yshift=-25pt]dot3.west); + \draw ([xshift=-10pt]h4) |- ([xshift=-20pt,yshift=-30pt]dot2.west); + + \foreach \step in {1,2,3} + \draw[arrow] (dot\step) -- ([yshift=-2pt]s\step); + + \foreach \step in {1,2,3} + \draw[arrow] (s\step) -- ([yshift=-2pt]r\step.south); + + \node[circle,above=of r1.south,yshift=10pt,fill=green!20,draw=green,outer sep=1mm,minimum size=0.8cm,scale=0.8] (mul1) {x}; + \node[circle,above=of r2.south,yshift=30pt,fill=green!20,draw=green,outer sep=1mm,minimum size=0.8cm,scale=0.8] (mul2) {x}; + \node[circle,above=of r3.south,yshift=50pt,fill=green!20,draw=green,outer sep=1mm,minimum size=0.8cm,scale=0.8] (mul3) {x}; + + \node[hid={3}{blue},above=of mul1,yshift=28pt] (W1) {}; + \node[hid={3}{blue},above=of mul2,yshift=8pt] (W2) {}; + \node[hid={3}{blue},above=of mul3,yshift=-10pt] (W3) {}; + + \node[label,above=of W1,yshift=-30pt] {hello}; + \node[label,above=of W2,yshift=-32pt] {my}; + \node[label,above=of W3,yshift=-30pt] {dear}; + + \foreach \step in {1,2,3} + \draw[arrow] (W\step) -- (mul\step); + + \draw[arrow] ([xshift=-2.535cm]r.north) -| (mul1.south); + \draw[arrow] ([xshift=-0.05cm]r.north) -| (mul2.south); + \draw[arrow] ([xshift=2.4cm]r.north) -| (mul3.south); + + \node[circle,right=of mul2.east,xshift=70pt,fill=green!20,draw=green,outer + sep=1mm,minimum size=0.8cm,scale=0.8] (sum) {+}; + + \node[hid={3}{red},right=of sum] (output) {}; + \node[label,above=of output,yshift=-30pt] (output_label) {bonjour}; + \draw[arrow] (sum) -- (output); + + \draw[arrow] (mul1.east) -| (sum.south); + \draw[arrow] (mul2.east) -- (sum); + \draw[arrow] (mul3.east) -| (sum.north); + + \node[label,left=of dot1, xshift=0.5cm] {Dot Product}; + \node[label,left=of s1, xshift=0.45cm] {Attention Score}; + \node[label,left=of r1, xshift=0.35cm] {Attention Weights}; + \node[label,left=of mul1,yshift=20pt,xshift=0.55cm] {Weighted Sum}; + + \node[label,below=of my.south,yshift=23pt] {\textbf{ENCODER}}; + \node[label,below=of eos.south,yshift=25pt] {\textbf{DECODER}}; + + \node[right=of dot1,xshift=-30pt,yshift=7pt] {\footnotesize{query}}; + \node[right=of dot2,xshift=-30pt,yshift=7pt] {\footnotesize{query}}; + \node[right=of dot3,xshift=20pt,yshift=7pt] {\footnotesize{query}}; + + \node[above=of h1,xshift=-12pt,yshift=-15pt] {\footnotesize{key}}; + \node[above=of h2,xshift=-12pt,yshift=-15pt] {\footnotesize{key}}; + \node[above=of h3,xshift=-12pt,yshift=-15pt] {\footnotesize{key}}; + + \node[right=of mul1,xshift=-25pt,yshift=7pt] {\footnotesize{value}}; + \node[right=of mul2,xshift=-25pt,yshift=7pt] {\footnotesize{value}}; + \node[right=of mul3,xshift=-25pt,yshift=7pt] {\footnotesize{value}}; + \end{tikzpicture} + \caption{Seq2Seq Learning With Attention Mechanism.} + \label{fig:attention} +\end{figure} + +In Figure \ref{fig:attention}, the Attention mechanism starts using the encoder +RNNs to generate their hidden states, similar to Figure \ref{fig:rnn}. Once +these hidden states have been generated, the context including these hidden +states is provided to each time step of the decoder RNNs. For each RNN decoder +block, the hidden state of decoding is calculated in three significant steps: +\begin{enumerate} +\item \textbf{Computation of the Attention/Alignment Score for each word}: to + know the most likely word to pay more attention to the translation of the + current word, a dot product is made between the previous decoding hidden state + with every encoding hidden state. + + The original research paper defines \emph{query}, \emph{key}, and \emph{value} + by making an analogy with a database. The query allows performing a search + (e.g., book) associated with a set of keys (e.g., book title and abstract) for + which each key is associated with a value. From then on, the \emph{Dot-Product + Attention} consists of computing the weighted matching between $m$ queries and + $n$ keys in an $m$ by $n$ matrix. + +\item \textbf{Computation of the Attention Weights}: the Attention scores are + normalized with a softmax function in such a way as to ease their processing + using a probability distribution whose sum is unitary. + \begin{definition}[Attention Score] + Let $h_1, \ldots, h_N \in \mathbb{R}^h$ be encoder hidden states, $s_t \in + \mathbb{R}^h$ be the decoder hidden state, and $t$ be the time + step. Mathematically, the $\mathrm{a}_t$ Attention score is defined as follows: + \begin{align} + \alpha^t &= \mathrm{softmax}\left(\left[ s_t^Th_1, \ldots, s_t^Th_N \right]\right) \in \mathbb{R}^N \\ + \mathrm{a}_t &= \sum^N_{i=1}\alpha^t_ih_i \in \mathbb{R}^N + \label{eq:def:attention:score} + \end{align} + \label{def:attention:score} + \end{definition} + +\item \textbf{Computation of the weighted sum}: After normalization, it is +necessary to multiply each embedded word with its weight to compute the hidden +state. +\end{enumerate} + +After the calculation of the hidden states, Attention picks the most likely word +for translation. This mechanism gives importance to these words by mapping them +to a higher or lower weight depending on the word’s relevance. Therefore, this +improves the accuracy of the output predictions~\citep{bahdanau}. However, the +Attention mechanism in Figure \ref{fig:attention} cannot be used in a neural +network since there are no weights to train by a model. In practice, the +Attention mechanism uses three weight matrices to multiply each key, value, and +query by their respective matrices called the key, query, and value matrices. + +Following the publication of Attention, another attention mechanism emerged +which gives attention within input elements. \emph{Self-Attention} also called +\emph{intra-attention}, is a Attention mechanism defines in 2016 and relates +different positions of a single sequence to compute a representation of the same +sequence~\citep{Cheng}. Unlike the primary Attention mechanism, where the query, +key, and value matrices may differ, Self-Attention has these three matrices +identically as generated from the same input sequence. Based on a gradient +signal, each self-attention block can use this signal to propagate information +to the weight matrices, namely the key, query, and values matrices. It is +largely thanks to Self-Attention that the \emph{Transformer} architecture was +created. + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "../../report" +%%% End: diff --git a/src/background/graphs.tex b/src/background/graphs.tex new file mode 100644 index 0000000..d104753 --- /dev/null +++ b/src/background/graphs.tex @@ -0,0 +1,147 @@ + +\section{Graphs} +\label{sec:background:graphs} + +Graphs have been used long before the introduction of ML and cover a wide range +of applications. To better understand the precise vocabulary of graphs, this +section provides some definitions. + +\begin{definition}[Graph] + Ordered pair ($V, E$), where $V$ is a finite and non-empty set of elements + called \emph{vertices} (or \emph{nodes}), and $E$ is a set of unordered pairs of + distinct nodes of $V$, called \emph{edges}. + \label{def:graph} +\end{definition} + +\noindent Basic types of graphs include: +\begin{figure}[!ht] + \begin{minipage}{0.45\linewidth} + \centering + \begin{tikzpicture}[minimum size=0.5cm,node distance=1cm] + \node[entity] (alpha) {1}; + \node[entity,above left=of alpha,xshift=15pt] (beta) {2}; + \node[entity,above right=of alpha,yshift=-5pt,xshift=-5pt] (gamma) {3}; + \node[entity,right=of gamma] (delta) {4}; + + \draw[arrow] (alpha) -- (beta); + \draw[arrow] (beta) -- (gamma); + \draw[arrow] (alpha) -- (gamma); + \draw[arrow] (gamma) -- (delta); + \end{tikzpicture} + \end{minipage} + % + \begin{minipage}{0.5\linewidth} + \begin{definition}[Oriented Graph] + Directed Graph where bidirected edges connect no pair of vertices. + \label{def:oriented:graph} + \end{definition} + \end{minipage} + \vfill + \vspace{\belowdisplayskip} + \begin{minipage}{0.45\linewidth} + \centering + \begin{tikzpicture}[minimum size=0.5cm,node distance=1cm] + \node[entity] (alpha) {1}; + \node[entity,above left=of alpha,xshift=15pt] (beta) {2}; + \node[entity,above right=of alpha,yshift=-5pt,xshift=-5pt] (gamma) {3}; + \node[entity,right=of gamma] (delta) {4}; + + \draw[arrow] (alpha) -- (beta); + \draw[arrow] (beta) -- (gamma); + \draw[arrow] (alpha) -- (gamma); + + \path[arrow] let \p1=($(gamma)-(delta)$),\n1={atan2(\y1,\x1)},\n2={180+\n1} in + ($ (delta.\n1)!2pt!90:(gamma.\n2) $) edge node {} ($ (gamma.\n2)!2pt!-90:(delta.\n1) $); + \path[arrow] let \p1=($(delta)-(gamma)$),\n1={atan2(\y1,\x1)},\n2={180+\n1} in + ($ (gamma.\n1)!2pt!90:(delta.\n2) $) edge node {} ($ (delta.\n2)!2pt!-90:(gamma.\n1) + $); + \end{tikzpicture} + \end{minipage} + % + \begin{minipage}{0.5\linewidth} + \begin{definition}[Directed Graph] + Named \emph{digraph}, it is defined as a graph whose edges have an + orientation, also known as \emph{directed edges}, \emph{directed links}, + \emph{arrows}, or \emph{arcs}. + \label{def:directed:graph} + \end{definition} + \end{minipage} + \caption{Basic Graph Types (Part I).} +\end{figure} + +\newpage + +\begin{figure}[!ht] + \begin{minipage}{0.45\linewidth} + \centering + \begin{tikzpicture}[minimum size=0.5cm,node distance=1cm] + \node[entity] (alpha) {1}; + \node[entity,above left=of alpha,xshift=15pt] (beta) {2}; + \node[entity,above right=of alpha,yshift=-5pt,xshift=-5pt] (gamma) {3}; + \node[entity,right=of gamma] (delta) {4}; + + \draw (alpha) -- (beta); + \draw (beta) -- (gamma); + \draw (alpha) -- (gamma); + \draw (gamma) -- (delta); + \end{tikzpicture} + \end{minipage} + % + \begin{minipage}{0.5\linewidth} + \begin{definition}[Undirected Graph] + Graph whose edges are bidirectional. + \label{def:undirected:graph} + \end{definition} + \end{minipage} + \vfill + \vspace{\belowdisplayskip} + \begin{minipage}{0.45\linewidth} + \centering + \begin{tikzpicture}[minimum size=0.5cm,node distance=1cm] + \node[entity] (alpha) {1}; + \node[entity,above left=of alpha,xshift=15pt] (beta) {2}; + \node[entity,above right=of alpha,yshift=-5pt,xshift=-5pt] (gamma) {3}; + \node[entity,right=of gamma] (delta) {4}; + + \draw[thick] (alpha) -- (beta); + \draw[thick] (beta) -- (gamma); + \draw[thick] (alpha) -- (gamma); + + \path[thick] let \p1=($(gamma)-(delta)$),\n1={atan2(\y1,\x1)},\n2={180+\n1} in + ($ (delta.\n1)!2pt!90:(gamma.\n2) $) edge node {} ($ (gamma.\n2)!2pt!-90:(delta.\n1) $); + \path[thick] let \p1=($(delta)-(gamma)$),\n1={atan2(\y1,\x1)},\n2={180+\n1} in + ($ (gamma.\n1)!2pt!90:(delta.\n2) $) edge node {} ($ (delta.\n2)!2pt!-90:(gamma.\n1) + $); + \end{tikzpicture} + \end{minipage} + % + \begin{minipage}{0.5\linewidth} + \begin{definition}[Multigraph] + Undirected graph that can store multiple edges between two nodes. + \label{def:multigraph} + \end{definition} + \end{minipage} + \caption{Basic Graph Types (Part II).} +\end{figure} + +\noindent Based on these definitions of graph types, the KG is defined. +\begin{definition}[Knowledge Graph] +Directed \emph{heterogeneous} multigraph whose node and relation types have +domain-specific semantics~\citep{website:kamakoti}. These nodes can be of +different types. From a terminology point of view, the nodes/vertices of a KG +are often called \emph{entities}, and the directed edges refer to as +predicates. Moreover, this multigraph has \emph{triple}\footnote{Also called +\emph{triplets}.} designing a 3-tuple, where each triple defines a +(\texttt{subject}, \texttt{predicate}, \texttt{object}) tuple\footnote{Some +authors define this tuple as \texttt{(h, r, t)}. In this definition, \texttt{h} +is the head entity, \texttt{t} the tail entity, and \texttt{r} the relation +associating the head with the tail entities.}. For ease of processing, the +multigraph aspect of the KG can be removed by representing each triple as two +2-tuple: (\texttt{subject} $\rightarrow$ \texttt{predicate}) and +(\texttt{predicate} $\rightarrow$ \texttt{object}). +\end{definition} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "../../report" +%%% End: diff --git a/src/background/ml.tex b/src/background/ml.tex new file mode 100644 index 0000000..4f5a7d6 --- /dev/null +++ b/src/background/ml.tex @@ -0,0 +1,264 @@ + +\section{Machine Learning} +\label{sec:background:ml} + +Machine Learning (ML) is a branch of AI focusing on improving the automatic +learning of models without having been explicitly programmed for it. ML comes +with three basic paradigms: supervised, unsupervised, and reinforcement +learning. Each of them is defined below. + +\begin{multicols}{2} + \begin{definition}[Supervised Learning] + Type of ML with human supervision, where a model looks for patterns in a data + set with labels~\citep{website:deepai:unsupervised:learning}. + \label{def:supervised:learning} + \end{definition} + + \begin{definition}[Unsupervised Learning] + Type of ML with minimal human supervision, where a model looks for patterns + in a data set without labels. + \label{def:unsupervised:learning} + \end{definition} +\end{multicols} + +Visually, supervised learning and unsupervised learning are defined as follows: +\begin{figure}[!ht] + \centering + \begin{minipage}{.45\textwidth} + \begin{tikzpicture}[baseline,scale=.7] + \begin{axis}[ + height=5.5cm, + width=9cm, + axis x line=center, + axis y line=center, + xlabel style={below right}, + ylabel style={above left}, + xlabel={$X$}, + ylabel={$Y$}, + xtick={4,10}, + xtick={5,14}, + clip mode=individual + ] + + % Trick to display the graph starting at (1,1) + \addplot[green,mark size=0] table [% + x = x, + y = y, + col sep = comma]{ + x,y + 0.5,0.5 + }; + + \addplot[blue, only marks, mark=*, mark size=3] table [% + x = x, + y = y, + col sep = comma]{ + x,y + 3,3 + 3.5,5 + 4,4.2 + 4.5,3.5 + 4.8,2 + 5,5 + 5.5,4 + 6,4.8 + 6.5,3.5 + }; + + \draw [dashed] (4,11) -- (15,3); + + \addplot[red, only marks, mark=*, mark size=3] table [% + x = x, + y = y, + col sep = comma]{ + x, y + 12,12.5 + 12.5,10.5 + 13,9 + 13.5,11 + 14,9.5 + 14.5,8 + 14.7,12 + 14.8,10.7 + 15.5,9.6 + 16,10.8 + }; + \end{axis} + \end{tikzpicture} + \captionof{figure}{Supervised Learning} + \label{tikz:background:supervised:learning} + \end{minipage} + \quad + \begin{minipage}{.45\textwidth} + \begin{tikzpicture}[baseline,scale=.7] + \begin{axis}[ + height=5.5cm, + width=9cm, + axis x line=center, + axis y line=center, + xlabel style={below right}, + ylabel style={above left}, + xlabel={$X$}, + ylabel={$Y$}, + xtick={4,10}, + xtick={5,14}, + clip mode=individual + ] + + % Trick to display the graph starting at (1,1) + \addplot[mark size=0] table [% + x = x, + y = y, + col sep = comma]{ + x,y + 0.5,0.5 + }; + + \addplot[black!70,only marks, mark=*, mark size=3] table [% + x = x, + y = y, + col sep = comma]{ + x,y + 3,3 + 3.5,5 + 4,4.2 + 4.5,3.5 + 4.8,2 + 5,5 + 5.5,4 + 6,4.8 + 6.5,3.5 + }; + + \draw [dashed] (5,4) circle[radius=2.8]; + + \addplot[black!70,only marks, mark=*, mark size=3] table [% + x = x, + y = y, + col sep = comma]{ + x, y + 12,12.5 + 12.5,10.5 + 13,9 + 13.5,11 + 14,9.5 + 14.5,8 + 14.7,12 + 14.8,10.7 + 15.5,9.6 + 16,10.8 + }; + \draw [dashed] (14.5,10) circle[radius=2.8]; + \end{axis} + \end{tikzpicture} + \captionof{figure}{Unsupervised Learning} + \label{tikz:background:unsupervised:learning} + \end{minipage} + \caption{Learning a Model Using Raspberry and Blueberry Data.} + \label{fig:background:supervised:vs:unsupervised} +\end{figure} + +In Figure \ref{tikz:background:supervised:learning}, supervised learning +contains raspberry and blueberry data already classified by their label. A model +learns to predict the values based on a \emph{cost function}, which allows it to +check and correct its predictions according to the actual values. With these +labeled data, the classification and regression problems can use this type of +learning. + +In Figure \ref{tikz:background:unsupervised:learning}, unsupervised learning +still contains raspberry and blueberry data. However, this time these data are +not labeled, which means that a model must find the patterns and structure +independently. The clustering and association problems use this type of +learning. For example, this clustering example creates two clusters, with one +raspberry not belonging to any cluster. + + +\begin{definition}[Reinforcement Learning] + Type of ML where a model learns from the experience and feedback of an + autonomous agent. +\end{definition} + +\noindent In ML, each neuron inside an Artificial Neural Networks (ANN) outputs +a number between $-\infty$ and $\infty$ propagating to its predecessor via an +activation function. Once the ANN has completed its processing through these +neurons, it generates \emph{logits}, a non-normalized vector of predictions +generated by a classification model. For ease of processing, it is usually +appropriate to convert these logits into probabilities to have a unitary +sum. According to the required type of classification, activation functions such +as \emph{softmax} and \emph{sigmoid} are helpful. These functions can help with +various tasks, such as predicting the most likely word to be the missing word in +a sentence in the Natural Language Processing (NLP) field. + +\begin{definition}[Softmax Function] + Also called \emph{softargmax}, a logistic regression model uses this + multi-classification function for transformation purposes. Specifically, this + model transforms a vector of $K$ real values into a vector of $K$ elements that + range between 0 and 1 with the particularity of having a unitary + sum~\citep{website:deepai:softmax}. Let $\mathbf{z}$ be an input vector and $K$ + be some classes in a multi-class classifier. Mathematically, the softmax + function of these classes is defined as follows: + \begin{equation} + \mathrm{\sigma}(\mathbf{z})_i = \frac{\me^{z_i}}{\sum^K_{j=1}\me^{z_j}} + \label{eq:softmax} + \end{equation} + \label{def:softmax} +\end{definition} + +\begin{definition}[Sigmoid Function] + Binary classification function recognizable with an ``S'' shaped curve used by + a logistic regression model for transformation purposes. Unlike the softmax + function, this model transforms a vector of $K$ real values into a vector of $K$ + elements range this time between -1 and 1 with still the particularity of having + a unitary sum. Let $\mathbf{x}$ be an input vector. Mathematically, the + sigmoid function is defined as follows: + \begin{equation} + \mathrm{\sigma}(\mathbf{x}) = \frac{1}{1 + e^{-x}} = \frac{e^x}{e^x + 1} + \label{eq:sigmoid} + \end{equation} + \label{def:sigmoid} +\end{definition} + +\begin{definition}[Rectified Linear Unit] + Commonly called \emph{ReLU}, the community considers this function as one of + the most straightforward functions. Let $\mathbf{x}$ be an input + vector. Mathematically, the ReLU function is defined as follows: + \begin{equation} + \mathrm{f}(\mathbf{x}) = \max(0, \mathbf{x}) + \label{eq:relu} + \end{equation} + \label{def:relu} +\end{definition} + +\noindent These functions can help with various tasks, such as predicting the +most likely word to be the missing word in a sentence in the NLP +field. Subsequently, in ML, it is essential to know the similarity of two +vectors. For example, it is helpful in NLP to tell if two words share semantic +similarities. As a result, the use of cosine similarity is relevant. + +\begin{definition}[Cosine Similarity] + Measures the cosine of the angle between two non-zero vectors of an inner + product space~\citep{website:deepai:cosine:similarity}. Let $\mathbf{u}, + \mathbf{v} \in \mathbb{R}^d$ be two non-zero $d$-dimensional vectors. + Mathematically, the cosine similarity between $\mathbf{u}$ and $\mathbf{v}$ is + defined as follows: + \begin{align} + \cos(\mathbf{u}, \mathbf{v}) = + \frac{\mathbf{u} \cdot \mathbf{v}} + {\left\lVert \mathbf{u} \right\rVert + \left\lVert \mathbf{v} \right\rVert} = + \frac{\sum\limits_{i = 1}^n u_i v_i} + {\sqrt{\sum\limits_{i = 1}^n u_i^2} + \sqrt{\sum\limits_{i = 1}^n v_i^2}} + \label{eq:cosine:similarity} + \end{align} + + where $\cos(\mathbf{u}, \mathbf{v})$ produces a value ranging from -1 to 1. + Specifically, the cosine similarity returns -1 if two vectors do not have any + similarities, 0 if they are unrelated, and 1 if they share every similarity. + \label{def:cosine:similarity} +\end{definition} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "../../report" +%%% End: diff --git a/src/background/nlp.tex b/src/background/nlp.tex new file mode 100644 index 0000000..307dbc7 --- /dev/null +++ b/src/background/nlp.tex @@ -0,0 +1,154 @@ + +\section{Natural Language Processing Techniques} +\label{sec:background:nlp:techniques} + +There are many NLP techniques. The objective is not to cover every one of them +but to define certain notions used by more advanced concepts such as Word2Vec. + +\begin{definition}[Distributed Representation] + Describes the same data features across multiple scalable and interdependent + layers~\citep{website:deepai:distributed:representation}. In a distributed word + representation, there is a distribution of the word information across vector + dimensions. + \label{def:distributed:reprensetation} +\end{definition} + +\begin{definition}[Bag-of-Words] + Vectorizes a text by counting the number of unique words (also called + \emph{tokens}) in a text. Let ``Suikoden is my favorite game, it is a wonderful + game!'' be a text. The representation of this text with Bag-of-Words (BoW) is + defined as follows: + \begin{equation} + \left\{\ \text{Suikoden: } 1,\ \text{is: } 2,\ \text{my: } 1,\ \text{favorite: } 1,\ + \text{game: } 2,\ \text{it: } 1, \ \text{a: } 1,\ \text{wonderful: } 1\ \right\} + \end{equation} + + for which this text can be characterized (e.g., \texttt{[1, 2, 1, 1, 2, 1, 1, + 1]}) by differences measures (e.g., word frequency). + \label{def:bow} +\end{definition} + +\begin{definition}[One-Hot Encoding] + Quantifies categorical data as binary vectors. Specifically, the belonging of + a data point to the $i$th category implies the acquisition of a zero value for + the components of this vector, except for the $i$th component, which receives a + unitary value. Let $K$ be several categories in a data set, and + $\mathbf{y}^{(i)}$ be a data point in the $i$th class. Mathematically, the + following vectorial representation defines such one-hot encoding: + \begin{equation} + \textbf{y}^{(i)} = \underbrace{\begin{bmatrix}0 & \ldots & 0 & + \underbrace{1}_{\textup{index} \;\; i} &0 & \ldots & + 0\end{bmatrix}^\top}_{K \times 1} + \label{eq:one-hot:encoding} + \end{equation} + + where one-hot encoding vectors allow ML algorithms to make better + predictions. Such an encoding does not capture words' semantic and syntactic + information. Therefore, it does not detect semantic and order difference between + the sentences the ``I like cats more than dogs'' and ``I like dogs more than + cats'' As a result, \emph{word embeddings} are privileged to detect these + differences and allow a better numerical representation of words. + \label{def:one-hot:encoding} +\end{definition} + +\begin{definition}[Word Embeddings] + Unsupervised model that captures words' semantic and syntactic information + using an \emph{embedding matrix}, where the embeddings of a \textit{w} word are + a vector $\mathbf{v}_w$. + \label{def:word:embeddings} +\end{definition} + +\begin{definition}[Embedding Matrix] + Randomized matrix of dimensions $\mathcal{W} \times \mathcal{F}$, where + $\mathcal{W}$ is the number of unique words in a document and $\mathcal{F}$ is + the number of features that each unique word in this vocabulary has. The + \emph{gradient descent} uses these matrix values to find the minima of a + function for several \emph{epochs}, the number of complete cycles on a training + data set. From then on, closer words in vector space are assumed to have a + similar meaning. + \label{def:embedding:matrix} +\end{definition} + +\begin{definition}[Window Size] + Determines the context words, also called \emph{training samples}, of a target + word from a sliding window along with a sentence. Therefore, a window size of + two means 2-triple context words, including the related target word and each of + the two words on its left and two on its right. Let ``I will always remember + her'' be a sentence. The following table defines the context words for a window + size of 2: + \begin{table}[!ht] + \centering + \caption{Context Words Determination for a Window Size of 2. } + \label{tab:window:size} + \begin{tabular}{ccc} + \toprule + \textbf{Input Text} & \textbf{Target Word} & \textbf{Context Words} \\ + \midrule + \multirow{2}{*}{\colorbox{blue!25}{I} \colorbox{myblue!25}{will} \colorbox{myblue!25}{always} remember her} & \multirow{2}{*}{i} & will \\ + & & always \\[1.2ex] + \multirow{3}{*}{\colorbox{myblue!25}{I} \colorbox{blue!25}{will} \colorbox{myblue!25}{always} \colorbox{myblue!25}{remember} her} & \multirow{3}{*}{will} & i \\ + & & always \\ + & & remember \\[1.2ex] + \multirow{4}{*}{\colorbox{myblue!25}{I} \colorbox{myblue!25}{will} \colorbox{blue!25}{always} \colorbox{myblue!25}{remember} \colorbox{myblue!25}{her}} & \multirow{4}{*}{always} & i \\ + & & will \\ + & & remember \\ + & & her \\[1.2ex] + \multirow{3}{*}{I \colorbox{myblue!25}{will} \colorbox{myblue!25}{always} \colorbox{blue!25}{remember} \colorbox{myblue!25}{her}} & \multirow{3}{*}{remember} & will \\ + & & always \\ + & & her \\[1.2ex] + \multirow{2}{*}{I will \colorbox{myblue!25}{always} \colorbox{myblue!25}{remember} \colorbox{blue!25}{her}} & \multirow{2}{*}{her} & always \\ + & & remember \\ + \bottomrule + \end{tabular} + \end{table} + + In Table \ref{tab:window:size}, the target word highlighted in blue is + modified at each iteration starting from left to right, considering two words + forward and backward (highlighted in a lighter blue). As such, the context for a + given sentence are known. + \label{def:window:size} +\end{definition} + +\begin{definition}[Stop Words] + Commonly used words (e.g., ``an'', ``the'', and ``is'') having little + value for training a model and are therefore considered noise in a training + data set. + \label{def:stop:words} +\end{definition} + + % \begin{definition}[Mean] Averages of some data. Let $n$ be the data and $\mathbf{x}$ be a + % sample. The mean of these data is defined as: + % \begin{equation} + % \mathrm{\mu} = \frac{1}{n}\sum^n_{i=1}x_i + % \label{eq:mean} + % \end{equation} + % \label{def:mean} + % \end{definition} + + % \begin{definition}[Variance] + % Measures how spread a data point is from an average. Let $\mathrm{\mu}$ be the + % mean of $n$ data. The variance of a random variable $X$ is defined as: + % \begin{equation} + % \mathrm{Var}(X) = E\left[\left(X - \mu\right)^2\right] + % \label{eq:variance} + % \end{equation} + % \label{def:variance} + % \end{definition} + + % \begin{definition}[Standard Deviation] + % Measures the dispersion of the data around their center or how they are spread + % out in a data set. Let $\mathrm{Var}$ be the variance of $n$ data. The standard + % deviation is defined as: + % \begin{equation} + % \mathrm{\sigma} = \sqrt{\mathrm{Var}(n)} + % \label{eq:standard:deviation} + % \label{def:standard:deviation} + % \end{equation} + + % where unlike variance, standard deviation is measured using the same units as the data. + % \end{definition} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "../../report" +%%% End: diff --git a/src/background/transformers.tex b/src/background/transformers.tex new file mode 100644 index 0000000..3855760 --- /dev/null +++ b/src/background/transformers.tex @@ -0,0 +1,207 @@ + +\section{Transformer} +\label{sec:transformer} + +The \emph{Transformer} architecture is an alternative to RNNs published in 2017, +questioning the need for RNNs following the discovery of the Attention +mechanism~\citep{vaswani:attention}. The original paper presents this +architecture for Machine Translation and introduces two new Attention +mechanisms: \emph{Scaled Dot-Product Attention} and \emph{Multi-Head Attention}. + +\subsection{Scaled Dot-Product Attention} +\label{subsec:transformer:scaled:dot-prodct:attention} + +\emph{Scaled Dot-Product Attention} provides an Attention score based on a Dot +Product Attention scaled by the square root inverse of the dimension of the +query and key matrices. This scaled version prevents the Dot-Product Attention +mechanism from growing large in magnitude when the dimensionality of the queries +has a high value. Specifically, this high value is due to the multiplication and +the addition of inputs, which push the softmax function into regions where its +gradients are minimal. +\begin{definition}[Scaled Dot-Product Attention] + Let $Q \in \mathbb{R}^{m\times d_k}$ be the matrix of queries and $K \in + \mathbb{R}^{n\times d_k}, V \in \mathbb{R}^{m\times d_v}$ be matrices of a set + of key-value pairs. Mathematically, the the Scaled Dot-Product Attention + mechanism is defined as follows: + \begin{equation} + \mathrm{A}(Q, K, V) = \mathrm{softmax}\left(\frac{QK^T}{\sqrt{d_k}}\right)V + \label{eq:def:scaled:dot-product:attention} + \end{equation} + + where $d_k$ is the dimensionality of queries as well as keys and $d_v$ the + dimensionality of values. +\end{definition} + +\subsection{Multi-Head Attention} +\label{subsec:transformer:multi-head:attention} + +\emph{Multi-Head Attention} (MHA) is an improved version of the Self-Attention +mechanism where each word not only brings excessive importance to itself, but +pays attention to the interactions with other words. As a result, MHA achieves +better results than Self-Attention, where the latter leads to a loss of +efficiency in the Attention embeddings. Finally, MHA still performs a weighted +average to generate the Attention vector for each token. However, the heads are +this time computed in parallel. + +\begin{definition}[Multi-Head Attention] + Let $f_o: \mathbb{R}^{kd} \to \mathbb{R}^D$ be a linear map, $f_{i,q}, f_{i, + k}, f_{i, v}: \mathbb{R}^D \to \mathbb{R}^d$ be a three sets of linear maps, + $\hat{Q} \in \mathbb{R}^{M\times D}$ be a queries vector, and $\hat{K}, \hat{V} + \in \mathbb{R}^{N\times D}$ be vectors of keys and values. Mathematically, the + MHA is defined as follows: + \[ + \textrm{MHA}(\hat{Q}, \hat{K}, \hat{V}) = f_o \left ( + \text{concat} \left ( + \left [ + A \left ( + f_{i,q}(\hat{Q}), + f_{i,k}(\hat{K}), + f_{i,v}(\hat{V}) + \right ) + \ + \forall \ i \in 1,\dots, k + \right ] + \right ) + \right ) + \] + where $\text{MHA}(\hat{Q}, \hat{K}, \hat{V}) \in \mathbb{R}^{M \times D}$ is + the output of the MHA, also known as a \emph{neural function} with $k$-headed + attention block. +\end{definition} + +\subsection{Architecture} +\label{subsec:transformer:architecture} + +The Transformer architecture mainly consists of an encoder and a decoder block, +including the Scaled Dot-Product and MHA mechanisms. Specifically, the encoder +and decoder are neural components composed of a stack of $N=6$ identical layers. + +Visually, one layer of the Transformer works as follows: +\begin{figure}[!ht] + \centering + \subfloat[Encoder\label{fig:transformer:encoder}]{% + \includegraphics[width=0.23\textwidth]{img/transformer/encoder} + } + \quad + \subfloat[Decoder\label{fig:transformer:decoder}]{% + \includegraphics[width=0.23\textwidth]{img/transformer/decoder} + } + \caption{One Layer of the Architecture of the Transformer.} + \label{fig:transformer:architecture:encoder} + \source{\textsc{Vaswani} et al. -- Attention Is All You Need.} +\end{figure} + +In Figure \ref{fig:transformer:encoder}, one layer of the encoder contains two +sub-layers: a MHA mechanism and a position-wise fully connected Feed-Forward +Neural Network (FFN). +\begin{definition}[Feed-Forward Neural Network] + Let $W_1 + b_1$ and $W_2 + b_2$ be two linear transformations. Mathematically, + the FFN is defined as follows: + \begin{equation} + \mathrm{FFN}(x) = \max\left(0, xW_1 + b_1\right)W_2 + b_2 + \label{eq:def:ffn} + \end{equation} + where a ReLU activation function is used. + \label{def:ffn} +\end{definition} + +Moreover, a residual connection followed by a normalization of the layers wraps +each of the two sublayers. Mathematically, the output of every sub-layer is +defined as follows: +\begin{equation} + \mathrm{LayerNorm}(x + \mathrm{Sublayer}(x)) + \label{eq:output:sub-layer} +\end{equation} +where $\mathrm{Sublayer}(x)$ refers to the implemented function by the sub-layer +itself. \\ + + +\noindent In Figure \ref{fig:transformer:decoder}, the decoder has layers that +differ from the encoder with two sub-layer changes. The first sublayer change is +defined using \emph{Masked MHA} as the first sub-layer to prevent positions from +attending subsequent positions. The last change is adding a new sub-layer, +called \emph{Encoder-Decoder Attention} which performs MHA over the Attention +vectors of the decoder and those of the encoder. The use of this sub-layer makes +it possible to determine the different relationships between these +vectors. Finally, the generated embeddings are sent to a position-wise fully +connected FFN. Like the encoder, each sub-layer is wrapped by a residual +connection followed by a layer normalization. + +From then one, the complete architecture of the Transformer is illustrated as follows: +\begin{figure}[!ht] + \centering + \includegraphics[width=0.6\textwidth]{img/transformer/architecture} + \caption{Model Architecture of the Transformer.} + \source{\textsc{Vaswani} et al. -- Attention Is All You Need} + \label{fig:transformer:architecture} +\end{figure} + +\newpage + +In Figure \ref{fig:transformer:architecture}, both encoding and decoding take +the sum of the input/output embeddings with positional embedding as +input. Unlike RNNs, Transformer do not have a time step so that input sequences +can be injected simultaneously and converted into input embeddings. Each token +is represented in the embedding space through these input embeddings where +semantically similar tokens are closer than others. However, the decoder has the +particularity of having its input shifted. This shift avoids that a model only +learns to copy the decoder input by allowing a model to predict the target +word/character for position $i$ according to the previous one from 1 to $i-1$. + +At last, the output of the decoding layer is sent to a linear layer. This layer +is nothing more than an FFN layer whose objective is to extend the dimension of +this vector to the number of words of the language concerned. Once expanded, +this vector is submitted to a softmax activation function to transform it into a +probability distribution and predict the next word according to the word with +the highest probability. Afterward, this decoding process is iterated several +times until the end-of-sentence token is generated. + +\subsection{Positional Encoding} +\label{subsec:transformer:positional:encoding} + +Considering that the transformer has no recurrence or convolution mechanism, the +architecture cannot know the order in an input sequence. From then on, the +transformer encodes the same meaning for different sentences. The easiest way to +take this context into account is to encode these positions as one-hot features. +\begin{definition}[Positional Encoding as One-Hot Features] + Let $x \in \mathbb{R}^{n \times d}$ be a matrice of sequentially ordered data + along the $n$-dimensional axis, and $e_k$ be a $k$'th standard basis vector in + $\mathbb{R}^n$. Mathematically, the $z \in \mathbb{R}^{n \times d}$ learned + combined representation is defined as follows: + \begin{equation} + \mathrm{z}_k = W^T_zReLU\left(W_x^Tx_k + W_e^Te_k\right), W_x \in + \mathbb{R}^{dim(x)\times m}, W_e \in \mathbb{R}^{n\times m}, W_z \in \mathbb{R}^{m\times d} + \label{eq:def:positional:encoding:one:hot} + \end{equation} + \label{def:positional:encoding:one:hot} +\end{definition} + +\noindent Another approach for positional encoding is to build distinct +representations of inputs and positions~\citep{gehring}. Despite these existing +approaches to differentiate meanings, the original Transformer paper uses a +sinusoid-wave-based positional encoding to inject absolute positional +information of tokens into the sequence. + +\begin{definition}[Positional Encoding by \textsc{Vaswani} et al.] + Let $d_{model}$ be the embedding dimension of words, and $pos \in \left[0, L - + 1\right]$ be the position of a $w$ word in the $w = (w_0,\dotsc,w_{L-1})$ input + sequence. Mathematically, the positional encoding of $w$ is defined as follows: + \begin{align} + \mathrm{PE}(pos,i) = \begin{cases} + \sin\displaystyle\left(\frac{pos}{10000^{2i/d_{model}}}\right)\,, & i = 2k \\\\ + \cos\displaystyle{\left(\frac{pos}{10000^{2i/d_{model}}}\right)}\,, & i = 2k + 1 + \end{cases} \ k \in \mathbb{N} + \label{eq:positional:encoding} + \end{align} + + where the positional encoding follows a specific, learned pattern to identify + word position or the distance between words in the sequence~\citep{alammar}. In + Equation \ref{eq:positional:encoding}, the sinusoidal representation works as + well as a learned representation and better generalizes sequences that are + longer than the training sequences~\citep{vaswani:attention}. +\end{definition} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "../../report" +%%% End: diff --git a/src/benchmarks.tex b/src/benchmarks.tex new file mode 100644 index 0000000..cff8b33 --- /dev/null +++ b/src/benchmarks.tex @@ -0,0 +1,42 @@ + +\chapter{Benchmarks} +\label{chap:benchmarks} + +For these benchmarks, only the maximum number of walks per entity and the +maximum depth per walk is varied. Furthermore, due to a time issue (cf. Section +\ref{sec:objectives:problems}) these benchmarks are performed on \texttt{MUTAG}, +a graph of moderate size composed of +\SI{74567}{triples}\footnote{\textbf{SELECT} (COUNT(*) AS ?triples) +\textbf{WHERE} \{ ?s ?p ?o \}} \SI{22534}{entities }\footnote{\textbf{SELECT} +(COUNT(\textbf{DISTINCT} ?s) AS ?entities) \textbf{WHERE} \{ ?s a \}}, and +\SI{24}{relations}\footnote{\textbf{SELECT} (COUNT(\textbf{DISTINCT} ?p) AS +?relations) \textbf{WHERE} \{ ?s ?p ?o \}}. Finally, each value entered in these +benchmarks is the result of the average of five values. + +\section{Setup} +\label{sec:setup} + +Benchmarks related to embeddings techniques and walking strategies are directly +launched on IDLab's\footnote{Research group of imec.} servers with \SI{4}{CPUs}, +\SI{64}{\giga\byte} RAM, and one GPU. Those related to sampling strategies are +launched directly on a ThinkPad machine with \SI{4}{CPUs} and +\SI{16}{\giga\byte} of RAM. This physical device change is made since, except +for \texttt{UniformSampler}, the sampling strategies only work on locally stored +KGs. As the IDLab servers interact with the KGs via SPARQL endpoints, they were +not used for these benchmarks. Finally, the benchmarks use 340 training entities +and attempt to predict 68 test entities, which is a standard for \texttt{MUTAG}. + +\section{Results} +\label{sec:results} + +This section contains the results of the different embedding techniques, walking +strategies, and sampling strategies for \texttt{MUTAG}. + +\input{src/benchmarks/embedders} +\input{src/benchmarks/walkers} +\input{src/benchmarks/samplers} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "../master-thesis" +%%% End: \ No newline at end of file diff --git a/src/benchmarks/embedders.tex b/src/benchmarks/embedders.tex new file mode 100644 index 0000000..c318309 --- /dev/null +++ b/src/benchmarks/embedders.tex @@ -0,0 +1,237 @@ + +\subsection{Embedding Techniques} +\label{subsec:embedding:techniques} + +FastText, BERT and Word2Vec are trained on the basis of ten epochs. In addition, +FastText and Word2Vec use twenty negative words with a vector size of 500. For +its splitting function, FastText uses a primary splitting function where the +\texttt{\#} symbol splits each entity Finally, each embedding technique uses a +\texttt{RandomWalker} and an \texttt{UniformSampler}. + +About the training of BERT, the latter is only trains on +\texttt{MUTAG}. However, in case of multiple KGs, it is important to re-train it +for each different KGs. Similarly, if BERT is trained with too few walks, it +will be necessary to retrain it with a larger number of walks. In this case, +online learning is important to avoid to retrain the whole model which can be +time-consuming. Unline BERT that can take hours, days for training the model, +Word2Vec and FastText take a few minutes to tens of minutes to train, which is +significant difference. + +\begin{table}[!ht] + \centering + \begin{tabular}{rl} + \toprule + \textbf{Hyperparameter} & \textbf{Value} \\ + \midrule + \textbf{Epochs} & 10 \\ + \textbf{Warmup Steps} & 500 \\ + \textbf{Weight Decay} & 0.01 \\ + \textbf{Learning Rate} & 2e-5 \\ + \textbf{Batch Size} & 16 \\ + \bottomrule + \end{tabular} + \caption{Basic Hyperparameters Used for Training the BERT Model.} + \label{tab:bert:hyperparameters} +\end{table} + +In Table \ref{tab:bert:hyperparameters}, The values of these basic +hyperparameters were chosen after several tests using a Grid Search with Cross +Validation and depending on the training time. More precisely, a training of the +BERT model with these hyperparameters with MUTAG and the same hardware +characteristics as those of the IDLab servers, is done between 25 minutes and +few hours. + +\begin{table}[!ht] + \centering + \resizebox{\textwidth}{!}{% + \begin{tabular}{cccS[table-format=2.2]@{${}\pm{}$}S[table-format=1.1]c} + \toprule + \textbf{Embedding Technique} & \textbf{Max. Depth} & \textbf{Max. Walks} + & \multicolumn{2}{c}{\textbf{Accuracy} (\SI{}{\percent})} & \textbf{Rank} \\ + \midrule + \texttt{FastText(negative=20,vector\_size=500)} & \multirow{3}{*}{2} & \multirow{3}{*}{250} & 79.71 & 2.35 & 1 \\ + \texttt{Word2Vec(negative=20,vector\_size=500)} & & & 76.76 & 1.71 & 2 \\ + \texttt{BERT(learning\_rate=2e-5,batch\_size=16)} & & & 70.59 & 5.88 & 3 \\ + \midrule + \texttt{FastText(negative=20,vector\_size=500)} & \multirow{3}{*}{4} & \multirow{3}{*}{250} & 77.06 & 1.50 & 1 \\ + \texttt{Word2Vec(negative=20,vector\_size=500)} & & & 75.00 & 1.61 & 2 \\ + \texttt{BERT(learning\_rate=2e-5,batch\_size=16)} & & & 74.26 & 2.21 & 3 \\ + \midrule + \texttt{FastText(negative=20,vector\_size=500)} & \multirow{3}{*}{6} & \multirow{3}{*}{250} & 82.35 & 1.86 & 1 \\ + \texttt{BERT(learning\_rate=2e-5,batch\_size=16)} & & & 76.32 & 3.24 & 2 \\ + \texttt{Word2Vec(negative=20,vector\_size=500)} & & & 74.71 & 2.35 & 3 \\ + \bottomrule + \end{tabular} + }% + \caption{Evaluation of the Embedding Techniques for \texttt{MUTAG} According + to the Maximum Depth per Walk.} + \label{benchmarks:embedders:mutag:depth} +\end{table} + +In Table \ref{benchmarks:embedders:mutag:depth}, regardless of the maximum depth +per walk chosen for the same number of walks per entity, FastText indicates a +model's accuracy above Word2Vec. Specifically, FastText allows an average +increase of the model's accuracy of 4.22 times the one given by Word2Vec. In +addition, FastText provides an excellent model's accuracy with \texttt{MUTAG} +for a maximum depth per walk of 6. For BERT, the latter shows better results for +larger maximum depth per walk. + +\begin{figure}[!ht] + \centering + \resizebox{\textwidth}{!}{% + \begin{tikzpicture} + \begin{axis}[ + scale only axis, + grid=major, + grid style={dashed,gray!30}, + height=6cm, + width=9cm, + legend cell align={left}, + legend entries={ + \footnotesize{\texttt{BERT(learning\_rate=2e-5,batch\_size=16)}}, + \footnotesize{\texttt{Word2Vec(negative=20,vector\_size=500)}}, + \footnotesize{\texttt{FastText(negative=20,vector\_size=500)}} + }, + legend style={ + legend pos=outer north east, + font=\small + }, + ylabel={Accuracy}, + xlabel={Maximum Depth per Walk}, + xtick={2,4,6}, + ytick={75,77,79.70,82.30}, + ] + + \addplot[red,mark=*,error bars/.cd, y dir=both, y explicit] + table[x=max_depth,y=accuracy,col sep=comma] {data/embedders/max-depth/bert.csv}; + \addplot[blue,mark=*,error bars/.cd, y dir=both, y explicit] + table[x=max_depth,y=accuracy,col sep=comma] {data/embedders/max-depth/word2vec.csv}; + \addplot[green,mark=*,error bars/.cd, y dir=both, y explicit] + table[x=max_depth,y=accuracy,col sep=comma] {data/embedders/max-depth/fasttext.csv}; + \end{axis} + \end{tikzpicture} + }% + \caption{Evaluation of the Embedding Techniques for \texttt{MUTAG} According + to the Maximum Depth per Walk.} + \label{fig:benchmarks:embedders:depth} +\end{figure} + +In Figure \ref{fig:benchmarks:embedders:depth}, the curves of Word2Vec and +FastText have an almost identical trajectory, except for a maximum depth per +walk of 6. In this case, the accuracy model of FastText increases, while the +accuracy model of Word2Vec decreases. Finally, BERT's accuracy is proportional +to the maximum depth per walk. As well as the time needed to train the model. + +\begin{table}[!ht] + \centering + \resizebox{\textwidth}{!}{% + \begin{tabular}{cccS[table-format=2.2]@{${}\pm{}$}S[table-format=1.2]c} + \toprule + \textbf{Embedding Technique} & \textbf{Max. Depth} & \textbf{Max. Walks} + & \multicolumn{2}{c}{\textbf{Accuracy} (\SI{}{\percent})} & \textbf{Rank} \\ + \midrule + \texttt{FastText(negative=20,vector\_size=500)} & \multirow{3}{*}{4} & \multirow{3}{*}{100} & 77.94 & 1.61 & 1 \\ + \texttt{Word2Vec(negative=20,vector\_size=500)} & & & 71.47 & 2.20 & 2 \\ + \texttt{BERT(learning\_rate=2e-5,batch\_size=16)} & & & 69.43 & 1.73 & 3 \\ + \midrule + \texttt{FastText(negative=20,vector\_size=500)} & \multirow{3}{*}{4} & \multirow{3}{*}{250} & 77.35 & 3.90 & 1 \\ + \texttt{Word2Vec(negative=20,vector\_size=500)} & & & 74.71 & 2.53 & 2 \\ + \texttt{BERT(learning\_rate=2e-5,batch\_size=16)} & & & 73.54 & 2.28 & 3 \\ + \midrule + \texttt{FastText(negative=20,vector\_size=500)} & \multirow{3}{*}{4} & \multirow{3}{*}{500} & 76.18 & 1.71 & 1 \\ + \texttt{BERT(learning\_rate=2e-5,batch\_size=16)} & & & 75.24 & 2.37 & 2 \\ + \texttt{Word2Vec(negative=20,vector\_size=500)} & & & 73.53 & 1.86 & 3 \\ + \midrule + \texttt{FastText(negative=20,vector\_size=500)} & \multirow{3}{*}{4} & \multirow{3}{*}{1000} & 77.35 & 2.73 & 1 \\ + \texttt{BERT(learning\_rate=2e-5,batch\_size=16)} & & & 76.58 & 1.17 & 2 \\ + \texttt{Word2Vec(negative=20,vector\_size=500)} & & & 74.41 & 3.03 & 3 \\ + \bottomrule + \end{tabular} + }% + \caption{Evaluation of the Embedding Techniques for \texttt{MUTAG} According + to the Maximum Number of Walks per Entity} + \label{benchmarks:embedders:mutag:walks} + +\end{table} + +In Table \ref{benchmarks:embedders:mutag:walks}, regardless of the number of +walks chosen for the same maximum depth per walk, FastText indicates a model's +accuracy above Word2Vec. Specifically, FastText allows an average increase of +the model's accuracy of 3.675 times the one given by Word2Vec. For BERT, the +latter shows better results for larger maximum depth per walk, but performs less +well for smaller maximum depth per walk. For BERT, the latter indicates an +interesting model's accuracy for 500 and 1000 walks. However, the results are +not as exceptional for a lower maximum of walks per entity. + +\begin{figure}[!ht] + \centering + \resizebox{\textwidth}{!}{% + \begin{tikzpicture} + \begin{axis}[ + scale only axis, + grid=major, + grid style={dashed,gray!30}, + height=6cm, + width=9cm, + legend cell align={left}, + legend entries={ + \footnotesize{\texttt{BERT(learning\_rate=2e-5,batch\_size=16)}}, + \footnotesize{\texttt{Word2Vec(negative=20,vector\_size=500)}}, + \footnotesize{\texttt{FastText(negative=20,vector\_size=500)}} + }, + legend style={ + legend pos=outer north east, + font=\small + }, + ylabel={Accuracy}, + xlabel={Maximum Number of Walks per Entity}, + xtick={100,250,500,1000}, + ytick={71.50,73.50,74.50,76.20,78} + ] + + \addplot[red,mark=*,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/embedders/max-walks/bert.csv}; + \addplot[blue,mark=*,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/embedders/max-walks/word2vec.csv}; + \addplot[green,mark=*,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/embedders/max-walks/fasttext.csv}; + \end{axis} + \end{tikzpicture} + }% + \caption{Evaluation of the Embedding Techniques for \texttt{MUTAG} According + to the Maximum Number of Walks per Entity.} + \label{fig:benchmarks:embedders:walks} +\end{figure} + +In Figure \ref{fig:benchmarks:embedders:walks}, the curves of Word2Vec and +FastText still have an almost identical trajectory, except for a maximum number +of walks per entity of 250. In this case, the accuracy model of Word2Vec +increases, while the accuracy model of FastText decreases. Finally, BERT's +accuracy is also proportional to the maximum number of walks per entity. As well +as the time needed to train the model. + +\newpage + +\begin{table}[!ht] + \centering + \begin{tabular}{lc} + \toprule + \textbf{Embedding Technique} & \textbf{Average Rank} \\ + \midrule + \texttt{FastText(negative=20,vector\_size=500)} & 1 \\ + \texttt{Word2Vec(negative=20,vector\_size=500)} & 2 \\ + \texttt{BERT(learning\_rate=2e-5,batch\_size=16)} & 3 \\ + \bottomrule + \end{tabular} + \caption{Evaluation of the Average Rank of the Embedding Techniques for \texttt{MUTAG}.} + \label{tab:benchmark:embedders:average:rank} +\end{table} + +In Figure \ref{tab:benchmark:embedders:average:rank}, Word2Vec is the winning +embedding techniques in these benchmarks for \texttt{MUTAG}, followed by +FastText, and BERT. + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "../../master-thesis" +%%% End: diff --git a/src/benchmarks/samplers.tex b/src/benchmarks/samplers.tex new file mode 100644 index 0000000..2de3fae --- /dev/null +++ b/src/benchmarks/samplers.tex @@ -0,0 +1,470 @@ + +\subsection{Sampling Strategies} +\label{subsec:samplers} + +To determine the accuracy impact of \texttt{WideSampler}, the latter is compared +to other sampling strategies in a first time using \texttt{MUTAG} where only the +number of walks and depth are variable. The number of standard entities for +\texttt{MUTAG} being fixed at 340 trained entities, 68 of these serve as testing +entities. As RDF2Vec is unsupervised, including the testing entities in the +training set is not an issue. + +\newpage + +\begin{table}[!ht] + \centering + \resizebox{\textwidth}{!}{% + \begin{tabular}{lcc S[table-format=2.2]@{${}\pm{}$}S[table-format=1.2]c} + \toprule + \textbf{Sampler} & \textbf{Max. Depth} & \textbf{Max. Walks} + & \multicolumn{2}{c}{\textbf{Accuracy} (\SI{}{\percent})} & \textbf{Rank} \\ + \midrule + \texttt{ObjPredFreqSampler} & \multirow{13}{*}{2} & \multirow{13}{*}{100} & \textbf{78.82} & 3.17 & 1 \\ + \texttt{ObjFreqSampler} & & & 77.94 & 3.35 & 2 \\ + \texttt{PredFreqSampler(inverse=True)} & & & 77.65 & 2.35 & 3 \\ + \texttt{WideSampler} & & & 76.76 & 1.95 & 4 \\ + \texttt{ObjPredFreqSampler(inverse=True)} & & & 76.76 & 2.16 & 5 \\ + \texttt{PredFreqSampler} & & & 76.76 & 4.87 & 6 \\ + \texttt{PageRankSampler(inverse=True,split=True,alpha=0.85)} & & & 76.18 & 2.16 & 7 \\ + \texttt{PageRankSampler(alpha=0.85)} & & & 76.47 & 2.08 & 8 \\ + \texttt{UniformSampler} & & & 76.18 & 4.50 & 9 \\ + \texttt{ObjFreqSampler(inverse=True,split=True)} & & & 75.88 & 4.01 & 10 \\ + \texttt{PageRankSampler(split=True,alpha=0.85)} & & & 74.71 & 1.71 & 11 \\ + \texttt{PageRankSampler(inverse=True,alpha=0.85)} & & & 74.41 & 1.50 & 12 \\ + \texttt{ObjFreqSampler(inverse=True)} & & & 73.53 & 2.79 & 13 \\ + \midrule + \texttt{WideSampler} & \multirow{13}{*}{2} & \multirow{13}{*}{250} & \textbf{77.35} & 1.99 & 1 \\ + \texttt{PredFreqSampler} & & & 76.18 & 3.14 & 2 \\ + \texttt{PageRankSampler(split=True,alpha=0.85)} & & & 75.88 & 1.50 & 3 \\ + \texttt{ObjFreqSampler(inverse=True,split=True)} & & & 75.88 & 3.03 & 4 \\ + \texttt{PageRankSampler(inverse=True,split=True,alpha=0.85)} & & & 75.88 & 5.06 & 5 \\ + \texttt{ObjFreqSampler(inverse=true)} & & & 75.59 & 1.99 & 6 \\ + \texttt{ObjFreqSampler} & & & 75.59 & 4.71 & 7 \\ + \texttt{ObjPredFreqSampler(inverse=True)} & & & 75.29 & 1.10 & 8 \\ + \texttt{UniformSampler} & & & 75.29 & 1.44 & 9 \\ + \texttt{ObjPredFreqSampler} & & & 75.29 & 2.35 & 10 \\ + \texttt{PageRankSampler(inverse=True,alpha=0.85)} & & & 75.00 & 2.46 & 11 \\ + \texttt{PageRankSampler(alpha=0.85)} & & & 74.12 & 1.99 & 12 \\ + \texttt{PredFreqSampler(inverse=True)} & & & 73.82 & 2.53 & 13 \\ + \midrule + \texttt{ObjFreqSampler} & \multirow{13}{*}{2} & \multirow{13}{*}{500} & \textbf{75.29} & 2.16 & 1 \\ + \texttt{PageRankSampler(alpha=0.85)} & & & 75.00 & 0.00 & 2 \\ + \texttt{WideSampler} & & & 74.71 & 1.10 & 3 \\ + \texttt{ObjFreqSampler(inverse=True,split=True)} & & & 74.71 & 3.14 & 4 \\ + \texttt{PageRankSampler(inverse=True,alpha=0.85)} & & & 74.12 & 2.56 & 5 \\ + \texttt{ObjPredFreqSampler(inverse=True)} & & & 73.82 & 2.53 & 6 \\ + \texttt{PageRankSampler(inverse=True,split=True,alpha=0.85)} & & & 73.82 & 2.16 & 7 \\ + \texttt{PageRankSampler(split=True,alpha=0.85)} & & & 73.82 & 2.53 & 8 \\ + \texttt{ObjPredFreqSampler} & & & 73.53 & 1.32 & 9 \\ + \texttt{UniformSampler} & & & 73.53 & 2.63 & 10 \\ + \texttt{PredFreqSampler} & & & 72.65 & 2.73 & 11 \\ + \texttt{ObjFreqSampler(inverse=True)} & & & 72.65 & 2.73 & 12 \\ + \texttt{PredFreqSampler(inverse=True)} & & & 72.35 & 1.95 & 13 \\ + \bottomrule + \end{tabular} + }% + \caption{Accuracy of Sampling Strategies for \texttt{MUTAG} (Part I).} + \label{tab:benchmarks:samplers:part:1} +\end{table} + +In Table \ref{tab:benchmarks:samplers:part:1}, for a maximum depth of walk of 2 with +a maximum number of walks of 250, \texttt{WideSampler} indicates the best +model's accuracy. In addition, the latter gives good precision models for a +maximum number of walks of 100 and 500. + + \begin{figure}[!ht] + \centering + \resizebox{0.9\textwidth}{!}{% + \begin{tikzpicture} + \begin{axis}[ + scale only axis, + grid=major, + grid style={dashed,gray!30}, + height=6cm, + width=9cm, + legend cell align={left}, + legend entries={ + \texttt{ObjFreqSampler(inverse=True,split=True)}, + \texttt{ObjFreqSampler(inverse=True)}, + \texttt{ObjFreqSampler}, + \texttt{ObjPredFreqSampler(inverse=True)}, + \texttt{ObjPredFreqSampler}, + \texttt{PageRankSampler(inverse=True,split=True,alpha=0.85)}, + \texttt{PageRankSampler(inverse=True,alpha=0.85)}, + \texttt{PageRankSampler(split=True,alpha=0.85)}, + \texttt{PageRankSampler(alpha=0.85)}, + \texttt{PredFreqSampler(inverse=True)}, + \texttt{PredFreqSampler}, + \texttt{UniformSampler}, + \texttt{WideSampler}, + }, + legend style={ + legend pos=outer north east, + font=\small + }, + ylabel={Accuracy}, + xlabel={Maximum Number of Walks per Entity}, + xtick={100,250,500}, + ytick={73,74,76,78}, + ] + + \addplot[medimumBlue,mark=diamond,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/samplers/max-depth/2/objfreq-inv-split.csv}; + \addplot[darkBlue,mark=square,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/samplers/max-depth/2/objfreq-inv.csv}; + \addplot[blue,mark=*,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/samplers/max-depth/2/objfreq.csv}; + + \addplot[darkRed,mark=square,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/samplers/max-depth/2/objpredfreq-inv.csv}; + \addplot[red,mark=*,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/samplers/max-depth/2/objpredfreq.csv}; + + \addplot[mediumGreen,mark=diamond,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/samplers/max-depth/2/pagerank-inv-split.csv}; + \addplot[darkGreen,mark=square,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/samplers/max-depth/2/pagerank-inv.csv}; + \addplot[yellow,mark=triangle,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma]{data/samplers/max-depth/2/pagerank-split.csv}; + \addplot[green,mark=*,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/samplers/max-depth/2/pagerank.csv}; + + \addplot[darkPurple,mark=square,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/samplers/max-depth/2/predfreq-inv.csv}; + \addplot[purple,mark=*,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/samplers/max-depth/2/predfreq.csv}; + + \addplot[brown,mark=*,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/samplers/max-depth/2/uniform.csv}; + \addplot[black,mark=*,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/samplers/max-depth/2/widesampler.csv}; + \end{axis} + \end{tikzpicture} + }% + \caption{Sampling Strategies for \texttt{MUTAG} According + to a Maximum Depth per Walk of 2.} + \label{fig:benchmarks:samplers:part:1} +\end{figure} + +In Figure \ref{fig:benchmarks:samplers:part:1}, the model's accuracy for the +different walking strategies is inversely proportional to the maximum number of +walks per entity. Moreover, \texttt{WideSampler} and \texttt{PredFreqSampler} +have two almost similar curves by their trajectory. + +\begin{table}[!ht] + \centering + \resizebox{0.94\textwidth}{!}{% + \begin{tabular}{lccS[table-format=2.2]@{${}\pm{}$}S[table-format=1.2]c} + \toprule + \textbf{Sampler} & \textbf{Max. Depth} & \textbf{Max. Walks} + & \multicolumn{2}{c}{\textbf{Accuracy} (\SI{}{\percent})} & \textbf{Rank} \\ + \midrule + \texttt{WideSampler} & \multirow{13}{*}{4} & \multirow{13}{*}{100} & \textbf{78.82} & 3.03 & 1 \\ + \texttt{PredFreqSampler(inverse=True)} & & & 78.24 & 2.53 & 2 \\ + \texttt{ObjPredFreqSampler} & & & 75.29 & 3.99 & 3 \\ + \texttt{PageRankSampler(inverse=True,alpha=0.85)} & & & 75.00 & 2.63 & 4 \\ + \texttt{PageRankSampler(split=True,alpha=0.85)} & & & 74.12 & 3.79 & 5 \\ + \texttt{ObjFreqSampler(inverse=True)} & & & 73.82 & 2.16 & 6 \\ + \texttt{PredFreqSampler} & & & 73.82 & 2.53 & 7 \\ + \texttt{UniformSampler} & & & 73.24 & 1.95 & 8 \\ + \texttt{ObjPredFreqSampler(inverse=True)} & & & 72.94 & 1.50 & 9 \\ + \texttt{PageRankSampler(inverse=True,split=True,alpha=0.85)} & & & 72.65 & 1.18 & 10 \\ + \texttt{ObjFreqSampler(inverse=True,split=True)} & & & 72.65 & 3.79 & 11 \\ + \texttt{PageRankSampler(alpha=0.85)} & & & 72.65 & 4.22 & 12 \\ + \texttt{ObjFreqSampler} & & & 69.12 & 5.73 & 13 \\ + \midrule + \texttt{ObjPredFreqSampler(inverse=True)} & \multirow{13}{*}{4} & \multirow{13}{*}{250} & \textbf{79.41} & 2.63 & 1 \\ + \texttt{ObjFreqSampler} & & & 78.53 & 2.56 & 2 \\ + \texttt{PageRankSampler(inverse=True,alpha=0.85)} & & & 77.06 & 2.56 & 3 \\ + \texttt{ObjFreqSampler(inverse=True)} & & & 76.18 & 3.14 & 4 \\ + \texttt{PageRankSampler(inverse=True,split=True,alpha=0.85)} & & & 75.59 & 2.88 & 5 \\ + \texttt{ObjFreqSampler(inverse=True,split=True)} & & & 75.59 & 1.76 & 6 \\ + \texttt{WideSampler} & & & 75.00 & 2.94 & 7 \\ + \texttt{PredFreqSampler(inverse=True)} & & & 74.71 & 2.85 & 8 \\ + \texttt{PredFreqSampler} & & & 74.41 & 2.73 & 9 \\ + \texttt{UniformSampler} & & & 74.41 & 2.56 & 10 \\ + \texttt{PageRankSampler(alpha=0.85)} & & & 73.53 & 2.28 & 11 \\ + \texttt{PageRankSampler(split=True,alpha=0.85)} & & & 71.18 & 2.39 & 12 \\ + \texttt{ObjPredFreqSampler} & & & 68.82 & 3.53 & 13 \\ + \midrule + \texttt{ObjPredFreqSampler(inverse=True)} & \multirow{13}{*}{4} & \multirow{13}{*}{500} & \textbf{77.94} & 0.93 & 1 \\ + \texttt{ObjFreqSampler(inverse=True)} & & & 77.65 & 1.95 & 2 \\ + \texttt{UniformSampler} & & & 77.35 & 1.18 & 3 \\ + \texttt{PageRankSampler(split=True,alpha=0.85)} & & & 77.35 & 2.73 & 4 \\ + \texttt{ObjPredFreqSampler} & & & 77.06 & 2.39 & 5 \\ + \texttt{ObjFreqSampler(inverse=True,split=True)} & & & 76.18 & 1.10 & 6 \\ + \texttt{PredFreqSampler} & & & 75.59 & 4.32 & 7 \\ + \texttt{PageRankSampler(alpha=0.85)} & & & 75.59 & 3.03 & 8 \\ + \texttt{PageRankSampler(inverse=True,split=True,alpha=0.85)} & & & 75.29 & 2.16 & 9 \\ + \texttt{PageRankSampler(inverse=True,alpha=0.85)} & & & 75.29 & 3.14 & 10 \\ + \texttt{WideSampler} & & & 74.41 & 2.20 & 11 \\ + \texttt{ObjFreqSampler} & & & 74.41 & 2.20 & 11 \\ + \texttt{PredFreqSampler(inverse=True)} & & & 74.12 & 4.12 & 12 \\ + \bottomrule + \end{tabular} + }% + \caption{Accuracy of Sampling Strategies for \texttt{MUTAG} (Part II).} + \label{tab:benchmarks:samplers:part:2} +\end{table} + +In Table \ref{tab:benchmarks:samplers:part:2}, for a maximum depth per walk of 4 +with a maximum number of walks of 100, \texttt{WideSampler} indicates the best +model's accuracy. However, the model's accuracy of \texttt{WideSampler} is +inversely proportional to the maximum number of walks per entity. + +\newpage + + \begin{figure}[!ht] + \centering + \resizebox{\textwidth}{!}{% + \begin{tikzpicture} + \begin{axis}[ + scale only axis, + grid=major, + grid style={dashed,gray!30}, + height=6cm, + width=9cm, + legend cell align={left}, + legend entries={ + \texttt{ObjFreqSampler(inverse=True,split=True)}, + \texttt{ObjFreqSampler(inverse=True)}, + \texttt{ObjFreqSampler}, + \texttt{ObjPredFreqSampler(inverse=True)}, + \texttt{ObjPredFreqSampler}, + \texttt{PageRankSampler(inverse=True,split=True,alpha=0.85)}, + \texttt{PageRankSampler(inverse=True,alpha=0.85)}, + \texttt{PageRankSampler(split=True,alpha=0.85)}, + \texttt{PageRankSampler(alpha=0.85)}, + \texttt{PredFreqSampler(inverse=True)}, + \texttt{PredFreqSampler}, + \texttt{UniformSampler}, + \texttt{WideSampler}, + }, + legend style={ + legend pos=outer north east, + font=\small + }, + ylabel={Accuracy}, + xlabel={Maximum Number of Walks per Entity}, + xtick={100,250,500}, + ytick={70,72,74,76,78} + ] + + \addplot[medimumBlue,mark=diamond,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/samplers/max-depth/4/objfreq-inv-split.csv}; + \addplot[darkBlue,mark=square,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/samplers/max-depth/4/objfreq-inv.csv}; + \addplot[blue,mark=*,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/samplers/max-depth/4/objfreq.csv}; + + \addplot[darkRed,mark=square,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/samplers/max-depth/4/objpredfreq-inv.csv}; + \addplot[red,mark=*,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/samplers/max-depth/4/objpredfreq.csv}; + + \addplot[mediumGreen,mark=diamond,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/samplers/max-depth/4/pagerank-inv-split.csv}; + \addplot[darkGreen,mark=square,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/samplers/max-depth/4/pagerank-inv.csv}; + \addplot[yellow,mark=triangle,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma]{data/samplers/max-depth/4/pagerank-split.csv}; + \addplot[green,mark=*,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/samplers/max-depth/4/pagerank.csv}; + + \addplot[darkPurple,mark=square,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/samplers/max-depth/4/predfreq-inv.csv}; + \addplot[purple,mark=*,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/samplers/max-depth/4/predfreq.csv}; + + \addplot[brown,mark=*,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/samplers/max-depth/4/uniform.csv}; + \addplot[black,mark=*,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/samplers/max-depth/4/widesampler.csv}; + \end{axis} + \end{tikzpicture} + }% + \caption{Sampling Strategies for \texttt{MUTAG} According + to a Maximum Depth per Walk of 4.} + \label{fig:benchmarks:samplers:part:2} +\end{figure} + +In Figure \ref{fig:benchmarks:samplers:part:2}, the model's accuracy for most of +the walking strategies is proportional to the maximum number of walks per +entity. + +\begin{table}[!ht] + \centering + \resizebox{0.85\textwidth}{!}{% + \begin{tabular}{lcc S[table-format=2.2]@{${}\pm{}$}S[table-format=1.2]c} + \toprule + \textbf{Sampler} & \textbf{Max. Depth} & \textbf{Max. Walks} + & \multicolumn{2}{c}{\textbf{Accuracy} (\SI{}{\percent})} & \textbf{Rank} \\ + \midrule + \texttt{PredFreqSampler} & \multirow{13}{*}{6} & \multirow{13}{*}{100} & \textbf{79.41} & 2.46 & 1 \\ + \texttt{PageRankSampler(split=True,alpha=0.85)} & & & 77.06 & 3.03 & 2 \\ + \texttt{ObjFreqSampler(inverse=True)} & & & 76.76 & 3.40 & 3 \\ + \texttt{WideSampler} & & & 76.76 & 3.40 & 3 \\ + \texttt{PageRankSampler(inverse=True,alpha=0.85)} & & & 76.76 & 3.88 & 4 \\ + \texttt{ObjFreqSampler} & & & 75.59 & 5.06 & 5 \\ + \texttt{ObjPredFreqSampler(inverse=True)} & & & 75.59 & 2.73 & 6 \\ + \texttt{PageRankSampler(inverse=True,split=True,alpha=0.85)} & & & 75.29 & 1.71 & 7 \\ + \texttt{PredFreqSampler(inverse=True)} & & & 75.29 & 1.71 & 8 \\ + \texttt{ObjFreqSampler(inverse=True,split=True)} & & & 74.12 & 3.03 & 9 \\ + \texttt{PageRankSampler(alpha=0.85)} & & & 73.53 & 3.35 & 10 \\ + \texttt{UniformSampler} & & & 73.24 & 3.77 & 11 \\ + \texttt{ObjPredFreqSampler} & & & 70.88 & 6.47 & 12 \\ + \midrule + \texttt{PageRankSampler(inverse=True,alpha=0.85)} & \multirow{13}{*}{6} & \multirow{13}{*}{250} & \textbf{80.00} & 1.50 & 1 \\ + \texttt{ObjFreqSampler(inverse=True,split=True)} & & & 78.53 & 3.17 & 2 \\ + \texttt{PredFreqSampler(inverse=True)} & & & 78.24 & 4.30 & 3 \\ + \texttt{ObjPredFreqSampler(inverse=True)} & & & 78.24 & 6.20 & 4 \\ + \texttt{PageRankSampler(alpha=0.85)} & & & 77.35 & 2.39 & 5 \\ + \texttt{PageRankSampler(inverse=True,split=True,alpha=0.85)} & & & 76.18 & 2.53 & 6 \\ + \texttt{ObjFreqSampler(inverse=True)} & & & 76.18 & 4.30 & 7 \\ + \texttt{UniformSampler} & & & 75.59 & 1.76 & 8 \\ + \texttt{PredFreqSampler} & & & 75.59 & 3.03 & 9 \\ + \texttt{ObjFreqSampler} & & & 75.00 & 2.08 & 10 \\ + \texttt{WideSampler} & & & 75.00 & 4.83 & 11 \\ + \texttt{ObjPredFreqSampler} & & & 73.24 & 4.78 & 12 \\ + \texttt{PageRankSampler(split=True,alpha=0.85)} & & & 72.65 & 2.56 & 13 \\ + \midrule + \texttt{PredFreqSampler} & \multirow{13}{*}{6} & \multirow{13}{*}{500} & \textbf{79.41} & 3.08 & 1 \\ + \texttt{ObjFreqSampler(inverse=True)} & & & 78.82 & 1.50 & 2 \\ + \texttt{WideSampler} & & & 78.53 & 1.18 & 3 \\ + \texttt{ObjFreqSampler} & & & 78.24 & 1.95 & 4 \\ + \texttt{PageRankSampler(inverse=True,split=True,alpha=0.85)} & & & 77.94 & 1.32 & 5 \\ + \texttt{UniformSampler} & & & 77.94 & 1.86 & 6 \\ + \texttt{PredFreqSampler(inverse=True)} & & & 77.35 & 1.50 & 7 \\ + \texttt{PageRankSampler(alpha=0.85)} & & & 77.35 & 1.50 & 7 \\ + \texttt{PageRankSampler(inverse=True,alpha=0.85)} & & & 77.35 & 1.99 & 8 \\ + \texttt{ObjPredFreqSampler} & & & 77.06 & 1.99 & 9 \\ + \texttt{PageRankSampler(split=True,alpha=0.85)} & & & 76.76 & 2.16 & 10 \\ + \texttt{ObjFreqSampler(inverse=True,split=True)} & & & 75.88 & 1.76 & 11 \\ + \texttt{ObjPredFreqSampler(inverse=True)} & & & 75.59 & 3.55 & 12 \\ + \bottomrule + \end{tabular} + }% + \caption{Accuracy of Sampling Strategies for MUTAG (Part III).} + \label{tab:benchmark:samplers:walks:part:3} +\end{table} + +In Table \ref{tab:benchmark:samplers:walks:part:3}, for a maximum depth of walk of 6 with +a maximum number of walks of 500, \texttt{WideSampler} indicates a good +model's accuracy. However, the latter indicates a poor model's accuracy for a +maximum number of walks of 500. + +\newpage + +\begin{figure}[!ht] + \centering + \resizebox{\textwidth}{!}{% + \begin{tikzpicture} + \begin{axis}[ + scale only axis, + grid=major, + grid style={dashed,gray!30}, + height=6cm, + width=9cm, + legend cell align={left}, + legend entries={ + \texttt{ObjFreqSampler(inverse=True,split=True)}, + \texttt{ObjFreqSampler(inverse=True)}, + \texttt{ObjFreqSampler}, + \texttt{ObjPredFreqSampler(inverse=True)}, + \texttt{ObjPredFreqSampler}, + \texttt{PageRankSampler(inverse=True,split=True,alpha=0.85)}, + \texttt{PageRankSampler(inverse=True,alpha=0.85)}, + \texttt{PageRankSampler(split=True,alpha=0.85)}, + \texttt{PageRankSampler(alpha=0.85)}, + \texttt{PredFreqSampler(inverse=True)}, + \texttt{PredFreqSampler}, + \texttt{UniformSampler}, + \texttt{WideSampler}, + }, + legend style={ + legend pos=outer north east, + font=\small + }, + ylabel={Accuracy}, + xlabel={Maximum Number of Walks per Entity}, + xtick={100,250,500}, + ytick={72,74,76,78,80} + ] + + \addplot[medimumBlue,mark=diamond,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/samplers/max-depth/6/objfreq-inv-split.csv}; + \addplot[darkBlue,mark=square,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/samplers/max-depth/6/objfreq-inv.csv}; + \addplot[blue,mark=*,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/samplers/max-depth/6/objfreq.csv}; + + \addplot[darkRed,mark=square,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/samplers/max-depth/6/objpredfreq-inv.csv}; + \addplot[red,mark=*,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/samplers/max-depth/6/objpredfreq.csv}; + + \addplot[mediumGreen,mark=diamond,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/samplers/max-depth/6/pagerank-inv-split.csv}; + \addplot[darkGreen,mark=square,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/samplers/max-depth/6/pagerank-inv.csv}; + \addplot[yellow,mark=triangle,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma]{data/samplers/max-depth/6/pagerank-split.csv}; + \addplot[green,mark=*,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/samplers/max-depth/6/pagerank.csv}; + + \addplot[darkPurple,mark=square,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/samplers/max-depth/6/predfreq-inv.csv}; + \addplot[purple,mark=*,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/samplers/max-depth/6/predfreq.csv}; + + \addplot[brown,mark=*,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/samplers/max-depth/6/uniform.csv}; + \addplot[black,mark=*,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/samplers/max-depth/6/widesampler.csv}; + \end{axis} + \end{tikzpicture} + }% + \caption{Sampling Strategies for \texttt{MUTAG} According + to a Maximum Depth per Walk of 6.} + \label{fig:benchmarks:samplers:part:3} +\end{figure} + +In Figure \ref{fig:benchmarks:samplers:part:3}, the curve of +\texttt{WideSampler} shows the same trajectory as \texttt{PredFreqSampler} and +\texttt{PageRankSampler(inverse=True,alpha=0.85)}. In addition, +\texttt{ObjPreqFreqSampler} is proportional to the maximum number of walks per +entity. + +\begin{table}[!ht] + \centering + \begin{tabular}{lc} + \toprule + \textbf{Sampler} & \textbf{Average Rank} \\ + \midrule + \texttt{WideSampler} & 1 \\ + \texttt{ObjPredFreqSampler(inverse=True)} & 2 \\ + \texttt{PredFreqSampler} & 3 \\ + \texttt{ObjFreqSampler} & 4 \\ + \texttt{ObjFreqSampler(inverse=True)} & 5 \\ + \texttt{PageRankSampler(inverse=True,alpha=0.85)} & 6 \\ + \texttt{PageRankSampler(inverse=True,split=True,alpha=0.85)} & 7 \\ + \texttt{ObjFreqSampler(inverse=True,split=True)} & 8 \\ + \texttt{PageRankSampler(split=True,alpha=0.85)} & 9 \\ + \texttt{PredFreqSampler(inverse=True)} & 10 \\ + \texttt{ObjPredFreqSampler} & 11 \\ + \texttt{UniformSampler} & 11 \\ + \texttt{PageRankSampler(alpha=0.85)} & 12 \\ + \bottomrule + \end{tabular} + \caption{Average Rank of the Sampling Strategies.} + \label{benchmark:samplers:average:rank} +\end{table} + +In Figure \ref{benchmark:samplers:average:rank}, \texttt{WideSampler} is the winning +sampler strategy in these benchmarks for \texttt{MUTAG}, followed by +\texttt{ObjPredFreqSampler(inverse=True)}, and \texttt{PredFreqSampler}. + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "../../master-thesis" +%%% End: diff --git a/src/benchmarks/walkers.tex b/src/benchmarks/walkers.tex new file mode 100644 index 0000000..225b025 --- /dev/null +++ b/src/benchmarks/walkers.tex @@ -0,0 +1,236 @@ + +\subsection{Walking Strategies} +\label{subsec:walkers} + +Each walking strategy is evaluated using \texttt{UniformSampler} as sampling strategy and +Word2Vec as embedding technique. For these benchmarks, Word2Vec keeps the same +hyperparameters as given in Section \ref{subsec:embedding:techniques}, namely +ten epochs, twenty negative words and a vector size of 500. + +\begin{table}[!ht] + \centering + \resizebox{\textwidth}{!}{% + \begin{tabular}{lccS[table-format=2.2]@{${}\pm{}$}S[table-format=1.2]c} + \toprule + \textbf{Walker} & \textbf{Max. Depth} & \textbf{Max. Walks} + & \multicolumn{2}{c}{\textbf{Accuracy} (\SI{}{\percent})} & \textbf{Rank} \\ + \midrule + \texttt{RandomWalker} & \multirow{6}{*}{2} & \multirow{6}{*}{250} & \textbf{77.94} & 2.08 & 1 \\ + \texttt{NGramWalker(grams=3)} & & & 76.47 & 1.32 & 2 \\ + \texttt{HALKWalker(freq\_threshold=0.01)} & & & 75.59 & 2.39 & 3 \\ + \texttt{SplitWalker} & & & 74.71 & 2.53 & 4 \\ + \texttt{WalkletWalker} & & & 72.06 & 1.32 & 5 \\ + \texttt{AnonymousWalker} & & & 65.29 & 1.76 & 6 \\ + \midrule + \texttt{HALKWalker(freq\_threshold=0.01)} & \multirow{6}{*}{4} & \multirow{6}{*}{250} & \textbf{78.82} & 1.50 & 1 \\ + \texttt{SplitWalker} & & & 77.35 & 4.01 & 2 \\ + \texttt{RandomWalker} & & & 76.76 & 6.06 & 3 \\ + \texttt{NGramWalker(grams=3)} & & & 75.88 & 3.90 & 4 \\ + \texttt{WalkletWalker} & & & 73.82 & 1.95 & 5 \\ + \texttt{AnonymousWalker} & & & 66.47 & 1.44 & 6 \\ + \midrule + \texttt{HALKWalker(freq\_threshold=0.01)} & \multirow{6}{*}{6} & \multirow{6}{*}{250} & \textbf{81.18} & 4.87 & 1 \\ + \texttt{SplitWalker} & & & 79.71 & 2.16 & 2 \\ + \texttt{NGramWalker(grams=3)} & & & 77.65 & 1.95 & 3 \\ + \texttt{RandomWalker} & & & 75.29 & 2.16 & 4 \\ + \texttt{WalkletWalker} & & & 71.76 & 1.10 & 5 \\ + \texttt{AnonymousWalker} & & & 67.65 & 1.86 & 6 \\ + \bottomrule + \end{tabular} + }% + \caption{Evaluation of the Accuracy of Walking Strategies for \texttt{MUTAG} According + to the Maximum Depth per Walk.} + \label{benchmarks:walkers:mutag:depth} +\end{table} + +In Table \ref{benchmarks:walkers:mutag:depth}, regardless of the maximum depth +per walk chosen for the same number of walks per entity, \texttt{HALKWalker} +indicates a model's accuracy above \texttt{SplitWalker}. However, these two +walking strategies provide better results for more significant maximum depths per +walk. While \texttt{RandomWalker} indicates a good model's accuracy for small maximum +depth per walk. + +\newpage + +\begin{figure}[!ht] + \centering + \resizebox{\textwidth}{!}{% + \begin{tikzpicture} + \begin{axis}[ + scale only axis, + grid=major, + grid style={dashed,gray!30}, + height=6cm, + width=9cm, + legend cell align={left}, + legend entries={ + \texttt{AnonymousWalker}, + \texttt{HALKWalker(freq\_threshold=0.01)}, + \texttt{NGramWalker(grams=3)}, + \texttt{RandomWalker}, + \texttt{SplitWalker}, + \texttt{WalkletWalker}, + }, + legend style={ + legend pos=outer north east, + font=\small + }, + ylabel={Accuracy}, + xlabel={Maximum Depth per Walk}, + xtick={2, 4, 6}, + ytick={65.30,67,71.80,73.80,76,78,79.70,81.20}, + ] + + \addplot[brown,mark=*,error bars/.cd, y dir=both, y explicit] + table[x=max_depth,y=accuracy,col sep=comma] {data/walkers/max-depth/anonymous.csv}; + \addplot[yellow,mark=*,error bars/.cd, y dir=both, y explicit] + table[x=max_depth,y=accuracy,col sep=comma] {data/walkers/max-depth/halk.csv}; + \addplot[blue,mark=*,error bars/.cd, y dir=both, y explicit] + table[x=max_depth,y=accuracy,col sep=comma] {data/walkers/max-depth/ngram.csv}; + \addplot[green,mark=*,error bars/.cd, y dir=both, y explicit] + table[x=max_depth,y=accuracy,col sep=comma] {data/walkers/max-depth/random.csv}; + \addplot[red,mark=*,error bars/.cd, y dir=both, y explicit] + table[x=max_depth,y=accuracy,col sep=comma] {data/walkers/max-depth/split.csv}; + \addplot[darkPurple,mark=*,error bars/.cd, y dir=both, y explicit] + table[x=max_depth,y=accuracy,col sep=comma] {data/walkers/max-depth/walklet.csv}; + \end{axis} + \end{tikzpicture} + }% + \caption{Evaluation of the Accuracy of Walking Strategies for MUTAG According to the Maximum Depth per Walk.} + \label{fig:benchmarks:walkers:depth} +\end{figure} + +In Figure \ref{fig:benchmarks:walkers:depth}, the curve of \texttt{SplitWalker} +and \texttt{HALKWalker} have an identical trajectory, except that +\texttt{HALKWalker} indicates better model's accuracy than +\texttt{SplitWalker}. In addition, they return better model's accuracy than the +other walking strategies. + +\begin{table}[!ht] + \centering + \resizebox{\textwidth}{!}{% + \begin{tabular}{lccS[table-format=2.2]@{${}\pm{}$}S[table-format=1.2]c} + \toprule + \textbf{Walker} & \textbf{Max. Depth} & \textbf{Max. Walks} + & \multicolumn{2}{c}{\textbf{Accuracy} (\SI{}{\percent})} & \textbf{Rank} \\ + \midrule + \texttt{SplitWalker} & \multirow{6}{*}{4} & \multirow{6}{*}{100} & \textbf{79.12} & 4.20 & 1 \\ + \texttt{HALKWalker(freq\_threshold=0.01)} & & & 77.65 & 2.53 & 2 \\ + \texttt{WalkletWalker} & & & 73.82 & 1.95 & 3 \\ + \texttt{RandomWalker} & & & 72.35 & 3.77 & 4 \\ + \texttt{NGramWalker(grams=3)} & & & 68.82 & 3.99 & 5 \\ + \texttt{AnonymousWalker} & & & 65.59 & 1.18 & 6 \\ + \midrule + \texttt{SplitWalker} & \multirow{6}{*}{4} & \multirow{6}{*}{250} & \textbf{77.35} & 2.56 & 1 \\ + \texttt{HALKWalker(freq\_threshold=0.01)} & & & 76.76 & 3.65 & 2 \\ + \texttt{RandomWalker} & & & 76.18 & 1.71 & 3 \\ + \texttt{NGramWalker(grams=3)} & & & 73.24 & 3.40 & 4 \\ + \texttt{WalkletWalker} & & & 71.76 & 1.10 & 5 \\ + \texttt{AnonymousWalker} & & & 66.76 & 1.18 & 6 \\ + \midrule + \texttt{HALKWalker(freq\_threshold=0.01)} & \multirow{6}{*}{4} & \multirow{6}{*}{500} & \textbf{79.12} & 3.99 & 1 \\ + \texttt{SplitWalker} & & & 77.35 & 1.50 & 2 \\ + \texttt{WalkletWalker} & & & 77.06 & 3.55 & 3 \\ + \texttt{RandomWalker} & & & 72.06 & 1.32 & 4 \\ + \texttt{NGramWalker(grams=3)} & & & 71.76 & 1.10 & 5 \\ + \texttt{AnonymousWalker} & & & 65.80 & 1.44 & 6 \\ + \bottomrule + \end{tabular} + }% + \caption{Evaluation of the Accuracy of Walking Strategies for \texttt{MUTAG} According + to the Maximum Number of Walks per Entity} + \label{tab:benchmarks:walkers:mutag:walks} +\end{table} + +In Table \ref{tab:benchmarks:walkers:mutag:walks}, regardless of the number of +walks chosen for the same maximum depth per walk, \texttt{SplitWalker} indicates +a correct model's accuracy above the average of walking +strategies. Specifically, \texttt{SplitWalker} allows an average model's +accuracy of \SI{78.53}{\percent}. + +\newpage + +\begin{figure}[!ht] + \centering + \resizebox{\textwidth}{!}{% + \begin{tikzpicture} + \begin{axis}[ + scale only axis, + grid=major, + grid style={dashed,gray!30}, + height=6cm, + width=9cm, + legend cell align={left}, + legend entries={ + \texttt{AnonymousWalker}, + \texttt{HALKWalker(freq\_threshold=0.01)}, + \texttt{NGramWalker(grams=3)}, + \texttt{RandomWalker}, + \texttt{SplitWalker}, + \texttt{WalkletWalker}, + }, + legend style={ + legend pos=outer north east, + font=\small + }, + ylabel={Accuracy}, + xlabel={Maximum Number of Walks per Entity}, + xtick={100,250,500}, + ytick={65.80,68.80,72,73.20,76,77.50,79.10}, + ] + + \addplot[brown,mark=*,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/walkers/max-walks/anonymous.csv}; + \addplot[yellow,mark=*,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/walkers/max-walks/halk.csv}; + \addplot[blue,mark=*,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/walkers/max-walks/ngram.csv}; + \addplot[green,mark=*,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/walkers/max-walks/random.csv}; + \addplot[red,mark=*,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/walkers/max-walks/split.csv}; + \addplot[darkPurple,mark=*,error bars/.cd, y dir=both, y explicit] + table[x=max_walk,y=accuracy,col sep=comma] {data/walkers/max-walks/walklet.csv}; + \end{axis} + \end{tikzpicture} + }% + \caption{Evaluation of the Walking Strategies for Different Data Sets + According to the Maximum Number of Walks per Entity.} + \label{fig:benchmarks:walkers:walks} +\end{figure} + +In Figure \ref{fig:benchmarks:walkers:walks}, the model's accuracy with +\texttt{SplitWalker} tends to stay around \SI{77}{\percent} after a maximum +number of walks of 250. In addition, \texttt{AnonymousWalker}, +\texttt{NGramWalker}, and \texttt{RandomWalker} follow the same curve +trajectory. Specifically, they have a peak of accuracy at a maximum number of +walks per entity of 250. In contrast, the other walking strategies have a +decrease of model's accuracy at this stage. + +\begin{table}[!ht] + \centering + \begin{tabular}{lc} + \toprule + \textbf{Walker} & \textbf{Average Rank} \\ + \midrule + \texttt{HALKWalker(freq\_threshold=0.01)} & 1 \\ + \texttt{SplitWalker} & 2 \\ + \texttt{RandomWalker} & 3 \\ + \texttt{NGramWalker(grams=3)} & 4 \\ + \texttt{WalkletWalker} & 5 \\ + \texttt{AnonymousWalker} & 6 \\ + \bottomrule + \end{tabular} + \caption{Evaluation of the Average Rank of the Walking Strategies.} + \label{tab:benchmark:walkers:average:rank} +\end{table} + +In Figure \ref{tab:benchmark:walkers:average:rank}, +\texttt{HALKWalker(freq\_threshold=0.01)} is the winning walking strategy in +these benchmarks for \texttt{MUTAG}, followed by \texttt{SplitWalker}, and +\texttt{RandomWalker}. + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "../../master-thesis" +%%% End: diff --git a/src/conclusion.tex b/src/conclusion.tex new file mode 100644 index 0000000..af40ba1 --- /dev/null +++ b/src/conclusion.tex @@ -0,0 +1,116 @@ + +\chapter{Conclusion} +\label{chap:conclusion} + +RDF is a W3C standard that ensures that the data diversity remains +machine-interpretable by encoding the semantics of these data. Semantic Web and +Linked Open Data use this standard by interconnecting several sources using KGs, +which are directed heterogeneous multigraphs composed of triples. Afterward, +this type of graph is converted into a numerical vector and used for downstream +ML tasks. + +This conversion can be done with RDF2Vec, an unsupervised task-agnostic +algorithm for numerically representing KG nodes. Since 2016, this algorithm has +provided good results using Word2Vec, an embedding technique initially used in +the NLP field. However, the NLP field has made other advances, notably related +to the Attention mechanism published in 2014 by \textsc{Bahdanau} to solve the +bottleneck problem of RNNs. Due to this mechanism, the Transformer architecture +published in 2017 by \textsc{Vaswani} et al. was an alternative to RNNs, +introducing two new Attention mechanisms: Scaled Dot-Product Attention and +Multi-Head Attention. This architecture led to the creation of BERT, a +state-of-the-art NLP embedding technique published in 2018. + +Unlike Word2Vec, BERT allows generating contextualized embeddings using +bidirectional representations. For this purpose, BERT can receive one or two +sentences which the WordPiece algorithm will then tokenize. WordPiece allows +BERT, on the one hand, to learn common sub-words and, on the other hand, not to +replace OOV words with a special token, being a rich source of information. Once +the text corpus is tokenized, the BERT model is pre-trained using MLM and NSP as +two unsupervised tasks. This pre-training is useful to mainly help overcome the +lack of training data and allow the model to understand better a bidirectional +representation of an input at the sentence and token level. + +The objectives of this Master's thesis were to evaluate BERT with Word2Vec and +FastText and extend RDF2Vec to a new walking strategy and sampling +strategy. Such an evaluation is essential because few research papers have +compared the classical BERT model with other embedding techniques. In addition, +the minor use made of BERT with the KGs is done by creating one of its dedicated +variances. Finally, creating new strategies allows improving the accuracy of a +model for specific use-cases by focusing on extracting walks from a KG. + +In order to evaluate BERT with FastText and Word2Vec on KGs, a dedicated +implementation has been proposed. For BERT, it was not possible to use a +pre-trained model and, therefore, necessary to create this model from +scratch. For this purpose, the creation of the vocabulary of this new model +included each special token and the nodes extracted from the walks by a walking +strategy and a sampling strategy. For the training of BERT, it was first useful +to tokenize the nodes by adding special tokens to the left and right of each +node. Then, the pre-training focused only on the MLM since the NSP is of no +interest since each walk has no semantic links with a second one. Finally, the +training was done on a data collator dedicated to MLM, and a set of +hyperparameters was provided, finding a compromise between training time and +model accuracy. + +BERT's evaluation on \texttt{MUTAG} indicated a training time ranging from 25 +minutes to several hours and a generally lower model accuracy than Word2Vec and +FastText. These results showed that the model's accuracy is proportional to the +maximum depth per walk and the maximum number of walks. Except for rare cases, +the use of this BERT model for KGs is not significant enough. The main reason +being its training time which can be excessively long with results similar to +Word2Vec and FastText. + +This Master's thesis proposed \texttt{SplitWalker} as a new walking +strategy. Its principle is based on the decomposition of nodes according to a +splitting function provided by the user. By default, \texttt{SplitWalker} splits +each node according to its symbols, capital letters, and numbers. When comparing +this strategy to others with \texttt{MUTAG}, the average rank of the walking +strategies shows \texttt{SplitWalker} in second place, behind +\texttt{HALKWalker}. However, a better splitting function could probably have +improved these results even more. + +In addition, a new sampling strategy has been introduced, namely +\texttt{WideSampler}. This strategy mimics the classification of objects by +humans, favoring as much as possible the common features between the +objects. More precisely, \texttt{WideSampler} tends to favor the most frequent +hops in a KG and those that allow access to more nodes. Moreover, its evaluation +with \texttt{MUTAG} gives a good model accuracy, allowing it to finish first in +the benchmarks' average. Added to that, it is likely that \texttt{WideSampler} +has more impact on larger KGs. + +Within this work, it was proposed to improve Word2Vec by extracting the parent +and child nodes of a root node on the one hand and focusing the positioning of +this root node within the walks. These recommendations can bring more contexts +to the root node and improve its frequency of occurrence within the samples +training. From then on, a better quality generation of root node embeddings. + +This Master's thesis had some internal problems that resulted in missing +benchmarks. These problems were related to the IDLab servers used. Their Stardog +infrastructure generated significant variants during the benchmarks. More +precisely, the version of Stardog used had a problem with the garbage collector, +which prevented the correct memory deallocation. In addition, some benchmarks +had exceptions thrown due to SPARQL endpoint not being available. This +unavailability being due to updates and internal problems with the servers. + +It was discussed the results obtained. The research papers using BERT pretended +that the classical BERT model was not interesting with KGs. One of the reasons +for this is that BERT is limited by its inputs and its architecture is not +optimized to be used for KGs. Most of the research papers have developed their +variant of BERT, which can be simple or complex. At most simple, some variants +have replaced the softmax activation function with a sigmoid activation +function. The traditional BERT model was only a tiny part of a more significant +architecture at the most complex. + +Research directions for future work have been proposed. Firstly it was +recommended to evaluate \texttt{SplitWalker} and \texttt{WideSampler} for larger +KGs to know more about their impact. Added to this, the traditional BERT model +with larger KGs reinforces the idea that its use is limited. However, another +test would be not to inject pairs of different walks, but rather pairs of +\texttt{(subject, object)} 2-tuple to let BERT deduce the predicate. It was said +that it would also be possible to compare Word2Vec and Fast to other BERT +variants to know their impact better. In case of bad results, there is also the +possibility to create a new BERT variant. + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "../report" +%%% End: diff --git a/src/discussion.tex b/src/discussion.tex new file mode 100644 index 0000000..4b8ae05 --- /dev/null +++ b/src/discussion.tex @@ -0,0 +1,156 @@ + +\chapter{Discussion} +\label{chap:discussion} + +The results obtained with BERT are less conclusive than those expected. Creating +a BERT model requires considerable time, taking at least several hours or days +of training. In addition, BERT has a lower accuracy than Word2Vec and FastText +and needs to be re-trained for each KG, making its use not pragmatic. However, +this evaluation does not mean that the use of BERT should be prohibited. Within +this report, the research focused on three main fields: +\begin{enumerate} +\item the walks extraction from a KG; +\item the implementation of the BERT model for \texttt{pyRDF2Vec}; +\item the fine-tuning of BERT. +\end{enumerate} + +The research papers referred to in Section \ref{section:related:work:bert} are +related to the implementation of BERT within KGs. However, most of them needed +to create a new architecture that bears few or many changes compared to +BERT. Therefore, it is interesting to examine the creation of these +architectures. + +\section{BERT's Architecture} +\label{sec:discussion:architecture} + +Understanding the implementation of the BERT variant architecture in the +research papers would provide insight into the causes of the inconclusive +results obtained. + +\subsection{KG-BERT} +\label{chap:discussion:kg-bert} + +KG-BERT completes a KG by predicting missing tuples based on other existing +tuples. The design of this architecture has the particularity that BERT can be +trained based on extracted triples. For this training purpose, each triple +injection consists of taking either the name or the description of their +nodes. In this way, KG-BERT considers every node as a word. However, KG-BERT +proposes two ways to inject these triples: +\begin{enumerate} +\item by varying the relevance of a relation using noise to train BERT to deduce +the plausibility of this relation; +\item by using pairs of entities to train BERT to deduce the relation between +these pairs of entities. +\end{enumerate} + +Based on this idea, this Master's thesis also tested BERT again on MUTAG and +BGs. However, the results were still not more conclusive than those of Word2Vec +and FastText. Looking at the +KG-BERT\footnote{\url{https://github.com/yao8839836/kg-bert}} implementation in +more detail, the latter uses a sigmoid function to calculate the triple score +instead of the original BERT softmax function. In addition, KG-BERT has adapted +its cross-entropy loss computation by mainly considering the triple +labels. These adjustments likely played an essential role in the success of +KG-BERT. However, this BERT variant has not been compared with Word2Vec and uses +other datasets than those used for this Master's thesis. + +\subsection{BERT-INT} +\label{subsec:discussion:bert-int} + +BERT-INT predicts two identical entities across multiple KGs by using the name +or description of the current entities, but this time, also of those of their +neighbors. Since there is no propagation of information within neighboring +entities, BERT-INT has the particularity to ignore the characteristic structure +of the KGs. + +Unlike KG-BERT, which has minor modifications compared to the BERT model, +BERT-INT uses BERT as a basic representation unit. Specifically, BERT is used to +generate embeddings of the entity name and description and their attributes, +including values. From then on, the BERT-INT architecture combines several BERT +units using a pairwise margin loss to fine-tune the resulting BERT interaction +model. As a result, the BERT-INT architecture is more consistent. The resulting +model consists of the name/description-view interaction plus the ones from the +neighbor-view and the attribute-view. + +\subsection{Graph-BERT} +\label{sec:discussion:graph-bert} + +Graph-BERT mainly helps with node classification and graph clustering tasks. The +main feature of this variant BERT is that it relies solely on the Attention +mechanism, without the necessity to use graph convolution or aggregation +operations. To train the model, Graph-BERT uses unbound subgraphs sampled in +their local contexts to avoid the use of KGs, which can be immense. For this +purpose, there is an injection of sampled nodes and their local context into the +model, which is then refined for the corresponding task. Finally, The +Graph-BERT architecture is composed of five parts: +\begin{multicols}{2} +\begin{enumerate} +\item a linkless subgraph batching; +\item the node input vector embeddings; +\item a graph transformer-based encoder; +\item a representation fusion; +\item a functional component that generates different output according to the + target application task. +\end{enumerate} +\end{multicols} + +\noindent Each of these parts plays an important role in the success of +Graph-BERT. In addition, this variant also uses BERT as a small part of its +architecture. + +\subsection{K-BERT} +\label{subsec:discussion:k-bert} + +With Graph-BERT, K-BERT has one of the most advanced architectures compared to +other BERT variants related to KG. The latter uses four modules: +\begin{enumerate} +\item Knowledge layer: injects relevant triples from a KG, converting the +original sentence into a knowledge-rich sentence tree. +\item Embedding layer: convert a phrase tree into an embedding representation as +the basic BERT architecture can do, except that the embedding layer is a +sentence tree instead of a sequence of tokens. +\item Seeing layer: uses a visible matrix to restrict the visible area of each +token. This restriction ensures that an excess of knowledge does not lead to +changes in the meaning of the original sentence. According to the authors, this +layer is an integral part of the K-BERT success. +\item Mask-Transformer layer: allows BERT to receive the visible matrix as input +using a multiple block stack of mask self-attention blocks.: +\end{enumerate} + +\noindent Even if there are similarities with BERT, K-BERT gets its good +performance to a more advanced architecture than the one initially presented by +BERT. + +\section{Future Works} +\label{sec:discussion:futur} + +From the set of architectures of the KG-oriented BERT variants stated above, +KG-BERT is the one that keeps an almost similar architecture to the basic BERT +architecture. Creating such a variant reinforces the idea that +applying the BERT model to a KG without modifying its architecture is probably +not interesting. This Master's thesis focused on only injecting pairs of walks +to BERT. Probably injecting subject/object pairs as KG-BERT does to train BERT +to predict predicates would lead to better results. However, given the lack of +context and a non-suitable internal architecture, it is likely that the +traditional BERT model would not be sufficient to have a clear improvement of +model accuracy compared to Word2Vec. In particular, if Word2Vec uses the +recommendations made by this Master's thesis to include the root node in more +training samples. + +As the objective of this Master's thesis was to evaluate BERT, no new variants +have been implemented. Such an implementation would probably be more suitable +for a PhD degree where more research time is allocated. However, this report has +the privileges to closes several bad leads. It has allowed understanding better +where its success comes from for its few evaluations within KGs. Added to that, +none of these papers have evaluated their version of BERT with Word2Vec. Various +possibilities for future work around this remain open such as evaluating the +previously stated KG-oriented BERT models with Word2Vec and other embedding +techniques. In addition, there is nothing to prevent the recreation of a new +BERT architecture for KGs if this proves necessary in the long run. Finally, it +may be interesting to evaluate \texttt{SplitWalker} and \texttt{WideSampler} on +larger KGs and to know their impact compared to other strategies. + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "../report" +%%% End: diff --git a/src/embedders.tex b/src/embedders.tex new file mode 100644 index 0000000..a79a221 --- /dev/null +++ b/src/embedders.tex @@ -0,0 +1,15 @@ + +\chapter{Embedding Techniques} +\label{chap:embedding:techniques} + +This chapter explains the Word2Vec, FastText, and Bidirectional Encoder +Representations from Transformers (BERT) embedding techniques. + +\input{src/embedders/word2vec} +\input{src/embedders/fasttext} +\input{src/embedders/bert} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "../report" +%%% End: diff --git a/src/embedders/bert.tex b/src/embedders/bert.tex new file mode 100644 index 0000000..e2d44bc --- /dev/null +++ b/src/embedders/bert.tex @@ -0,0 +1,244 @@ + +\newpage + +\section{BERT} +\label{sec:bert} + +Bidirectional Encoder Representations from Transformers (BERT) is a +state-of-the-art NLP embedding technique published in 2018. BERT relies on the +encoder part of the Transformer and whose objective is to generate an +unsupervised language representation model. Unlike Word2Vec, the embeddings +generated by BERT are contextualized using bidirectional representations. In the +original paper, two pre-trained BERT models trained on the English Wikipedia +(\SI{2500}{M} words) and the Toronto BookCorpus (\SI{800}{M} words) are +available: +\begin{enumerate} +\item \textbf{BERT-Base}: 12-layer Transformer, 768-hidden, 12-heads, \SI{110}{M} parameters. +\item \textbf{BERT-Large}: 24-layer Transformer, 1024-hidden, 16-heads, \SI{340}{M} parameters. +\end{enumerate} + +Since these models are pre-trained based on a corpus, their use fixes the +learning vocabulary. From then on, as Word2Vec and FastText, BERT could face the +presence of OOV words. As a result of these unknown words, BERT uses an adaptive +tokenization algorithm. + +\subsection{Tokenization} +\label{subsec:tokenization} + +BERT uses a WordPiece tokenization algorithm for the pre-training of a +model. This tokenization proposed in 2015 by Google takes its main advantage to +not replace unknown words with a \texttt{[UNK]} special token, which implies a +loss of information about the input sequence. As an alternative to this +conversion, WordPiece uses a segmentation method which breaks down a word into +several word pieces units prefixed by \texttt{\#\#}\footnote{Except for Chinese +characters, which are surrounded by spaces before any tokenization.} and +converted into unique identifiers. From then on, this algorithm allows BERT to +learn common sub-words and does not considers OOV and rares words. As for the +vocabulary ($\simeq$ \SI{30 000}{words}), the latter is initializing itself by +taking the individual characters of a language, and adding the most frequent +combinations\footnote{For example, ``u'', followed by ``g'', would have only +been merged if the probability of ``ug'' divided by ``u'', ``g'' would have been +greater than for any other symbol pair.} of a corpus. + +\begin{table}[!ht] + \centering + \caption{Example of Tokenization With BERT.} + \label{tab:bert:tokenization} + \begin{tabular}{cccccccccc} + & The & machine & loves & embeddings. & & & & & \\ + \texttt{[CLS]} & the & machine & loves & em & \#\#bed & \#\#ding & \#\#s & . & \texttt{[SEP]} \\ + 101 & 1996 & 3698 & 7459 & 7861 & 8270 & 4667 & 2015 & 1012 & 102 \\ + \end{tabular} +\end{table} + +In Table \ref{tab:bert:tokenization}, the input sequence of BERT allows +receiving either one sentence (e.g., for text classification) or two sentences +(e.g., for question answering) where each of them is limited to 512 +characters. Beyond this limit, it is necessary to truncate the +sentence. Finally, WordPiece uses three main special tokens: +\begin{enumerate} +\item \texttt{[CLS]}: classification token inserted at the beginning of the + input used for prediction. +\item \texttt{[SEP]}: separator token used to indicates the end of each sentence; +\item \texttt{[PAD]}: padding token used when batching sequences of different lengths. +\end{enumerate} + +\subsection{Input Embeddings} +\label{subsec:bert:input:embeddings} + +Unlike Transformer, BERT accepts one or two sentences as input sentences. From +then on, BERT encodes these inputs to use them for the model pre-training. + +\newpage + +\begin{figure}[!ht] + \centering + \includegraphics[width=\textwidth]{img/embedders/bert/input-embeddings} + \caption{Example of Sentence Pair Encodding.} + \source{\textsc{Devlin} et al. -- BERT} + \label{fig:sentence:pair:encoding} +\end{figure} + +In Figure \ref{fig:sentence:pair:encoding}, the encoding of the BERT's input +requires the sum of three vector embeddings: +\begin{enumerate} +\item \textbf{Token embeddings}: the word pieces embeddings (cf. Section +\ref{subsec:tokenization}). +\item \textbf{Segment embeddings}: the embeddings that associate a token with +its belonging sentence. In the case of a single sentence input sequence, the +vector contains only unitary values. Otherwise, the \texttt{[SEP]} token and the +tokens related to the first sentence are assigned a zero value. Those tokens of +the second sentence are assigned a unitary value. +\item \textbf{Position embeddings}: embeddings that preserve the contextual +information of the tokens by injecting their positioning into the input +embeddings, as the Transformer architecture does. +\end{enumerate} + +\subsection{Pre-training} +\label{subsec:bert:pre-training} + + +The BERT model's pre-training gives it the ability to learn language by training +simultaneously on two unsupervised tasks: the \emph{Masked Language Model} (MLM) +and \emph{Next Sentence Prediction} (NSP). These two tasks mainly help overcome +the lack of training data and allow the model to understand better a +bidirectional representation of an input at the sentence and token level. + +\subsubsection{Masked Language Model} +\label{subsubsec:bert:mlm} + +MLM is the first task use by the pre-training BERT model. This task helps BERT +learn bidirectional contextual representations of tokens through the encoder +layers by predicting masked tokens from the input sequence. For this purpose, +MLM masks and predicts tokens from the input sequence. Mathematically, the +following equation defines this prediction of masked tokens. + +\begin{equation} + p\left(x_1,\dotsc,x_n\right) = \sum_{i = 1}^np\left(x_i|x_1,\dotsc,x_{i - 1}, x_{i + 1},\dotsc, x_n\right) +\label{eq:def:mlm} +\end{equation} + +where each input sequence generally has \SI{15}{\percent} of its tokens hidden +according to the following subrules: +\begin{itemize} +\item a token is replaced by a \texttt{[MASK]} token in \SI{80}{\percent} of the + cases; +\item a token is replaced randomly in \SI{10}{\percent} of the cases; +\item a token remains unchanged in \SI{10}{\percent} of the cases. +\end{itemize} + +These subrules prevent the Transformer encoder from being forced to maintain a +distributive contextual representation of each input token. From then on, it is +not recommended to modify the default token masking. Too little masking would +imply a too expensive model to train, and too much masking would mean a lack of +context for a token. + +\subsubsection{Next Sentence Prediction} +\label{subsubsec:bert:nsp} + +The NSP is the second task use by the pre-training BERT model. This task helps +BERT learn sentence relationships by solving a binary classification problem +using Attention information shared between sentences. +\begin{table}[!ht] + \centering + \caption{Example of NSP With BERT.} + \label{tab:bert:nsp} + \begin{tabular}{lll} + \textbf{Sentence $\mathcal{A}$} & \textbf{Sentence $\mathcal{B}$} & \textbf{Label} \\ + GNU Emacs is the best text editor. & I should use it. & \texttt{isNextSentence} \\ + GNU Emacs is the best text editor. & I have a cat. & \texttt{NotNextSentence} \\ + \end{tabular} +\end{table} + +In Table \ref{tab:bert:nsp}, NSP allows the model to train itself to predict +whether sentence $\mathcal{B}$ is a continuation of sentence $\mathcal{A}$. For +this purpose, the generation of the input sequences ensures continuity of +$\mathcal{A}$ \SI{50}{\percent} of the time, labeled as \texttt{isNext}. The +rest of the time, $\mathcal{B}$ is related to a random sentence from the +provided training data set, labeled as \texttt{NotNextSentence}. + +\subsubsection{Output} +\label{subsubsec:output} + +Once the BERT model understands the language representation, this model is +suitable for most NLP tasks. These tasks include Neural Machine Translation, +question answering, sentiment analysis, and text summarization. +\begin{figure}[!ht] + \centering + \includegraphics[width=0.6\textwidth]{img/embedders/bert/pre-training} + \caption{Pre-Training With BERT.} + \source{\textsc{Devlin} et al. -- BERT} + \label{fig:pre-training} +\end{figure} + +In Figure \ref{fig:pre-training}, BERT produces the hidden states of each input +token where each hidden state consists of a vector of the same size (e.g., 768 +for BERT-Base) as the others, containing float numbers. Among these hidden +states, the first position is related to the hidden state of the token +\texttt{[CLS]}. This hidden state is interesting as it determines the continuity +of two sentences, which can later be used for fine-tuning tasks. + +Furthermore, the hidden states pass through a last FFN containing as many +neurons as tokens in the vocabulary used. The pre-training phase ends by +obtaining probability distribution on the hidden states using a softmax +activation function at the output of this FFN. Finally, BERT compares the +distribution of the current one-hot encoded vector token with the predicted word +and train the network using cross-entropy. It is important to note that the loss +only considers the prediction of masked tokens produced by the network to raise +awareness of the context during the network's training. + +\subsection{Fine-Tuning} +\label{subsec:bert:fine-tuning} + +The fine-tuning consists of training the BERT model on a specific NLP +task. Depending on the use case, either the final hidden state of the +\texttt{[CLS]} token or the hidden of the other tokens will be taken. The former +is use for classification-related tasks and the latter for more complex tasks +such as the Stanford Question Answering Dataset (SQuAD), Named Entity +Recognition (NER), and Multi-Genre Natural Language Inference (MNLI). +\begin{figure}[!ht] + \centering + \includegraphics[width=0.7\textwidth]{img/embedders/bert/fine-tuning} + \caption{Fine-Tuning for SQuAD.} + \source{\textsc{Devlin} et al. -- BERT} + \label{fig:bert:fine-tuning} +\end{figure} + +In Figure \ref{fig:bert:fine-tuning}, the fine-tuning of the model for SQuAD +takes as input sequence a question and a paragraph containing the answer to this +question. Regarding the model's output for this NLP task, BERT returns the +answer to a submitted question. For this purpose, BERT highlights the starting +and ending word of a given paragraph that includes the answer to that question +only if that answer is in the paragraph. Therefore, it is interesting to look at +the probability that a word is the start/end of the answer span. + +\begin{definition}[Word Probability -- Start/End of the Answer Span] + Let $S \in \mathbb{R}^H$ be the start vector, $E \in \mathbb{R}^H$ be the end + vector, $T_i \in \mathbb{R}^H$ be the final hidden vector for the + i\textsuperscript{th} input token, and $j$ be the position of the ending + word. Mathematically, the following two equations represent the probability that + the word $i$ is the start/end of the answer span. + \begin{equation} + \mathrm{PS_i} = \frac{e^{ST_i}}{\sum_je^{ST_j}} \qquad \mathrm{PE_i} = \frac{e^{ET_i}}{\sum_je^{ET_j}} + \label{eq:def:bert:word:probabilities} + \end{equation} + + where the sum of $ST_i$ and $ET_j$ defines the score of a candidate span from + position $i$ to position $j$. Afterward, the maximum scoring span where $j \geq + i$ is used as a prediction. + \label{def:squad:word:probability} +\end{definition} + +The starting and ending tokens containing the answer are determined using the +softmax activation function on the dot product between the output embeddings and +the set of weights. From then on, the word with the highest probability is +assigned as the start word, and the process continues to iterate to determine +the end word. As most hyperparameters are similar to those of the pre-training, +the only new hyperparameters added during the fine-tuning concern a +classification layer. From then on, an exhaustive search of values can be done +to choose the best model according to these hyperparameters. + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "../../report" +%%% End: diff --git a/src/embedders/fasttext.tex b/src/embedders/fasttext.tex new file mode 100644 index 0000000..a594781 --- /dev/null +++ b/src/embedders/fasttext.tex @@ -0,0 +1,146 @@ + +\section{FastText} +\label{sec:fasttext} + +FastText is an extension to Word2Vec created by Facebook in 2016, based on the +decomposition of a word into character $n$-grams to improve the embeddings +obtained by an SG model. Unlike Word2Vec, which treats each word in a corpus as +an atomic entity, the decomposition made by FastText mainly solves the +embeddings creation for OOV words and parameter sharing between words of the +same radical. Finally, FastText can be used for unsupervised learning and +supervised learning with text classification for tasks such as spam filtering. + +\subsection{Sub-Word Generation} +\label{subsec:fasttext:sub-word} + +The generation of sub-words called $n$-grams is an integral part of the success +of FastText. Therefore, it is good to know the details of such a generation. + +\begin{definition}[Sub-word Generation] + Consists of adding angular brackets on either side of a word used as a + delimiter and generating character $n$-grams of length $n$. In practice, picking + this length allows extraction of $n$-grams $\geq$ 3 and $\geq + 6$~\citep{DBLP:journals/tacl/BojanowskiGJM17}. Let ``flying'' be a word. The + following table illustrates the sub-word generation for character $n$-grams of + length 3, 4, 5, and 6. + + \begin{table}[!ht] + \centering + \caption{Sub-word Generation for Character $N$-Grams of Length 3, 4, 5, and 6.} + \label{tab:fasttext:sub-word} + \begin{tabular}{ccl} + \toprule + \textbf{Word} & \textbf{Length} & \textbf{Character $n$-grams} \\ + \midrule + \multirow{4}{*}{flying} & 3 & \\ + & 4 & \\ + & 5 & \\ + & 6 & \\ + \bottomrule + \end{tabular} + \end{table} + + In Table \ref{tab:fasttext:sub-word}, each character $n$-grams of length $n$ + is generated by sliding a 2-characters window from the beginning of the bracket + to its end. + \label{def:sub-word:generation} +\end{definition} + +As a result, the vector of a word corresponds to the sum of these $n$-grams of +characters. This word decomposition into character $n$-grams comes at a storage +cost since storing all the unique $n$-grams can quickly be significant. The +original paper uses a variant of the Fowler-Noll-Vo (FNV) hash function, called +\emph{FNV-1a}, to hash character sequences into integer values to reduce this +memory cost. The use of FNV is helpful for this use case since FNV was not +designed for cryptography but for the fast use of hash tables and +\emph{checksums}. The checksum results of performing a cryptographic hash +function on a piece of data, usually a file, to ensure that the data is +authentic and error-free. Moreover, it is necessary to learn a certain amount of +embeddings to hash character sequences. Specifically, this amount designates the +hash bucket's size to better distribute these character $n$-grams for sorting +and retrieval purposes. From then on, the hashing of each $n$-gram to a number +between one and $N$, reduces the vocabulary size in the counterpart of potential +\emph{collisions}. This hash collision means that several character $n-grams$ +stored as a key can result in the same hash and checksum. Therefore no longer +ensure the authenticity of a value. + +In some circumstances, the model size may be excessive. In this case, it is +still possible to reduce the hash size where the appropriate value is near +$20000$. However, it is also possible to reduce the size of the vectors at the +expense of smaller model accuracy. + +\subsection{Training} +\label{subsec:fasttext:training} + +Like Word2Vec, the training of FastText’s SG model can use HSM or Negative +sampling. To better understand its application with negative sampling, one can +take the following ``I always remember her'' sentence is taken. Let ``remember'' +be the target word, using 3-grams and a window size of 3. This example predicts +the ``always'' and ``her'' context words. First of all, this model computes the +embeddings of the target word by summing the embeddings for the character +$n$-grams and the whole word itself: +\begin{align} + \mathrm{E}_{remember} = e_{} + e_{remember} + \label{eq:fasttext:embeddings} +\end{align} + +Afterward, each context word is taken directly from their embeddings without +adding the character $n$-grams. Then, several random negative samples are selected +with a probability proportional to the square root of the unigram +frequency. From then on, a context word is related to five random negative +words. In the absence of $n$-gram embeddings, the Word2Vec model is used, +specifying a maximum $n$-gram length of zero. + +After selecting samples, the dot product between the target word and the actual +context words computes the probability distribution. Unlike Word2Vec, there is +this time use of the sigmoid function instead of the softmax function. Finally, +the embeddings are updated with an SGD optimizer according to the calculated +loss to bring the actual context words closer to the target word. Afterward, +there is an incrementation in the distance of the negative samples. + +This update of hyper-parameters for embeddings of $n$-grams adds a significant +amount of extra computation to the training process. Moreover, CBOW generates +the word embeddings by summing and averaging $n$-grams embeddings, which adds cost +compared to SG. However, these additional calculations benefit from a set of +embeddings containing the sub-words embeddings. From then on, they allow a +better accuracy of a model in most cases. + +\subsection{Advantages and Disadvantages} +\label{subsec:fasttext:pro:cons} + +In a non-exhaustive way, the advantages of the FastText: +\begin{multicols}{2} +\begin{itemize} +\item The use of unsupervised learning and supervised learning with text +classification for tasks such as spam filtering. +\item Captures the meaning of suffixes/prefixes for the words given in a corpus. +\item Generation of better word embeddings for rare words as their character +$n$-grams are shared with other more frequent words, adding more neighboring +contextual words and improving its probability of being selected. +\columnbreak + \item Generation of word embeddings for OOV words. +\item Better semantic similarity between two words (e.g., king and kingdom) by +using extra information about the sub-words. +\item No compromise of accuracy when stopwords are present. +\item Significant improvement in model accuracy when used to perform syntactic +word analogy tasks for morphologically rich languages (e.g., French and German). +\end{itemize} +\end{multicols} + +As for its main disadvantages, they are the following: +\begin{multicols}{2} +\begin{itemize} +\item Requires much more RAM than Word2Vec due to the sub-words generation for +each word. +\item Lower accuracy compared to Word2Vec when a model is used on semantic +analogy tasks. +\item FastText is \SI{50}{\percent} slower to train than the regular Skip-Gram model due +to the added overhead of $n$-grams compared to Word2Vec. +\item Difficulty in determining the best value for the $n$-grams generation. +\end{itemize} +\end{multicols} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "../../report" +%%% End: diff --git a/src/embedders/word2vec.tex b/src/embedders/word2vec.tex new file mode 100644 index 0000000..a5cb943 --- /dev/null +++ b/src/embedders/word2vec.tex @@ -0,0 +1,467 @@ + +\section{Word2Vec} +\label{sec:w2v} + +Word2Vec is an unsupervised learning algorithm published in 2013, which, based +on a corpus of text, provides a vector representation for each word of that +text, using a two-layer neural network. This algorithm was initially implemented +to learn word representations from large data sets efficiently but emerged as a +standard embedding technique. According to the use case, two models are +available: Continuous Bag-Of-Words (CBOW) and Skip-Gram (SG). + +\subsection{Continuous Bag-of-Words Model} +\label{subsec:w2v:cbow} + +CBOW is an unsupervised model that predicts a target word based on context words +and window size. From a semantic point of view, the model is named +``Bag-of-Words'' since the order of the context words does not influence its +training. +\begin{figure}[!ht] + \centering + \includegraphics[width=0.75\textwidth]{img/embedders/w2v/cbow} + \caption{CBOW Model Architecture.} + \source{ + \href{https://lilianweng.github.io/lil-log/2017/10/15/learning-word-embedding.html} + {Lilian Weng -- Learning Word Embedding} + } + \label{fig:w2v:cbow:architecture} +\end{figure} + +In Figure \ref{fig:w2v:cbow:architecture}, the CBOW model architecture starts by +taking one or several targets word as input, represented as a $V$-dimensional +one-hot encoding vector. $V$ is the dictionary's size of unique words present in +a text or in a training data set. Using a dot product, this/these input +vector(s) is then multiplied by a first $W$ weight matrix, named embedding +matrix. This matrix is of dimension $V \times N$, where $N$ is the number of +features that each unique word in this vocabulary has defining the +\emph{embedding size}. Therefore, these dot products produce an $N$-dimensional +hidden vector for each input vector. However, if there multiple input context +vectors, these hidden vectors are then averaged element-wise into a single +hidden vector, where this vector chooses the size of the vectors that will be +used later. + +According to the semantics of the words of the dictionary, a new dot product is +made, but this time, between the calculated hidden vector and another $W'$ +weight matrix, named \emph{context matrix}. This matrix being now of dimension +$N \times V$. Then, their product generates an output vector of dimension $V$ +subjected to a softmax activation function. Therefore, this function ends by +calculating a probability distribution and returns the probability that a word +is a target word for the given context words. Finally, a cross-entropy loss +function is applied to compute the loss between the true probability +distribution of the given target word and the calculated model probability. + +\begin{definition}[Cross-Entropy] + Measures the difference between two probability distributions for a given + random variable. Let $p$ be a true probability distribution, $q$ be a computed + model probability, and $c$ be the predicted result by an ML + algorithm. Mathematically, the cross-entropy loss can be defined as follows: + \begin{equation} + H(p, q) = -\sum_{c=1}^Cp(c)\log\left(q(c)\right) + \label{eq:cross-entropy} + \end{equation} + \label{def:cross-entropy} +\end{definition} + +After computation with the cross-entropy loss, the back-propagation updates the +weights of the embedding matrix according to this loss. These steps are then +repeated with other context words and another target word for a specified number +of epochs. Once the training is done, the embedding matrix is used to generate +the word embeddings from the one-hot encodings. Formally, given a sequence of +training words $w_1, w_2, \dotsc, w_t$, and a context window $c$, the objective +of the CBOW model is to maximize the average log probability: +\begin{equation} + \frac{1}{T}\sum_{t=1}^T\log\left(p\left(w_t|w_{t-c}, \ldots, w_{t + c}\right)\right) + \label{eq:w2v:cbow:probability} +\end{equation} + +where $T$ is the number of training samples, and the probability +$p\left(w_t|w_{t-c}, \ldots, w_{t + c}\right)$ is computed using the softmax +function (cf. Definition \ref{def:softmax}): +\begin{equation} + p\left(w_t|w_{t-c}, \ldots, w_{t + c}\right) = + \frac{\exp\left(v^{-T}v'_{w_t}\right)}{\sum_{w=1}^W\exp\left(v^{-T}v'_w\right)} + \label{eq:w2v:cbow:probability:details} +\end{equation} + +where $W$ is the vocabulary size, $v'_w$ is the output vector of the $w$ word, +and $v$ is the averaged input vector of all the context words: +\begin{equation} + \overline{w}_t = \frac{1}{2c}\sum_{-c\leq j \leq c,j \neq 0}w_{t + j} + \label{eq:w2v:cbow:probability:details2} +\end{equation} + +\noindent Finally, the whole network is not used regarding the generation of embeddings, +but only its first layer. + +\subsection{Skip-Gram Model} +\label{subsec:w2v:sg} + +SG is an unsupervised model that predicts context words from a target word, +according to window size and a sentence. Unlike CBOW, these context words are +defined as multiple pairs of words (cf. Table \ref{def:window:size}), serving as +training samples for this model. Such training allows this model to learn word +vector representations suitable for predicting nearby words within a text, +except for common words and stop words (cf. Section +\ref{subsec:w2v:sfw}). Finally, SG compresses the information in a low +dimensional space, such that this model learns a continuous low dimensional +representation for the words. + +The window size for each target word is arbitrarily chosen between one and a +small positive number. This choice allows to add randomness during training and +improves future predictions. In the case of a window size greater than two, the +context words for a target word likely are more than two. If such a situation +occurs, SG randomly picks a word from these word contexts to form a pair with +the context word. Then, this model counts the number of times this pair of words +appear, and the model starts to be trained. + +Similar to CBOW, given a sequence of target words $w_1, w_2, \ldots, w_t$, and a +context window $c$, the objective of the SG model is to maximize the average log +probability: +\begin{equation} + \frac{1}{T}\sum_{t=1}^T\sum_{-c \leq j \leq c, j \neq 0}\log\left(p\left(w_{t+j}|w_t\right)\right) + \label{eq:w2v:sg:probability} +\end{equation} + +where $T$ is the number of training samples, and the probability $p\left(w_{t + +j}|w_t\right)$ is also computed using the softmax function (cf. Definition +\ref{def:softmax}): +\begin{equation} + p\left(w_o|w_i\right) = \frac{\exp\left(u_{w_o}^Tv_{w_i}\right)}{\sum_{w=1}^W\exp\left(u_w^Tv_{w_i}\right)} + \label{eq:w2v:sg:probability:details} +\end{equation} +where $W$ is the vocabulary size, $v$ the input representation of a word, and +$u$ the output representation of a word. + +\begin{figure}[!ht] + \centering + \includegraphics[width=0.8\textwidth]{img/embedders/w2v/skip-gram} + \caption{SG Model Architecture.} + \source{ + \href{https://lilianweng.github.io/lil-log/2017/10/15/learning-word-embedding.html} + {Lilian Weng -- Learning Word Embedding} + } + \label{fig:w2v:sg:architecture} +\end{figure} + +In Figure \ref{fig:w2v:sg:architecture}, the SG model architecture can be seen +as the inverse of the CBOW architecture. With this architecture, instead of +having context words and predicting a target word, it takes two words. From then +on, a model will predict a target word according to a context word. In addition, +since there is only one input word, the embedding matrix directly generates a +hidden layer with no need to do an average. Finally, the cross-entropy loss +function is applied this time to compute the loss between the true probability +distribution of the given context word and the calculated model probability. + +\subsection{Subsampling Frequent Words} +\label{subsec:w2v:sfw} + +Subsampling frequent words is a technique whose objective is to reduce the +number of training examples for a Word2Vec model. To accomplish this, it assumes +that predicting context words that are too frequent (e.g., ``the'') provides +little semantic value to differentiate a context +~\citep{inproceedings:mikolov}. In contrast, infrequent words are more likely to +convey specific information. Therefore, to improve the balance between +infrequent and frequents words, this technique randomly eliminates words from a +more frequent corpus than a certain threshold. This suppression occurs before a +corpus is processed in word-context pairs. + +Let $w_i$ be a word, $f_{w_i}$ be a word frequency in a corpus, and $t$ be a +chosen threshold, typically around $10^{-5}$. Mathematically, the discarding of +a word from a corpus is done as follows: +\begin{equation} + P(w_i) = 1 - \sqrt{\frac{t}{f(w_i)}} + \label{eq:w2v:sfw} +\end{equation} + +Therefore, each word $w_i$ present in a text for a window of size $c$ has a +probability of being deleted, where each deleted word reduces the training +samples by most $c$ times. Therefore, words whose frequency is above this +threshold, will be aggressively subsampled, preserving the frequency +ranking. However, even though this formula speeds up learning and even +significantly improves the accuracy of learned vectors of infrequent +words~\citep{inproceedings:mikolov}, the Word2Vec implementation uses another +more elaborate formula to discard a word: +\begin{equation} + P(w_i) = \left(\sqrt{\frac{z(w_i)}{t}} + 1\right)\frac{t}{z(w_i)} + \label{eq:w2v:sfw:real} +\end{equation} + +where $t$ has a default threshold of $10^{-3}$ and $z(w_i)$ is the fraction of +the total words in the corpus that corresponds to this word. For example, if the +``cat'' word occurs 1000 times in a billion words corpus, then $z($``cat''$) = +10^{-6}$. Therefore, $P(w_i) = 1$ when $z(w_i) \leq 0.0032z(w_i) \leq 0.0032$ +means to keep every instance of a word that represented \SI{0.32}{\percent} or +less and subsampled those that have a higher percentage. Please note that +$P(w_i)$ does not correspond to a probability since it is no longer bounded +between 0 and 1. Finally, from the accuracy point of view, subsampling frequent +words can improve some accuracy and decrease one of the others. + +\subsection{Hierarchical Softmax} +\label{subsec:w2v:hsm} + +Hierarchical Softmax (HSM) is an efficient softmax approximation technique that +uses a multilayer binary tree structure to reduce the computational cost of +training a softmax neural network~\citep{DBLP:conf/aistats/MorinB05}. In this +data structure, each node without child nodes, called \emph{leaf nodes}, +corresponds to a word and each internal node stands for relative probabilities +of the children nodes. + +For better accuracy, HSM structures the Word2Vec vocabulary using a +\textsc{Huffman} tree, a binary tree data structure where data is stored in leaf +nodes, without any particular order. To structure this vocabulary, HSM uses this +tree so that frequent words are closer to the root node of the tree while +infrequent words are deeper in this tree. Therefore, more frequent words have a +greater weight than infrequent words, where the \emph{path length} is +proportional to the frequency of a word. The path length of a tree is defined as +the number of nodes that must be traversed to reach a specific +word. Consequently, a \textsc{Huffman} tree always has $n$ leaf nodes for $n-1$ +internal nodes, where each node is characterized by a weight defined by a +numerical identifier. As a result, the weight of each parent node is equal to +the sum of the lower weights of its children. + +To compute the probability distribution of reaching a word, HSM uses a sigmoid +activation function and two matrices. One for the inputs and one for the outputs +differ on the values stored in each row. +\begin{table}[!ht] + \centering + \begin{subtable}[b]{0.5\textwidth} + \centering + \begin{tabular}{cc} + \toprule + \textbf{Target Word} & \textbf{Context Words} \\ + \midrule + \dots & \dots, \dots \\ + sleep & sleep, cat \\ + \bottomrule + \end{tabular} + \caption{Input Matrix} + \end{subtable}% + \begin{subtable}[b]{0.5\textwidth} + \centering + \begin{tabular}{ccc} + \toprule + \textbf{Node} & \textbf{Sigmoid Value} & \textbf{Label} \\ + \midrule + \dots & \dots & \dots \\ + 14 & 0.84 & 1 \\ + 20 & 0.23 & 0 \\ + \bottomrule + \end{tabular} + \caption{Output Matrix} + \end{subtable} + \caption{HSM Matrices for the SG Model.} + \label{fig:w2v:hsm:matrices} +\end{table} + +In Table \ref{fig:w2v:hsm:matrices}, the input matrix of a SG model contains +training samples for different target words. On the other hand, the output +matrix has rows of node weights related to labels and a probability determined +by the sigmoid function. This label, which can only have two values (zero or +one), helps informs navigation in the tree based on a node. By convention, zero +means to browse the left branch of this tree and one, the other +branch. Therefore, the output matrix reports that the ``cat'' context word is +found for the ``sleep'' target word by turning left at node 20 and turning right +at node 14. + +\begin{figure}[!ht] + \centering + \resizebox{0.6\textwidth}{!}{% + \begin{tikzpicture} + \node[entity,minimum size=0.9cm,fill=myblue] (node_20) at (0,0) {20}; + + \node[entity,minimum size=0.9cm,fill=myblue] (node_14) at (-2.5,-1) {14}; + \node[entity,minimum size=0.9cm,fill=myblue] (node_6) at (2.5,-1) {6}; + + \node[entity,minimum size=0.9cm,fill=myblue] (node_dog) at (-4,-2.5) {8}; + \node[circle,draw,fill=myred] (node_cat) at (-1,-2.5) {9}; + + \node[entity,minimum size=0.9cm,fill=myblue] (node_rabbit) at (1,-2.5) {4}; + \node[entity,minimum size=0.9cm,fill=myblue] (node_2) at (4,-2.5) {2}; + + \node[entity,minimum size=0.9cm,fill=myblue] (node_horse) at (2.5,-4) {1}; + \node[entity,minimum size=0.9cm,fill=myblue] (node_fish) at (5.5,-4) {1}; + + \draw[color=red,text=black] (node_20) -- (node_14) node[edge] {\textcolor{red}{0}}; + \draw (node_20) -- (node_6) node[edge] {1}; + + \draw[color=red,text=black] (node_14) -- (node_cat) node[edge] {\textcolor{red}{1}}; + \draw (node_14) -- (node_dog) node[edge] {0}; + + \draw (node_6) -- (node_rabbit) node[edge] {0}; + \draw (node_6) -- (node_2) node[edge] {1}; + + \draw (node_2) -- (node_horse) node[edge] {0}; + \draw (node_2) -- (node_fish) node[edge] {1}; + + \node[label,below of=node_cat] {\textcolor{red}{\textbf{cat}}}; + \node[label,below of=node_dog] {dog}; + \node[label,below of=node_rabbit] {rabbit}; + \node[label,below of=node_horse] {horse}; + \node[label,below of=node_fish] {fish}; + \end{tikzpicture} + }% + \caption{\textsc{Huffman} Tree for Word2Vec.} + \label{fig:w2v:hsm:huffman} +\end{figure} + +In Figure \ref{fig:w2v:hsm:huffman}, a vocabulary of five words is structured in a +\textsc{Huffman} tree containing four internal nodes, where each edge indicates a +label. This training aims to teach the model to navigate in the tree by finding +a context word based on a target word. For this search, the tree is traversed +from top to bottom, where HSM does the dot product between the target word +vector and the current node. Afterward, the result is sent to a sigmoid +activation function which returns a probability value. According to this value, +HSM checks that this probability is correct based on a label and updates the +neurons' weights if needed. This process is repeated until the word context for +a target word is found. Since training is not done on all words, there is no +need to traverse every tree node. As a result, the complexity of the gradient +goes from $\mathcal{O}(W)$ to $\mathcal{O}(\log_2(w))$. Once the training is +completed, the SG model (the same reasoning is used for CBOW) can use this tree +to predict a context word for a target word, where this time the label is not +specified in the output matrix. + +\begin{figure}[!ht] + \centering + \resizebox{0.6\textwidth}{!}{% + \begin{tikzpicture} + \node[entity,minimum size=0.9cm,fill=myblue] (node_20) at (0,0) {20}; + + \node[entity,minimum size=0.9cm,fill=myblue] (node_14) at (-2.5,-1) {14}; + \node[entity,minimum size=0.9cm,fill=myblue] (node_6) at (2.5,-1) {6}; + + \node[entity,minimum size=0.9cm,fill=myblue] (node_dog) at (-4,-2.5) {8}; + \node[entity,minimum size=0.9cm,fill=myblue] (node_cat) at (-1,-2.5) {9}; + + \node[entity,minimum size=0.9cm,fill=myred] (node_rabbit) at (1,-2.5) {4}; + \node[entity,minimum size=0.9cm,fill=myblue] (node_2) at (4,-2.5) {2}; + + \node[entity,minimum size=0.9cm,fill=myblue] (node_horse) at (2.5,-4) {1}; + \node[entity,minimum size=0.9cm,fill=myblue] (node_fish) at (5.5,-4) {1}; + + \draw (node_20) -- (node_14) node[edge] {0.73}; + \draw[color=red,text=black] (node_20) -- (node_6) node[edge] {\textcolor{red}{0.27}}; + + \draw (node_14) -- (node_cat) node[edge] {0.55}; + \draw (node_14) -- (node_dog) node[edge] {0.45}; + + \draw[color=red,text=black] (node_6) -- (node_rabbit) node[edge] {\textcolor{red}{0.62}}; + \draw (node_6) -- (node_2) node[edge] {0.38}; + + \draw (node_2) -- (node_horse) node[edge] {0.81}; + \draw (node_2) -- (node_fish) node[edge] {0.19}; + + \node[label,below of=node_cat] {cat}; + \node[label,below of=node_dog] {dog}; + \node[label,below of=node_rabbit] {\textcolor{red}{\textbf{rabbit}}}; + \node[label,below of=node_horse] {horse}; + \node[label,below of=node_fish] {fish}; + \end{tikzpicture} + }% + \caption{\textsc{Huffman} Tree for Word2Vec.} + \label{fig:w2v:hsm:huffman:prediction} +\end{figure} + +In Figure \ref{fig:w2v:hsm:huffman:prediction}, the tree edges provide the +number of occurrences that a context word is to the left or right of a node, +according to a given target word. After training this SG model for training +data, the output matrix indicates that \SI{27}{\percent} of the time, the +context word for the same target word was in the right branch of the root node, +and \SI{73}{\percent} of the time, this context word was left branch. Based on +this principle, the other nodes also return a probability distribution for their +left and right branches that varies according to the input vector of a target +word. + +Therefore, the probability of having ``rabbit'' as a context word for the +``sleep'' target word is equal to the product of the probabilities ($\simeq$ +\SI{17}{\percent}). Added to the probability distribution, each word in the +vocabulary guarantees that its sum is unitary. Finally, through HSM, Word2Vec +can retrieve word input vectors where the probability distribution of two +synonymous words will have a cosine similarity close to one. + +\subsection{Negative Sampling} +\label{subsec:w2v:ns} + +Negative sampling is an alternative technique to HSM, which also reduces the +training speed but combined with Subsampling Frequent Words, it can improve the +word embeddings' quality. To achieve this, \textsc{Mikolov} et al. assume that +updating all the neurons of a ANN for each training sampling is computationally +expensive. From then on, negative sampling focuses on making each training +sample change only a tiny percentage of the weights rather than all of +them~\citep{mccormick}. However, with or without negative sampling, the hidden +layer only updates the input word weights. + +The way negative sampling works can be considered a simplified version of the +Noise Contrastive Estimation (NCE) metric, whose purpose of NCE is to learn a +data distribution by comparing it against a noise distribution. In the context +of negative sampling, the latter differentiates a target word from noise samples +using a logistic regression classifier~\citep{DBLP:journals/jmlr/GutmannH10}. + +The words being stored in one-hot vectors, this technique updates the weights of +the ``positive'' and ``negative'' words. A word is considered positive if it was +initially in the training sample, while a word is negative if it is considered +noise. Specifically, this noise results from the return of the zero value in +these one-hot vectors by the ANN. A small number makes selecting these negative +words of random words using a ``unigram distribution'', where the most frequent +words are more likely to be chosen as negative samples~\citep{mccormick}. + +Let $w_i$ be a word from a corpus, $f_{w_i}$ be a word frequency, and $w_j$ be a +total number of negative words in the corpus. The probability that a $w_i$ word +is selected as a negative word is defined as follows: +\begin{equation} P(w_i) = \frac{f(w_i)}{\sum_{j=0}^nf(w_j)} + \label{eq:w2v:ns:selection:intro} +\end{equation} + +However, the published version increases the number of words to 3/4 power to +provide better results. The following formula also increases the probability of +infrequent words and decreases the likelihood of frequent words: +\begin{equation} P(w_i) = \frac{f(w_i)^{3/4}}{\sum_{j=0}^nf(w_j)^{3/4}} + \label{eq:w2v:ns:selection} +\end{equation} + +In practice, Word2Vec implements this negative sampling selection by filling a +table called \emph{unigram table}, including the index of each word present in a +vocabulary~\citep{mccormick}. Then, the selection of a negative sample is made +by generating a random index, where the index of a word appears $P(w_i) * +{table}_{\text{size}}$ times in a table. Therefore, the more frequent words are +more likely to be negative words. Finally, for the choice of the number of +negative words, it is recommended to take five to twenty words for small data +sets instead of large data sets where it is preferable to take two to five +words.~\citep{inproceedings:mikolov}. + +\subsection{Advantages and Disadvantages} +\label{subsec:w2v:pro:cons} + +In a non-exhaustive way, the advantages of the Word2Vec are: +\begin{itemize} +\item The use of unsupervised learning and can therefore work on any plain text. +\item Requires less RAM compared to other words/vectors representations. +\end{itemize} + +As for its main disadvantages, they are the following: +\begin{multicols}{2} +\begin{itemize} +\item No embeddings are available for Out of Vocabulary (OOV) words. Therefore, +if Word2Vec has trained with the ``cat'' and ``fish'' words, it will not generate +the embedding of the ``catfish'' compound +\item No suffixes/prefixes meaning capture for given words in a corpus. +\columnbreak +\item Generation of low quality word embeddings for rare words. +\item Difficulty in determining the best value for the dimensionality of the + word vectors and the window size. +\item The use of the softmax activation function is computationally expensive. +\end{itemize} +\end{multicols} + +For the choice of the model, it is recommended to use SG when it is essential to +predict infrequent words with a small amount of training +data~\citep{inproceedings:mikolov}. However, CBOW is preferable for the +prediction of frequent words. Added to that, SG performs significantly on +semantic accuracy tests (e.g., ``Athens'' $\rightarrow$ ``Greece'' and ``Oslo'' +$\rightarrow$ ``Norway''). At the same time, CBOW offers better results in +syntactic accuracy tests (e.g., ``apparent'' $\rightarrow$ ``apparently'' and +``rapid'' $\rightarrow$ ``rapidly'')~\citep{sijun_he}. + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "../../report" +%%% End: diff --git a/src/flyleaf.tex b/src/flyleaf.tex new file mode 100755 index 0000000..8fbbe63 --- /dev/null +++ b/src/flyleaf.tex @@ -0,0 +1,82 @@ +\begin{titlepage} + \begin{center} + + \textsc{\Large Master's Thesis at IDLab, Ghent University - imec}\\[1cm] + + \includegraphics[width=.5\linewidth]{img/logo/heh-technical}\\[1cm] + + \begin{vc} + \begingroup + \HRule\\ + \flushleft + \Huge A Trip to Sesame Street: Evaluation of BERT and Other Recent Embedding Techniques Within RDF2Vec + \HRule\\ + \endgroup + \end{vc} + + \begin{minipage}[t]{0.4\textwidth} + \begin{flushleft} \large + \emph{Author:}\\ + \hspace{0.1em} + Terencio \textsc{Agozzino} + \end{flushleft} + \end{minipage} + \hspace{5em} + \begin{minipage}[t]{0.4\textwidth} + \begin{flushleft} \large + \emph{Advisor:}\\ + \hspace{0.1em} + Prof. Dr. Femke \textsc{Ongenae} + \end{flushleft} + \begin{flushleft} \large + \emph{Supervisors:}\\ + \hspace{0.1em} + Dr. Ir. Gilles \textsc{Vandewiele}\\ + \hspace{0.1em} + Dr. Ir. Samuel \textsc{Cremer}\\ + \hspace{0.1em} + Ir. Bram \textsc{Steenwinckel} + \end{flushleft} + \end{minipage}\\[1cm] + + \parbox{100mm}{\textit{Master's thesis submitted in fulfillment of the + requirements for the degree of Master in Industrial Engineering}}\\[1cm] + + \begin{minipage}[c]{0.3\textwidth} + \centering + \includegraphics[width=.6\linewidth]{img/logo/imec} + \end{minipage} + \hfill + \begin{minipage}[c]{0.3\textwidth} + \centering + \includegraphics[width=.6\linewidth]{img/logo/ugent} + \end{minipage} + \hfill + \begin{minipage}[c]{0.3\textwidth} + \centering + \includegraphics[width=.6\linewidth]{img/logo/idlab} + \end{minipage}\\[1.5cm] + \begin{minipage}[c]{0.3\textwidth} + \centering + \includegraphics[width=.5\linewidth]{img/logo/wbe_vertical} + \end{minipage} + \hfill + \begin{minipage}[c]{0.3\textwidth} + \centering + \includegraphics[width=.5\linewidth]{img/logo/pole_hainuyer_horizontal} + \end{minipage} + \hfill + \begin{minipage}[c]{0.3\textwidth} + \centering + \includegraphics[width=.4\linewidth]{img/logo/cti} + \end{minipage}\\[1cm] + + \large Academic year 2020-2021 + \vfill + \end{center} +\end{titlepage} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "../report" +%%% End: diff --git a/src/introduction.tex b/src/introduction.tex new file mode 100644 index 0000000..a18cd9d --- /dev/null +++ b/src/introduction.tex @@ -0,0 +1,122 @@ + +\chapter{Introduction} +\label{chap:introduction} + +In an increasingly digital world, data generation applies different semantic and +syntactic origins~\citep{DBLP:journals/jodsn/CeravoloAACCDMK18}. However, this +data diversity must remain interpretable by the computer. In the absence of +semantics, the evaluation of the validity of the data is more +constraining. Without it, the same data point might not represent the same +thing. For example, the value of a sensor may be correct in one context but an +anomaly in another. Therefore, semantics makes it possible to make the context +of these data precise and understand their relationships. + +The usage of the Resource Description Framework (RDF) standard of the World Wide +Web Consortium (W3C) enables the semantic encoding of data. Such a standard +allows the management of this diversity of data through the Semantic Web and +Linked Open Data by interconnecting the different data sources. Disregarding the +\emph{knowledge base}, which contains semantic information, one way to make this +interconnection is to use graphs. A \emph{graph} is an ordered pair ($V, E$), +where $V$ is a finite and non-empty set of elements called \emph{vertices} (or +\emph{nodes}), and $E$ is a set of unordered pairs of distinct nodes of $V$, +called \emph{edges}. + +Based on this alternative representation of RDF data, the concept of Knowledge +Graph (KG) was published~\citep{singhal_2012}. Mathematically, a KG is a +\emph{directed heterogeneous multigraph}. This graph can store multiple directed +labeled edges between two nodes whose edges and nodes can be of different +types. Additionally, a KG can unite various sources and enhance conventional +data formats such as Comma Separated Values (CSV) by explicitly encoding the +relations between various nodes. Due to the richness of relations that these +types of graphs bring, several Machine Learning (ML) techniques can benefit from +them. From then on, there is a restricted usage of KGs due to their symbolic +constructs as most ML techniques require converting these KGs into numerical +input feature vectors. + +During this decade, different techniques +emerged~\citep{inproceedings:ristoski:strategies} to create these numerical +feature vectors, called \emph{embeddings}. One of them is to use Resource +Description Framework To Vector (RDF2Vec), an unsupervised and task-agnostic +algorithm to numerically represent nodes of a +KG~\citep{article:ristoski:rdf2vec} in an \emph{embedding matrix} used for +downstream ML tasks. For this purpose, RDF2Vec uses a walking strategy to +extract \emph{walks} of a KG, where a walk is an $n$-tuple of nodes starting +with a root node. In addition to this strategy, it is possible to use a sampling +strategy to better deal with larger KGs~\citep{inproceedings:cochez} by +privileging some hops over others through edge weights. Once extracted, these +walks are injected into an \emph{embedding technique} to learn the embeddings of +the provided root nodes of a KG and generate the corresponding embedding matrix. + +Following the significant advances in Natural Language Processing (NLP), the +community developed multiple embedding techniques. Among them, the release of +Word2Vec in 2013 initially learns the vector representation of a +word~\citep{inproceedings:mikolov}. However, KGs used this NLP technique where +walks can be an analogy of sentences and nodes as words. Word2Vec is the default +embedding technique of RDF2Vec and has shown promising +results~\citep{DBLP:journals/semweb/RistoskiRNLP19} in its use with +KGs. However, other significant advances in the NLP field have taken place. + +One of these advances was the creation of FastText, a Word2Vec extension to +improve the obtained embeddings. Published in 2016, FastText has improved these +embeddings in many use-cases at the expense of Random Access Memory (RAM) +consumption and training time, but more recent techniques have emerged. Since +2018, Bidirectional Encoder Representations from Transformers (BERT) is the +state-of-the-art NLP technique~\citep{inproceedings:devlin} whose objective is +to generate an unsupervised language representation model. This new technique +outperformed Word2Vec in everyday NLP +tasks~\citep{DBLP:conf/embc/SahaLG20,article:beseiso,DBLP:conf/acl/HendrycksLWDKS20}. Due +to its efficiency, the community published many variants of BERT, each bringing +its specificity. However, BERT's benefits with KGs are still debatable. Few +research papers have used this technique in KGs to compare it with other +embedding techniques. + +As a result of this finding, the main purpose of this Master's thesis is to +provide a research work to focus on evaluating BERT with KGs based on Word2Vec +and FastText. Such an evaluation would help determine its impact on the created +embeddings and improve the generation of a 2D feature matrix from a KG. + +To achieve this evaluation, an implementation of BERT and FastText will have to +be made to the \texttt{pyRDF2Vec} library, a central Python implementation of +the Java-based version of the RDF2Vec algorithm~\citep{pyrdf2vec}. In addition, +since BERT works differently from Word2Vec, and FastText, it will be necessary +to adapt the extraction and formatting of the walks of a KG to improve its +training. Finally, the choice of hyperparameters will be a determining criterion +on the accuracy of the BERT model, so it may be wise to find a compromise +between training time and the model's accuracy. + +Besides this primary objective, this Master's thesis proposes one more walking +strategy and sampling strategy to those already provided by +\texttt{pyRDF2Vec}~\citep{inproceedings:cochez}. Specifically, a walking +strategy called \texttt{SplitWalker} uses a splitting function to pre-format the +extracted walks before being injected into an embedding technique. In addition +to this strategy, the \texttt{WideSampler} sampling strategy focuses on features +shared between several entities by maximizing common relationships. Such +additions could improve a model's accuracy and the extraction time for specific +use cases according to a user's needs. + +The result of this Master's thesis work is structured as follows. Chapter +\ref{chap:related:work} introduces more context on the work related to BERT and +RDF2Vec with KGs. Chapter \ref{chap:objectives} focuses on providing the +specifications for this Master's thesis and stating the problems +encountered. Chapter \ref{chap:background} provides background information on +the fundamental concepts of graphs, ML, and NLP. This chapter also introduces +advanced concepts such as the Attention mechanism and the Transformer +architecture, both used by BERT. In addition, Chapter +\ref{chap:embedding:techniques} focuses on covering in detail the functioning of +each embedding technique, dedicating a section to the adaptation of BERT with a +graph. From then on, Chapter \ref{chap:rdf2vec} refers to RDF2Vec, including the +walking strategies and the sampling strategies proposed by this Master's +thesis. Chapter \ref{chap:work:performed} describes the work done behind this +Master's thesis, explaining the different implementations that were put in +place. Chapter \ref{chap:benchmarks} focuses on providing the setup and results +obtained from the different benchmarks related to the embedding techniques, +walking and sampling strategies. Following these results, Chapter +\ref{chap:discussion} discusses the correlation of the results with those of +other research papers and provides some leads for future research with +BERT. Finally, Chapter \ref{chap:conclusion} is dedicated to the conclusion of +this Master's thesis, summarizing the issues and solutions proposed. + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "../report" +%%% End: diff --git a/src/objectives.tex b/src/objectives.tex new file mode 100644 index 0000000..c8fbb80 --- /dev/null +++ b/src/objectives.tex @@ -0,0 +1,118 @@ + +\chapter{Objectives} +\label{chap:objectives} + +This chapter covers the specifications expected by this Master's thesis and the +problems faced in its elaboration. In addition, each specification is followed +by a summary of what was done to get a better idea of the overall report. + +\section{Specifications} +\label{sec:objectives:specifications} + +In 2018, BERT was released and outperformed all other existing techniques on +various ML tasks related to various fields. This Master's thesis aims to +integrate BERT into +\texttt{pyRDF2Vec}\footnote{\url{https://github.com/IBCNServices/pyRDF2Vec/}}, +but more specifically to evaluate its impact in terms of runtime, predictive +performance, and memory usage using different combinations of walking and +sampling strategies. Moreover, by reading literature from general graph-based ML +and NLP research, inspiration can be found to design new sampling and walking +strategies that result in improved predictive performances by exploiting the +properties of BERT. The specifications of this Master's thesis are composed of +the following four points: +\begin{enumerate} +\item \textbf{Support BERT and other embedding techniques for comparison +purposes}: at least the BERT embedding technique should be integrated into +\texttt{pyRDF2Vec} and be compared to the Word2Vec technique, which is currently +used. Additionally, the extension of Word2Vec, namely FastText, will also have +to be implemented and be compared to know its impact. + +For this Master's thesis, BERT and FastText have been implemented and integrated +within the \texttt{pyRDF2Vec} library. Added to this implementation is a new +architecture for \texttt{pyRDF2Vec} that easily allows other embedding +techniques. Since Word2Vec already exists in the library, this Master thesis +proposed a better walk extraction to improve the model's accuracy. + +\item \textbf{Evaluate the impact of BERT}: A thorough benchmarking study to +evaluate the impact of the BERT embedding technique on different dimensions will +have to be conducted. For this, data sets having different properties and +stemming from different domains will have to be selected. Moreover, a rigorous +framework that performs the required experiments and logs all of these results +will have to be developed. + +For this Master's thesis, BERT, Word2Vec, and FastText are compared on +\texttt{MUTAG}, a small KG. In addition to these benchmarks of embedding +techniques, the \texttt{pyRDF2Vec} library was modernized, allowing to get more +information with the \texttt{verbose} parameter of the +\texttt{RDF2VecTransformer} class. + +\newpage + +\item \textbf{Support of new walking strategies for RDF2Vec}: while an initial +set of five simple walking strategies are already implemented in +\texttt{pyRDF2Vec}, many other alternatives exist. Implementing more walking +strategies would allow more extensive and detailed comparisons for embedding +techniques. + +For this Master's thesis, the \texttt{SplitWalker} walking strategy is proposed and +implicitly introduced some of its variants. Finally, this Master's thesis offers +some benchmarks related to \texttt{SplitWalker} and other existing walking strategies. + +\item \textbf{Support of new sampling strategies for RDF2Vec}: similarly, other +sampling strategies can be created and implemented in +\texttt{pyRDF2Vec}. Therefore, it will be possible to see the impact of the +choice of a walking strategy and a sampling strategy with the performances +related to BERT and other embeddings techniques. + +For this Master's thesis, the \texttt{WideSampler} walking strategy is proposed, +leading to other variants of the latter. In addition, this Master's thesis +evaluates \texttt{WideSampler} with other existing sampling strategies to knows +its impact. +\end{enumerate} + +\section{Problems Encountered} +\label{sec:objectives:problems} + +This section discusses the problems that have been encountered and why some +benchmarks are missing. Initially, benchmarks related to bigger KGs such as +\texttt{AM} and \texttt{DBP:Cities} should have been done. Therefore, it is +helpful to understand the reasons for this to prevent these errors from +recurring. + +\subsection{Garbage Collector} +\label{subsec:garbage:collector} + +This Master's thesis being coupled with the internship, the same servers were +used. Due to an internal problem with IDLab's server infrastructure, a loss of +time equivalent to one and a half months of work was made. Therefore, this loss +of time had repercussions on this Master's thesis. Specifically, the benchmarks +related to BERT are not presented for this version of the report. However, they +will be added for the next version. Moreover, some benchmarks had to be +shortened due to time constraints. + +For more information related to this issue, IDLab servers use the +Stardog\footnote{\url{https://www.stardog.com/}} infrastructure, which is +implemented in Java. Therefore, the different benchmarks for the internship and +Master's thesis recorded high variants. After several weeks of debugging, +thinking that this was a \texttt{pyRDF2Vec} issue, a Stardog engineer confirmed +that the issue was related to their infrastructure. In more detail, the concern +was the lack of RAM release from the servers due to garbage collection. As a +result, new data was being saved directly to a physical disk, which resulted in +much higher latencies than RAM. From then on, this was reflected in the variance +of the results. + +\subsection{Exceptions Raised} +\label{subsec:exception:raised} + +In addition to the problems related to the garbage collector, exceptions are +encountered from time to time during SPARQL Protocol and RDF Query Language +(SPARQL) queries. These exceptions are due to the inaccessible locally hosted +SPARQL endpoint during updates or internal network problems. As a result, after +more than three attempts to retrieve the walks of a provided entity, an +exception is thrown, which makes the benchmarks stop. Since these benchmarks can +take several days, it also delayed other benchmarks. + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "latex" +%%% End: diff --git a/src/rdf2vec.tex b/src/rdf2vec.tex new file mode 100644 index 0000000..c2c99da --- /dev/null +++ b/src/rdf2vec.tex @@ -0,0 +1,225 @@ + +\chapter{RDF2Vec} +\label{chap:rdf2vec} + +Resource Description Framework To Vector (RDF2Vec) is an unsupervised and +task-agnostic algorithm to numerically represent nodes of a KG in an embedding +matrix that downstream ML tasks can use. RDF2Vec is unsupervised as it only +relies on the neighborhood of an entity to create embeddings and therefore does +not require any information about the node labels. Precisely, the dimensions +(e.g., $K \times 500$) of this embedding matrix result from the walk extraction +(e.g., $K$) and vector size (e.g., 500). + +\section{Walk Extraction} +\label{sec:rdf2vec:walk:extraction} + +This algorithm starts using a \emph{walking strategy} on a provided KG to +extract these walks, collecting an $n$-tuple of nodes starting with a root node +following a sequence of predicates and objects. Using the similarities shared by +natural language and graphs, these walks then serve as sentences for existing +NLP techniques, such as Word2Vec, to learn the embeddings of the root nodes of +this KG provided by a user. + +\begin{figure}[!ht] + \centering + \subfloat[Step I]{ + \begin{tikzpicture}[minimum size=2cm,node distance=1cm] + \node[entity,fill=myblue,font=\large,scale=0.6] (john) {\textsc{John}}; + \node[entity,font=\large,left=of john,scale=0.6] (friendOf){friendOf}; + \node[entity,font=\large,left=of friendOf,scale=0.6] (smith) {\textsc{Smith}}; + \node[entity,font=\large,right=of john,scale=0.6] (hasCat) {hasCat}; + \node[entity,font=\large,right=of hasCat,scale=0.6] (felix) {\textsc{Felix}}; + + \draw[arrow] (john) -- node[midway,yshift=0.4cm] {\small{2}} (hasCat); + \draw[arrow] (hasCat) -- node[midway,yshift=0.4cm] {\small{1}} (felix); + \draw[arrow] (john) -- node[midway,yshift=0.4cm] {\small{1}} (friendOf); + \draw[arrow] (friendOf) -- node[midway,yshift=0.4cm] {\small{1}} (smith); + \end{tikzpicture} + } + \vfill + \subfloat[Step II]{ + \begin{tikzpicture}[minimum size=2cm,node distance=1cm] + \node[entity,font=\large,scale=0.6] (john) {\textsc{John}}; + \node[entity,font=\large,left=of john,scale=0.6] (friendOf){friendOf}; + \node[entity,font=\large,left=of friendOf,scale=0.6] (smith) {\textsc{Smith}}; + \node[entity,fill=myblue,font=\large,right=of john,scale=0.6] (hasCat) {hasCat}; + \node[entity,font=\large,right=of hasCat,scale=0.6] (felix) {\textsc{Felix}}; + + \draw[arrow] (john) -- node[midway,yshift=0.4cm] {\small{2}} (hasCat); + \draw[arrow] (hasCat) -- node[midway,yshift=0.4cm] {\small{1}} (felix); + \draw[arrow] (john) -- node[midway,yshift=0.4cm] {\small{1}} (friendOf); + \draw[arrow] (friendOf) -- node[midway,yshift=0.4cm] {\small{1}} (smith); + \end{tikzpicture} + } + \vfill + \subfloat[Step III]{ + \begin{tikzpicture}[minimum size=2cm,node distance=1cm] + \node[entity,font=\large,scale=0.6] (john) {\textsc{John}}; + \node[entity,font=\large,left=of john,scale=0.6] (friendOf){friendOf}; + \node[entity,font=\large,left=of friendOf,scale=0.6] (smith) {\textsc{Smith}}; + \node[entity,font=\large,right=of john,scale=0.6] (hasCat) {hasCat}; + \node[entity,fill=myblue,font=\large,right=of hasCat,scale=0.6] (felix) {\textsc{Felix}}; + + \draw[arrow] (john) -- node[midway,yshift=0.4cm] {\small{2}} (hasCat); + \draw[arrow] (hasCat) -- node[midway,yshift=0.4cm] {\small{1}} (felix); + \draw[arrow] (john) -- node[midway,yshift=0.4cm] {\small{1}} (friendOf); + \draw[arrow] (friendOf) -- node[midway,yshift=0.4cm] {\small{1}} (smith); + \end{tikzpicture} + } + \caption{Walk Extraction for an Oriented Graph.} + \label{fig:rdf2vec:walk:extraction} +\end{figure} + +In Figure \ref{fig:rdf2vec:walk:extraction}, a KG is composed of five nodes and +four edges. Each edge is related to a weight determined by a \emph{sampling +strategy} that can assign these weights either randomly or guided by a +particular metric, called \emph{biased walks}. These edge weights are helpful to +the walking strategy to identify the following neighboring entity to extract +in a walk. The walk extraction starts with \texttt{John} as the root node, +including \texttt{friendOf} and \texttt{hasCat} as possible candidates for the +next hop. However, as the \texttt{hasCat} edge has a higher weight than the +\texttt{friendOf} edge, the hop to \texttt{hasCat} is preferred. After this hop, +the walking strategy updates its list of candidates with the neighbors of the +current node. Finally, the process continues to iterates until this walking +strategy returns an exhaustive list of walks or reaches a specified predefined +depth covering the number of successive tuples within a walk. From then on, +there is the extraction of the 3-tuple (\texttt{John}, \texttt{hasCat}, +\texttt{Felix}) walk. + +The original RDF2Vec implementation uses a random walking strategy to extract a +limited number. The particularity of this walking strategy implies the +extraction of a random hop\footnote{Originally RDF2Vec preferred a random walk.} +when neighboring hops have the same weight. The random walking strategy applies +two algorithms to extract walks: the Depth-first search (DFS) and Breadth-first +search (BFS). The former traverses a graph as deep as possible before retracing +its steps. In contrast, the latter crosses every neighboring node of the same +depth before crossing those of a different depth. Therefore, if there is a +necessity to extract a specific number of walks, DFS is used by this +strategy. Otherwise, the random walker strategy picks BFS to extract every walks +of a KG. + +\subsection{Walking Strategies} +\label{subsec:rdf2vec::walking:strategies} + +After the publication of RDF2Vec, several walking strategies became +available~\citep{inproceedings:cochez}, where every walking strategy can be an +extraction (\texttt{type 1}) or transformation (\texttt{type 2}) technique +~\citep{article:vandewiele}. Each of these strategies brings its particularity, +making it preferable to choose them in at least one use case. + +As the name implies, extraction techniques focus on extracting walks, usually so +that these walks provide richer information to produce a model resulting in the +highest possible accuracy. This category includes random walking strategy and +\emph{Community Hops}. Based on relationships not explicitly modeled in a KG, +the latter groups' nodes with similar properties through community detection. However, +both walking strategies rely on the BFS and DFS algorithms, including or not +some variations. + +The transformation techniques categorize the walking strategies that transform +the extracted walks provided by a \texttt{type 1} walking strategy. As they are +easier to implement, this type includes more walking strategies than +\texttt{type 1}. This technique's primary purpose is to define +\emph{one-to-many} or \emph{many-to-one} cardinality between the old node's +labels and the new ones. If there is a \texttt{one-to-one} cardinality, no +additional information is gained and the original walking strategy could be +used. + +In a non-exhaustive way, the following walking strategies of \texttt{type 2} +rely on the transformation of randomly extracted walks: +\begin{itemize} +\item \textbf{Anonymous Walk}: transforms each vertex name other than the root +node into positional information to anonymize the randomly extracted walks. + +\item \textbf{Hierarchical Random Walks} (\textbf{HALK}): removes rare hops from randomly +extracted walks, increasing the quality of the generated embeddings while +reducing memory usage. + +With this strategy, the suppression of a walk occurs when this walk only +contains the root node following one or more infrequent hop(s), as it will not +provide additional information. + +\item \textbf{N-Gram}: transforms the $n$-grams in random walks to define a +mapping from \emph{one-to-many}. The intuition behind this strategy is that the +predecessors of a node that two different walks have in common can be different. + +\item \textbf{Walklets}: transforms randomly extracted walks into walklets which +are walks of size one or two, including the root node and potentially another +node that can be a predicate or an object. + +\item \textbf{Weisfeiler-Lehman}: transforms the nodes of the extracted random +walks, providing additional information about the entity representations only +when a maximum number of walks is not specified. +\end{itemize} + +However, the implementations of these sampling strategies in \texttt{pyRDF2Vec} +relied on extracting child nodes, not parent nodes, which lost context for a +root node. + +\subsection{Sampling Strategies} +\label{subsec:rdf2vec:sampling:strategies} + +The sampling strategies essentially allow to better deal with larger KGs. A +naive implementation randomly samples a fixed number of walks for each entity to +keep the total number of walks limited. Since then, the +community~\citep{inproceedings:cochez,article:mukherjee,article:taweel} has +suggested several metrics to compute the sampling weights while walking. + +Although sampling strategies allow the extraction of large KGs, most of these +strategies require working on the entire KG to assign weights to edges. However, +some KGs are so large that they need to be stored in a +\emph{triplestore}\footnote{Database designed for the storage and retrieval of +RDF.} and made available through a SPARQL endpoint. Therefore, one way to use +these sampling strategies is to load parts of large KGs, assign weights, and +start the walk extraction. Finally, the different walks extracted for these +parts of KGs would be concatenated and returned. + +\section{Shortcomings} +\label{sec:rdf2vec:shortcomings} + +The node representation made by RDF2Vec has already achieved great predictive +performances on several data sets in various fields. However, RDF2Vec still has +a few shortcomings. In a non-exhaustive way: +\begin{itemize} +\item \textbf{RDF2Vec does not scale to large KGs}: the walk extraction grows +exponentially with the predefined depth. This behavior is unacceptable with KGs +containing many nodes, mainly when these KGs contain many highly connected +nodes. + +\item \textbf{RDF2Vec cannot deal with literals in the KG}: this algorithm +extracts node as \emph{non-ordinal categorical} data, which discard a +considerable amount of rich information that \emph{literals} can provide. In +other words, nodes can be from different types, but RDF2Vec extracts these nodes +as a name without any classification instead of conserving their types. + +\item \textbf{RDF2Vec cannot deal with dynamic graphs}: adding a new entity in a +KG implies re-training the model generated by the embedding technique. This +re-training is undesirable, especially when the training time of a model is +substantial. + +\item \textbf{RDF2Vec uses a simple data structure for storing walks}: +Extracting more complex data structures, such as trees, or modifying the walking +algorithm to introduce different inductive \emph{biases} could result in higher +quality embeddings. Consequently, these quality embeddings would improve the +model's accuracy. + +\item \textbf{RDF2Vec uses an embedding technique that is no longer state of the +art in NLP}: currently, RDF2Vec uses Word2Vec as an embedding +technique. However, more recent NLP techniques such as BERT could be a better +alternative to Word2Vec and improve the model's accuracy. +\end{itemize} + +The community has proposed solutions to address the shortcomings mentioned above +to improve this representation of nodes. Among these, optimization mechanisms +(e.g., caching and multiprocessing) to better handle large KGs and an +\emph{online learning} implementation to update the vocabulary of nodes learned +by RDF2Vec. In addition, a user could extract interesting literals by specifying +a sequence of predicates followed by a walking strategy. Finally, other +embedding techniques than Word2Vec were also proposed, such as +\emph{KGloVe}\footnote{\url{https://datalab.rwth-aachen.de/embedding/KGloVe/}}, +which uses the Global Vectors for Word Representation (GloVe) embedding +technique. + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "latex" +%%% End: diff --git a/src/references.tex b/src/references.tex new file mode 100644 index 0000000..97bcec9 --- /dev/null +++ b/src/references.tex @@ -0,0 +1,7 @@ + +\bibliography{bibli} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "../report" +%%% End: diff --git a/src/related-work.tex b/src/related-work.tex new file mode 100644 index 0000000..3d0c652 --- /dev/null +++ b/src/related-work.tex @@ -0,0 +1,122 @@ + +\chapter{Related Work} +\label{chap:related:work} + +This chapter presents the related work around BERT and RDF2Vec with KGs to +understand better the study done by this Master's thesis. + +\section{BERT} +\label{section:related:work:bert} + +Over the last few years after the publication of +BERT~\citep{inproceedings:devlin}, several variants of this model emerged and +were evaluated with its original version. One of these variants is DistilBERT, a +smaller, cheaper, and lighter version of BERT. The comparison of DistilBERT with +BERT and ELMo, another embedding technique, showed promising results across +several data sets. Specifically, DistilBERT~\citep{distilbert} had almost as +excellent performance as BERT surpassing ELMo's score in most data sets. + +In the NLP related to biomedical and clinical texts, a benchmark of five tasks +with ten datasets of different sizes and difficulties also compared BERT and +ELMo~\citep{peng}. In this benchmark, BERT showed better overall results +compared to ELMo. Another evaluation provides lower accuracy for BERT than GloVe +when using a dataset related to tweets with or without +sarcasm~\citep{khatri}. According to the authors, these lower BERT scores are +due to the lack of context provided by the sarcastic tweets. Finally, another +benchmark is interested in comparing BERT with ELMo, GloVe, and FastText by +performing principal component static embeddings~\citep{ethayarajh}. In this use +case, BERT shows the best results in most data sets. + +Meanwhile, the community has released other KG-oriented variants of BERT, such +as KG-BERT, released in 2019. This BERT-based framework achieves +state-of-the-art performance in triple classification and link and relationship +prediction tasks~~\citep{DBLP:journals/corr/abs-1909-03193}. Shortly after the +publication of KG-BERT, K-BERT is also released, which has the particularity of +not using pre-training. K-BERT uses BERT to infer relevant knowledge in a domain +text to solve the lack of domain-specific knowledge within a general language +representation from large-scale corpora~\citep{DBLP:conf/aaai/LiuZ0WJD020}. In +this paper, K-BERT significantly outperforms BERT in NLP tasks from different +fields such as finance, law, and medicine. + +After the release of KG-BERT and K-BERT, others variants followed, such as +Graph-BERT published in 2020. Graph-BERT relies solely on the Attention +mechanism without using graph convolution or aggregation operations. This +KG-variant also shows promising results overcoming Graph Neural Networks (GNNs) +in the learning efficiency for node classification and graph clustering +tasks~\citep{zhang}. + +BERT-INT is also another variation of BERT, which predicts the identity of two +entities across multiple KGs. BERT-INT works on proximity information to predict +such identity without relying on the KG structure +itself~\citep{DBLP:conf/ijcai/Tang0C00L20}. Precisely, BERT-INT mimics entity +comparison as humans would by comparing their name, description, and +attributes. When these two entities share the same information, a second +comparison consists of assessing the similarity of neighbors between entities, +but this time based on their name and description only. + +Finally, the last paper uses BERT with Transfer Learning to answer questions +based on a domain-specific KG~\citep{DBLP:conf/aics/VegupattiNC20}. Specifically +in the field of medical biology using a dataset of 600 questions. In this paper, +BERT succeeded in answering these questions with more than acceptable results. + +The discoveries made around BERT suggest that the usage of this embedding +technique with KGs is possible. However, too few research papers compare BERT +with other embedding techniques. This lack of articles makes it unclear what the +context of BERT's application is. The work of \textsc{Khatri} et al. gives a +lead, but it is not enough. + +\section{Graph-Based Machine Learning} +\label{section:related:work:graph} + +From a data modeling perspective, the use of KG since its publication has become +a standard in the Semantic Web. This specific type of graph has its use in many +fields to model a knowledge domain. However, despite the valuable information +such a graph can provide, an ML model cannot directly learn from +them~\citep{article:ristoski:rdf2vec}. Therefore, this decade proposed several +techniques to convert KGs into embeddings for downstream ML tasks. In the field +of KG embeddings, three categories of embedding creations are distinguished: +\emph{direct encoding} based, Deep Learning (DL) based, and \emph{path/walk} +based. + +The first category includes algorithms such as RESCAL and Translating Embeddings +(TransE) that mainly stand out in tasks related to graph completion as well as +link prediction and entity classification, also called \emph{node +classification}~\citep{DBLP:conf/nips/BordesUGWY13}. It is still possible to +perform mathematical operations with direct encoding while remaining the +\emph{embedded space} node classification result. This embedded space ensures +the data embedding after dimensionality reduction. However, two of the drawbacks +of direct encoding are their limited use with dynamic graphs and support for +literals. + +Modeling Relational Data with Graph Convolutional Networks (R-GCNs) mainly +dominates the second category. R-GCNs is a supervised algorithm published in +2017 working directly on graphs. This algorithm illustrates DL's power in the +Statistical Relational Learning tasks as link prediction and entity +classification~\citep{DBLP:conf/esws/SchlichtkrullKB18}. However, a significant +disadvantage of R-GCNs is their memory consumption due to loading the KG +upstream, limiting its use to KGs of reasonable size. Another drawback concerns +their dependency on manual labeling of the training datasets due to the +\emph{supervised learning}, which can be time-consuming depending on its +size. Besides that, the support of literals is theoretically possible, but only +a few studies have investigated the subject. + +The last category includes RDF2Vec, which is the state-of-the-art unsupervised +algorithm since 2016. Unlike the other two categories, in this category, the +creation of embeddings is done by traversing a KG using a walking and sampling +strategy. Therefore, an essential drawback of RDF2Vec is that without caching +and other optimization mechanisms, the walk extraction time can be significant +for large KGs. + +Each of these three categories of algorithms ensures the generation of +embeddings. However, according to the use case, one category may be preferred to +another. For example, since R-GCNs explicitly remove edges in a KG before +training a model, RDF2Vec could be preferred. Furthermore, RDF2Vec can decide +whether or not to prioritize a hop due to its walking and sampling strategy, +which avoids training a model over the whole KG. Finally, these categories can +support an online learning implementation and guarantee that a model remains up +to date. + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "latex" +%%% End: diff --git a/src/work-performed.tex b/src/work-performed.tex new file mode 100644 index 0000000..1eb2547 --- /dev/null +++ b/src/work-performed.tex @@ -0,0 +1,649 @@ + +\chapter{Work Performed} +\label{chap:work:performed} + +This chapter is dedicated to the solutions provided by this Master's +thesis. These solutions include: +\begin{itemize} +\item \textbf{Improving the accuracy of the Word2Vec model}: using a user-defined +depth to extract the child and parent nodes of a current node for each walk. In +addition, the centralization of the root node in the extracted walks +maximizes the number of training samples containing this root node and therefore +generates better quality embeddings. +\item \textbf{A BERT implementation}: builds its vocabulary only based on +special tokens and single extracted nodes, not allowing WordPiece splitting in +the tokenization of nodes. Finally, this version of BERT only considers +the MLM as a pre-training step, with training that tends to find a trade-off +between its time and the accuracy that this model will generate. +\item \textbf{A FastText implementation}: unlike its original version, its +implementation does not allow splitting $n$-grams on a defined minimum and maximum +length, but only according to a splitting function provided by a user. In +addition, the reimplementation of the Cython $n$-grams computation function in +Python to facilitate the use of \texttt{pyRDF2Vec} on Google +Colaboratory\footnote{Website that allows to run code on Google's cloud +servers.}. +\item \textbf{WideSampler}: sampling strategy that maximizes the extraction of + shared features between entities. +\item \textbf{SplitWalker}: walking strategy that extracts walks according to a + splitting function. +\item \textbf{A better architecture}: the \texttt{pyRDF2Vec} library now allows +to easily add walking strategies, sampling strategies, and embedding techniques +by reimplementing only a few functions. +\end{itemize} + +Finally, this Master's thesis implicitly proposes some research for future work +related to BERT. Among these, the injection of \texttt{(subject, object)} +2-tuples in BERT instead of two walks. Such an injection would allow BERT to +focus to predict predicates instead of seeing correlations between two different +walks. + +\section{Improving the Accuracy of the Word2Vec Model} +\label{sec:work:performed:word2vec} + +To better understand how it is possible to improve the model's accuracy +generated by Word2Vec, it is helpful to consider the initial problem with the +walk extraction. With RDF2Vec, the transformation for a $n$-tuple without any walks +limitation and concerning {\footnotesize\texttt{"URL\#Alice"}} as the root node +can be achieved with each walking strategy as follows: +\begin{table}[!ht] + \centering + \begin{threeparttable}[t] + \centering + \resizebox{\textwidth}{!}{% + \begin{tabular}{cll} + \toprule + \textbf{Walking Strategy} & \textbf{Initial/Transformed $\mathbf{n}$-tuple} \\ + \midrule + \multirow{2}{*}{Anonymous Walk} & {\footnotesize\texttt{("URL\#Alice", "URL\#knows","URL\#Bob")}} \\ + & {\footnotesize\texttt{("URL\#Alice", "1", "2")}} \\ + \midrule + \multirow{2}{*}{HALK} & {\footnotesize\texttt{("URL\#Alice", "URL\#knows", "URL\#Bob")}, \texttt{("URL\#Alice", "URL\#loves", "URL\#Bob")},} $\dotsc$ \\ + & {\footnotesize\texttt{("URL\#Alice", "URL\#knows","URL\#Bob")}}\tnote{\textcolor{blueLink}{1}} \\ + \midrule + \multirow{2}{*}{N-Gram} & {\footnotesize\texttt{("URL\#Alice", "URL\#knows", "URL\#Bob")}, \texttt{("URL\#Alice", "URL\#loves", "URL\#Dean")}} \\ + & {\footnotesize\texttt{("URL\#Alice", "URL\#knows", "0")}, \texttt{("URL\#Alice", "URL\#loves", "1")}}\tnote{\textcolor{blueLink}{2}} \\ + \midrule + \multirow{2}{*}{Walklets} & {\footnotesize\texttt{("URL\#Alice", "URL\#knows","URL\#Bob")}} \\ + & {\footnotesize\texttt{("URL\#Alice", "URL\#knows")}, \texttt{("URL\#Alice", "URL\#Bob")}} \\ + \midrule + \multirow{2}{*}{Weisfeiler-Lehman} & {\footnotesize\texttt{("URL\#Alice", "URL\#knows","URL\#Bob")}} \\ + & {\footnotesize\texttt{("URL\#Alice", "URL\#knows", "URL\#Bob")}, \texttt{("URL\#Alice", "URL\#knows", "URL\#Bob-URL\#knows")}}\tnote{\textcolor{blueLink}{3}} \\ + \bottomrule + \end{tabular} + }% + \begin{tablenotes} + \item[1] + Assuming a minor threshold frequency and an infrequent + {\footnotesize\texttt{"URL\#loves"}} hop compared to \\ other hops. + \item[2] Assuming at least one gram to relabel. If grams $> 2$, every object + names will remain \\ identical for this example. + \item[3] Assuming a Weisfeiler Lehman iteration of 1. + \end{tablenotes} + \end{threeparttable}% + \caption{Example of $n$-tuple Transformation for Type 2 Walking Strategies.} + \label{tab:walking:strategies} +\end{table} + +The walking strategies in Table \ref{tab:walking:strategies} already give good +results. However, the {\footnotesize\texttt{"URL\#Alice"}} root node is always +positioned at the beginning of each walk, reducing the richness of these walks +for embedding techniques like Word2Vec, which works with window size. As the +solicitation of nodes placed in the middle of a walk is higher due to selecting +context words, including the root node as close as possible to the middle for +each walk could generate better quality embeddings. Indeed, much more training +sampling would contain this root node. + +In addition to this positioning issue of the root node, \texttt{type 1} walking +strategies have the main disadvantage of continuously extracting child nodes of +a root node. In other words, the embedding techniques never know the root node's +parents. An alternative would be to extract the whole child and parent nodes of +a root node. Such extraction maximizes the extracted walk information and, +therefore, improves a model's accuracy after being trained with an embedding +technique. However, this alternative is not suitable when extracted walks are +limited, mainly used to process large KGs. Furthermore, when it comes to +positioning, the extraction of parent nodes from a root node also implies a +wrong positioning. Specifically, this root node would be this time placing as +the last node of walks, preceded by a sequence of predicates and objects, which +is not desirable. + +Based on these constraints, this Master's thesis proposes to apply a +user-defined depth to extract the child and parent nodes of a current node for +each walk. Assuming that the root node has parent nodes, each extracted walk +will have a better position for this root node. Indeed, each root node will be +preceded by a part of its parent nodes and succeeded by a part of its child +nodes. + +In Table \ref{tab:window:size}, assuming the sentence ``I will always remember +her'' and considering the word ``I'' as the root node of a walk, the latter is +only included twice in the context words. However, suppose now this word is +positioned in the center instead of the word "always". In that case, its +frequency of occurrence can be doubled, i.e., from two to four times for this +example. As a result, the embeddings generated for the different root nodes are +of better quality by the number of occurrence of root nodes and by the context +provided. + +\section{BERT Implementation} +\label{sec:bert:implementation} + +The recommended library to implement BERT is +\texttt{huggingface/transformers}\footnote{\url{https://huggingface.co/transformers/}} +which provides many pre-trained +models\footnote{\url{https://huggingface.co/models}} and essential functions to +create a model. As no pre-training model exists for BERT with KGs, it is +necessary to create this model from scratch, which requires three main steps: +\begin{enumerate} +\item \textbf{Build the vocabulary}: based on the nodes, including one line per + special token and one line per unique node, as part of a KG. +\item \textbf{Fits the BERT model}: based on the corpus of walks provided, including three main goals: + \begin{multicols}{2} + \begin{enumerate} + \item \textbf{Node tokenization}: in such a way that special tokens are + inserted on both sides of the nodes, taking care not to split them. Which unlike + words, splitting a URI is not desired. + \item \textbf{Pre-training}: only done with MLM, as the NSP pre-training + task is not helpful since the walks do not share any continuity. + \item \textbf{Training}: is done by providing a training set of formatted + walks, a data collator (e.g., \texttt{DataCollatorForLanguageModeling}), and the + training parameters. The walk formatting is necessary to ensure added + padding, truncating walks that are too long ($\geq$ 512 characters). + \end{enumerate} + \end{multicols} +\item \textbf{Transforms the provided entities into embeddings}: returns entity embeddings. +\end{enumerate} + +\begin{lstlisting}[caption=Creation of the Walk Data Set.,label=bert:walk:dataset] +class WalkDataset(Dataset): + def __init__(self, corpus, tokenizer): + self.walks = [ + tokenizer( + " ".join(walk), padding=True, truncation=True, max_length=512 + ) + for walk in corpus + ] + + def __len__(self): + return len(self.walks) + + def __getitem__(self, i): + return self.walks[i] +\end{lstlisting} + +In Algorithm \ref{bert:walk:dataset}, creating the walks data set for BERT +is done by creating a dedicated class. Within this class, tokenization is necessary. +Each walk is truncated to 512 characters, followed by padding to handle +walks of the same size. Finally, it is also useful to implement the +Dunder\footnote{Also called \emph{magic} methods.} \texttt{\_\_len\_\_} and +\texttt{\_\_getitem\_\_} methods to define the size of a sample of training data +and for the fetching of this sample. + +\begin{lstlisting}[caption=Creation of Node Vocabulary.,label=bert:node:vocabulary] +def _build_vocabulary(self, nodes, is_update = False): + with open(self.vocab_filename, "w") as f: + if not is_update: + for token in ["[PAD]", "[UNK]", "[CLS]", "[SEP]", "[MASK]"]: + f.write(f"{token}\n") + self._vocabulary_size += 1 + for node in nodes: + f.write(f"{node}\n") + self._vocabulary_size += 1 +\end{lstlisting} + +In Algorithm \ref{bert:node:vocabulary}, each walk node is stored in a file with +special tokens at the beginning of the file, namely: \texttt{[PAD]}, +\texttt{[UNK]}, \texttt{[CLS]}, \texttt{[SEP]}, and \texttt{[MASK]}. Finally, a +boolean is also sent to update or not an already existing vocabulary and avoid +the complete re-training of the model. + +\begin{lstlisting}[caption=Fitting the BERT Model According to the Provided Walks.,label=bert:fit] +def fit(self, walks, is_update = False): + walks = [walk for entity_walks in walks for walk in entity_walks] + nodes = list({node for walk in walks for node in walk}) + self._build_vocabulary(nodes, is_update) + self.tokenizer = BertTokenizer( + vocab_file=self.vocab_filename, + do_lower_case=False, + never_split=nodes, + ) + self.model_ = BertForMaskedLM( + BertConfig( + vocab_size=self._vocabulary_size, + max_position_embeddings=512, + type_vocab_size=1, + ) + ) + Trainer( + model=self.model_, + args=self.training_args, + data_collator=DataCollatorForLanguageModeling( + tokenizer=self.tokenizer + ), + train_dataset=WalkDataset(walks, self.tokenizer), + ).train() + \end{lstlisting} + +In Algorithm \ref{bert:fit}, the training of the BERT model consists of +retrieving each unique node from the provided walks, tokenizing these walks, +choosing a suitable hyperparameter config, and running the training based on a +set of walks data. + +BERT needs to be trained on a large enough corpus of walks to provide good +results. Having such a corpus is not always possible, depending on the size of +some KGs. In addition, hyperparameters for training BERT impact the model's +accuracy and training time. This training time can take hours, days, weeks, if +not more. Therefore it is necessary to improve as much as possible the quantity +and quality of the walks corpus with RDF2Vec to reduce this training time. + +\begin{lstlisting}[caption=Getting the Entities' Embeddings with BERT.,label=bert:embeddings] +def transform(self, entities): + check_is_fitted(self, ["model_"]) + return [ + self.model_.bert.embeddings.word_embeddings.weight[ + self.tokenizer(entity)["input_ids"][1] + ] + .cpu() + .detach() + .numpy() + for entity in entities + ] +\end{lstlisting} + +In Algorithm \ref{bert:embeddings}, the retrieving of embeddings for the +requested entities, i.e., the root notes, consists of recovering the generated +embeddings and ensuring their good formatting. + +These methods are sufficient for a classical implementation of BERT. All the +subtlety of generating a correct model is characterized by the extraction and +injection of walks and the values of chosen hyperparameters. + +\section{FastText Implementation} +\label{sec:fasttext:implementation} + +To implement FastText, the +\texttt{gensim}\footnote{\url{https://github.com/RaRe-Technologies/gensim}} +library is recommended to be used. However, \texttt{pyRDF2Vec} had to +reimplement much of the code in order: +\begin{itemize} +\item \textbf{To remove the \texttt{min\_n} and \texttt{max\_n} parameters for $n$-grams + splitting}: the \texttt{object} nodes in \texttt{pyRDF2Vec} are encoded in MD5 + to reduce their storage in RAM. Therefore, splitting them into $n$-grams is pointless. +\item \textbf{To allow a user to compute $n$-grams for walks only by separating} (default + split by their symbols) \textbf{the URIs of subjects and predicates}: a user + will likely want to provide an alternative splitting strategy for computing entity + $n$-grams on the KG. If this is the case, \texttt{pyRDF2Vec} allows a user + to implement this function that FastText will use. +\item \textbf{To avoid dependency on Cython}: Cython is a programming language between +Python and C. Its main interest is to obtain performances of calculation time +similar to C for specific functions in Python by reimplementing them in +Cython. The gensim library uses Cython for the calculation of n-grams +hashes. However, \texttt{pyRDF2Vec} has chosen to reimplement this function in +Python to facilitate its use on Google Colaboratory. +\end{itemize} + +\begin{lstlisting}[caption=Reimplementation of the Hash Calculation Functions in + \texttt{gensim}.,label=fasttext:hash] + def compute_ngrams_bytes(entity): + if "http" in entity: + ngrams = " ".join(re.split("[#]", entity)).split() + return [str.encode(ngram) for ngram in ngrams] + return [str.encode(entity)] + + def ft_hash_bytes(self, bytez: bytes) -> int: + h = 2166136261 + for b in bytez: + h = h ^ b + h = h * 16777619 + return h + + def ft_ngram_hashes(entity, num_buckets = 2000000): + encoded_ngrams = func_computing_ngrams(entity) + hashes = [ft_hash_bytes(n) % num_buckets for n in encoded_ngrams] + return hashes + + def recalc_char_ngram_buckets(bucket, buckets_word, index_to_key) -> None: + if bucket == 0: + buckets_word = [np.array([], dtype=np.uint32)] * len(index_to_key) + return + self.buckets_word = [None] * len(index_to_key) + for i, word in enumerate(index_to_key): + buckets_word[i] = np.array(ft_ngram_hashes(word, 0, 0, self.bucket), dtype=np.uint32) +\end{lstlisting} + +In Algorithm \ref{fasttext:hash}, the functions present in \texttt{gensim} are +reimplemented in such a way to include the splitting function of +\texttt{pyRDF2Vec}. Added to that this reimplementation does not consider the +use of Cython anymore. + +\begin{lstlisting}[caption=Fitting the FastText Model According to the Provided Walks.,label=fasttext:fit] +def fit(self, walks, is_update = False): + corpus = [walk for entity_walks in walks for walk in entity_walks] + self._model.build_vocab(corpus, update=is_update) + self._model.train( + corpus, + total_examples=self._model.corpus_count, + epochs=self._model.epochs, + ) + return self +\end{lstlisting} + +In Algorithm \ref{fasttext:fit}, training with FastText consists of extracting +each node from each walk, building the vocabulary, and training the model based +on the corpus of walks. + +\begin{lstlisting}[caption=Getting the Entity Embeddings with FastText.,label=fasttext:transform] +def transform(self, entities): + if not all([entity in self._model.wv for entity in entities]): + raise ValueError( + "The entities must have been provided to fit() first " + "before they can be transformed into a numerical vector." + ) + return [self._model.wv.get_vector(entity) for entity in entities] +\end{lstlisting} + +In Algorithm \ref{fasttext:transform}, even though FastText can generate entity +embeddings that it has not learned, \texttt{pyRDF2Vec} throws an exception +instead of avoiding any unpleasant surprises from the model’s accuracy. + +\section{SplitWalker} +\label{sec:split:walker} + +Based on the idea of FastText, but directly applied to the extraction of walks, +this Master's thesis proposes \texttt{SplitWalker} as a new \texttt{type +2}. Specifically, this strategy splits the vertices of the random walks for a +based entity. To achieve this, each vertex, except the root node, is split +according to symbols, capitalization, and numbers by removing any duplication. + +\begin{table}[!ht] + \centering + \resizebox{\textwidth}{!}{% + \begin{tabular}{cll} + \toprule + & \textbf{Initial Node} & \textbf{Node After Splitting} \\ + \midrule + \multirow{4}{*}{\footnotesize Walk 1} & \footnotesize\texttt{http://dl-learner.org/carcinogenesis\#d19} & \footnotesize\texttt{http://dl-learner.org/carcinogenesis\#d19} \\ + & \multirow{2}{*}{\footnotesize\texttt{http://dl-learner.org/carcinogenesis\#hasBond}} & \footnotesize\texttt{has} \\ + & & \footnotesize\texttt{bond} \\ + & \footnotesize\texttt{http://dl-learner.org/carcinogenesis\#bond3209} &\footnotesize\texttt{3209} \\ + \midrule + \multirow{3}{*}{\footnotesize Walk 2} & \footnotesize\texttt{http://dl-learner.org/carcinogenesis\#d19} & \footnotesize\texttt{http://dl-learner.org/carcinogenesis\#d19} \\ + & \footnotesize\texttt{http://www.w3.org/1999/02/22-rdf-syntax-ns\#type} & \footnotesize\texttt{type} \\ + & \footnotesize\texttt{http://dl-learner.org/carcinogenesis\#Compound} & \footnotesize\texttt{compound} \\ + \bottomrule + \end{tabular} + }% + \caption{Example of Use of \texttt{SplitWalker}.} + \label{work:performed:splitwalker} +\end{table} + +In Table \ref{work:performed:splitwalker}, two walks are transformed by +\texttt{SplitWalker}. Both keep their root node intact. However, the first walk +has the \texttt{.../hasBond} split by the letter \texttt{B} into two nodes: +\texttt{has} and \texttt{bond}. In addition, its third node +\texttt{.../bond3209} is also split into two nodes: \texttt{bond} and +\texttt{3209}, but since \texttt{bond} is an existing node in the walk, it is +removed from it. Finally, the second walk has the particularity to have a node +with a capital letter. In this case, this node is rewritten in lowercase. + +\begin{lstlisting}[caption=Splits Nodes of Random Walks with \texttt{SplitWalker}.,label=splitwalker:split] +def basic_split(self, walks): + canonical_walks = set() + for walk in walks: + canonical_walk = [walk[0].name] + for i, _ in enumerate(walk[1::], 1): + vertices = [] + if "http" in walk[i].name: + vertices = " ".join(re.split("[\#]", walk[i].name)).split() + if i % 2 == 1: + name = vertices[1] if vertices else walk[i].name + preds = [ + sub_name + for sub_name in re.split(r"([A-Z][a-z]*)", name) + if sub_name + ] + for pred in preds: + canonical_walk += [pred.lower()] + else: + name = vertices[-1] if vertices else walk[i].name + objs = [] + try: + objs = [str(float(name))] + except ValueError: + objs = re.sub("[^A-Za-z0-9]+", " ", name).split() + if len(objs) == 1: + match = re.match( + r"([a-z]+)([0-9]+)", objs[0], re.I + ) + if match: + objs = list(match.groups()) + for obj in objs: + canonical_walk += [obj.lower()] + canonical_walk = list(dict(zip(canonical_walk, canonical_walk))) + canonical_walks.add(tuple(canonical_walk)) + return canonical_walks +\end{lstlisting} + +Algorithm \ref{splitwalker:split} starts by traversing each provided +walk, making sure to save the root node characterized by the first vertex of the +walk. Then, this function looks to see if that node has the prefix ``http'' for +each node. If it does, then that node is split by the \texttt{\#} +symbol. Otherwise, if the current node is a predicate, this function does an +uppercase split to create other nodes. Finally, this process is also done in the +case where the node contains numbers. In the end, this function deletes all the +duplicated nodes and returns the walks. + +\section{WideSampler} +\label{sec:wide:sampler} + +Based on the principle that humans tend to classify objects according to common +features (e.g., color and shape), this Master's thesis proposes a new sampling +strategy called \texttt{WideSampler}. This strategy addresses the assumption +that single entity-specific features would have a negligible impact on the +quality of the generated embeddings. \texttt{WideSampler} assigns higher weights +to edges that lead to the most significant number of predicates and objects in +the neighborhood and terms of occurrence in a graph to extract a maximum of +shared features between entities. + +After training the model, this walking strategy can retrieve the weight of a +neighboring hop as shown below. +\begin{algorithm} + \caption{\texttt{get\_weight(h, d, c)}} + \label{alg:wide:sampler:get:weight} + \begin{algorithmic}[1] + \REQUIRE a $\mathcal{H}$ 2-tuple that contains a predicate and an object. + \REQUIRE a $\mathcal{D}$ array of $n \geq 1$ degree indexed from $0$ to $n - 1$ + \REQUIRE a $\mathcal{C}$ array of $n \geq 1$ counter of neighbors indexed from $0$ to $n - 1$ + \ENSURE The weight of the hop for this predicate + \IF{$\mathcal{D}_{preds}$ and $\mathcal{D}_{objs}$ and $\mathcal{C}$} + \RETURN $\left(\mathcal{C}[\mathcal{H}[0]_{name}]\ +\ \mathcal{C}[\mathcal{H}[1]_{name}]\right)$ $\left(\dfrac{\mathcal{D}_{preds}[\mathcal{H}[0]_{name}] + \mathcal{D}_{objs}[\mathcal{H}[1]_{name}]}{2}\right)$ + \ENDIF + \end{algorithmic} +\end{algorithm} + +Algorithm \ref{alg:wide:sampler:get:weight} assigns a weight to a +\texttt{(predicate, object)} hop according to the multiplication of two +sums. The first one considers the child nodes of a predicate and the parent +nodes of an object node. The second one considers the number of occurrences of +this predicate and this node in the whole KG. Finally, the second sum is divided +by half to provide a slight preference to a hop that reaches multiples nodes. + +\newpage + +\begin{algorithm} + \caption{\texttt{fit(v)}} + \label{alg:wide:sampler:fit} + \begin{algorithmic}[1] + \REQUIRE an $\mathcal{V}$ array of $n \geq 1$ edges indexed from $0$ to $n - 1$ + \ENSURE Fits the WideSampler sampling strategy + \STATE $\mathcal{C}_{objs}$ $\leftarrow$ new array of $n$ objects. + \STATE $\mathcal{C}_{preds}$ $\leftarrow$ new array of $n$ predicates. + \FORALL{$vertex \in \mathcal{V}$} + \IF{$vertex$ is predicate} + \STATE $\mathcal{C}_{neighbors}[vertex_{name}] = |\texttt{get\_children(vertex)}|$ + \STATE $\mathcal{C}_{tmp} \leftarrow \mathcal{C}_{preds}$ + \ELSE + \STATE $\mathcal{C}_{neighbors}[vertex_{name}] = |\texttt{get\_parents(vertex)}|$ + \STATE $\mathcal{C}_{tmp} \leftarrow \mathcal{C}_{objs}$ + \ENDIF + + \IF{$vertex_{name}$ in $\mathcal{C}_{tmp}$} + \STATE $\mathcal{C}_{tmp}[vertex_{name}] \leftarrow \mathcal{C}[vertex_{name}] + 1$ + \ELSE + \STATE $\mathcal{C}_{tmp}[vertex_{name}] \leftarrow 1$ + \ENDIF + \ENDFOR + \end{algorithmic} +\end{algorithm} + +Algorithm \ref{alg:wide:sampler:fit} trains the \texttt{WideSampler} strategy by +iterating through a set of vertices. Depending on the vertex, the algorithm +considers the number of children or parents of this vertex. If it is a +predicate, then the number of its child nodes is stored in a counter. Otherwise, +the algorithm stores the number of parent nodes in another counter. Finally, the +number of occurrences of each identical vertex in the whole KG is also +collected. + +\section{Library Architecture} +\label{sec:pyRDF2Vec} + +\texttt{pyRDF2Vec}\footnote{\url{https://github.com/IBCNServices/pyRDF2Vec}} is +the Python library created by IDLab that allows to use RDF2Vec. Through the +internship and this Master's thesis, this library has undergone many changes in +its architecture to improve its use. +\begin{figure}[!ht] + \centering + \resizebox{\linewidth}{!} { + \begin{tikzpicture}[>=stealth', + extract_walks/.style={draw,minimum width=.8cm,minimum height=.8cm,fill=mygreen!40}, + process/.style={draw,minimum width=1cm,minimum height=1cm,node distance=0.35cm,fill=mybrown!20} + ] + \node[draw,minimum width=2.5cm,minimum height=3cm,loosely dashed,color=darkBlue] at (0,0) (graph_entities) {}; + \node[draw,minimum width=2cm,minimum height=1cm,yshift=-65pt,above=of graph_entities,fill=myblue] (graph) {Graph}; + \node[draw,minimum width=2cm,minimum height=1cm,yshift=15pt,below=of graph,fill=myblue] (entities) {Entities}; + \node[draw,minimum width=2cm,minimum height=1cm,yshift=2pt,above=of graph,fill=myblue!50] (connector) {Connector}; + + \node[inner sep=0pt,xshift=-20pt,above=of connector] (rdf) {\includegraphics[width=0.074\textwidth]{img/rdf}}; + \node[inner sep=0pt,xshift=20pt,above=of connector] (sparql) {\includegraphics[width=0.08\textwidth]{img/sparql}}; + + \node[label,below of=graph_entities,yshift=-1.1cm,color=darkBlue] {\textbf{Inputs}}; + + \node[draw,minimum width=3cm,minimum height=1cm,right=of graph_entities,fill=myyellow] (transformer) {Transformer}; + \node[draw,minimum width=2.5cm,minimum height=3cm,loosely dashed,color=darkRed,right=of transformer] (walker_sampler) {}; + \node[draw,minimum width=2cm,minimum height=1cm,yshift=-65pt,above=of walker_sampler,fill=myred] (walker) {Walker}; + \node[draw,minimum width=2cm,minimum height=1cm,yshift=15pt,below=of walker,fill=myred] (sampler) {Sampler}; + \node[draw,minimum width=3cm,minimum height=1cm,above=of transformer,fill=mypurple!50] (embedder) {Embedder}; + \node[draw,ellipse,minimum width=3cm,minimum height=1cm,above=of embedder,fill=mypurple] (embeddings) {Embeddings}; + \node[draw,ellipse,minimum width=3cm,minimum height=1cm,node distance=0.5cm,right=of embeddings,fill=mypurple] (literals) {Literals}; + + \node[label,above of=walker_sampler,xshift=0.3cm,yshift=20pt,color=darkRed] {\textbf{Strategy}}; + + \node[inner sep=0pt,xshift=-50pt,above right=of embeddings] (sklearn) {\includegraphics[width=0.15\textwidth]{img/scikit-learn}}; + + \node[process,node distance=9cm,right=of connector] (p1) {P1/T1}; + + \node[process,below=of p1] (p2) {P2/T2}; + \node[process,below=of p2] (p3) {P3/T3}; + \node[process,below=of p3] (p4) {P4/T4}; + + \node[extract_walks,right=of p1] (extract_walks_1) {Extract Walks}; + \node[extract_walks,right=of p2] (extract_walks_2) {Extract Walks}; + \node[extract_walks,right=of p3] (extract_walks_3) {Extract Walks}; + \node[extract_walks,right=of p4] (extract_walks_4) {Extract Walks}; + + \node[draw,minimum width=7.5cm,minimum height=1.5cm,xshift=1.8cm,yshift=-2.3cm,above=of embeddings,loosely dashed,color=darkPurple] (output) {}; + \node[label,above of=output,xshift=2.5cm,yshift=-0.1cm,color=darkPurple] {\textbf{Outputs}}; + + \node[label,below of=p4,yshift=-0.10cm] {\dots}; + \node[label,below of=extract_walks_4,yshift=-0.10cm] {\dots}; + + \node[draw,ellipse,minimum width=3cm,minimum height=1cm, node distance=8cm,right=of walker,fill=mygreen] (walks) {Walks}; + + \draw[arrow,shorten >=0.2cm,shorten <=0.2cm] (transformer) -- (walker_sampler) node[midway,above] {(2)}; + + \draw[arrow,shorten >=0.2cm,shorten <=0.2cm] (rdf.south) -- ([xshift=-20pt]connector.north); + \draw[arrow,shorten >=0.2cm,shorten <=0.2cm] (sparql.south) -- ([xshift=20pt]connector.north); + \draw[arrow,shorten >=0.05cm,shorten <=0.2cm] (connector) -- (graph); + + \draw[arrow,shorten >=0.2cm,shorten <=0.2cm] (p1) -- (extract_walks_1); + \draw[arrow,shorten >=0.2cm,shorten <=0.2cm] (p2) -- (extract_walks_2); + \draw[arrow,shorten >=0.2cm,shorten <=0.2cm] (p3) -- (extract_walks_3); + \draw[arrow,shorten >=0.2cm,shorten <=0.2cm] (p4) -- (extract_walks_4); + + \draw[arrow,shorten >=0.2cm,shorten <=0.2cm] (literals) -- (sklearn); + + \draw[shorten <=0.1cm] ([yshift=12pt]walker.east) -| ([xshift=-20pt]p1.west); + \draw[arrow,shorten >=0.1cm] ([xshift=-20pt]p1.west) -- (p1.west); + + \draw[shorten <=0.1cm] ([yshift=4pt]walker.east) -| ([xshift=-15pt]p2.west); + \draw[arrow,shorten >=0.1cm] ([xshift=-15pt]p2.west) -- (p2.west); + + \draw[shorten <=0.1cm] ([yshift=-4pt]walker.east) -| ([xshift=-15pt]p3.west); + \draw[arrow,shorten >=0.1cm] ([xshift=-15pt]p3.west) -- (p3.west); + + \draw[shorten <=0.1cm] ([yshift=-12pt]walker.east) -| ([xshift=-20pt]p4.west); + \draw[arrow,shorten >=0.1cm] ([xshift=-20pt]p4.west) -- (p4.west); + + \draw[shorten <=0.1cm] (extract_walks_1.east) -| ([xshift=-15pt,yshift=12pt]walks.west); + \draw[arrow,shorten >=0.1cm] ([xshift=-15pt,yshift=12pt]walks.west) -- ([yshift=12pt]walks.west); + + \draw[shorten <=0.1cm] (extract_walks_2.east) -| ([xshift=-20pt,yshift=4pt]walks.west); + \draw[arrow,shorten >=0.1cm] ([xshift=-20pt,yshift=4pt]walks.west) -- ([yshift=4pt]walks.west); + + \draw[shorten <=0.1cm] (extract_walks_3.east) -| ([xshift=-20pt,yshift=-4pt]walks.west); + \draw[arrow,shorten >=0.1cm] ([xshift=-20pt,yshift=-4pt]walks.west) -- ([yshift=-4pt]walks.west); + + \draw[shorten <=0.1cm] (extract_walks_4.east) -| ([xshift=-15pt,yshift=-12pt]walks.west); + \draw[arrow,shorten >=0.1cm] ([xshift=-15pt,yshift=-12pt]walks.west) -- ([yshift=-12pt]walks.west); + + \draw[arrow,shorten >=0.1cm,shorten <=0.1cm] (sampler) -- (walker); + \draw[arrow,shorten >=0.2cm,shorten <=0.2cm] (transformer) -- (embedder) node[midway,right] {(3)}; + \draw[arrow,shorten >=0.05cm,shorten <=0.2cm] (embedder) -- (embeddings); + \draw[arrow,shorten >=0.2cm,shorten <=0.2cm] (embeddings) -- (sklearn); + + \draw[arrow,shorten >=0.2cm,shorten <=0.2cm] (graph_entities) -- (transformer.west) node[midway,above] {(1)}; + + \draw[shorten <=0.2cm] ([xshift=0.2cm]transformer) -- ([yshift=1.3cm]walker_sampler.north); + \draw[arrow,shorten >=0.05cm] ([yshift=1.3cm]walker_sampler.north) -- (literals); + + \draw ([xshift=10pt]walks.east) |- ([yshift=-20pt]extract_walks_4.south); + \draw[shorten <=0.1cm] (walks) -- ([xshift=10pt]walks.east); + \draw[arrow,shorten >=0.2cm] ([yshift=-20pt]extract_walks_4.south) -| (transformer.south); + \end{tikzpicture} + } + \caption{Workflow of \texttt{pyRDF2Vec}.} + \label{tikz:workflow} +\end{figure} + +In Figure \ref{tikz:workflow}, the workflow of \texttt{pyRDF2Vec} includes three +primary operations and is divided into seven main consecutive significant +blocks: +\begin{multicols}{2} +\begin{enumerate} +\item \textbf{Connector}: in charge of interaction with a local or remote graph. +\item \textbf{Graph}: in charge of providing a graph encoding the knowledge-based. +\item \textbf{Entities}: in charge of provides the entities in a +\texttt{rdflib.URI.term} or \texttt{str} type to generate the embeddings. +\item \textbf{Transformer}: in charge of converting graphs into embeddings for +downstream ML tasks, using a walking strategy and sampling strategy and an +embedder. +\item \textbf{Sampler}: in charge of prioritizing the use of some paths over +others using a weight allocation strategy. +\item \textbf{Walker}: in charge of extracting walks in a KG from provided +entities and optionally from a sampling strategy using multiple +processors/threads. +\item \textbf{Embedder}: in charge of training a model with an embedding +technique using extracted walks and therefore generate embeddings of entities +provided by a user. +\end{enumerate} +\end{multicols} + +The design of such architecture allows having a long-term vision. Due to this +architecture, a user can contribute to \texttt{pyRDF2Vec} and easily add new +walking strategies and sampling and embedding techniques. For this Master’s +thesis, implementing this architecture was necessary to facilitate the +comparison of embedding techniques. Each new embedding technique is added in an +\texttt{Embedder} package and must reimplement the \texttt{fit} and +\texttt{get\_weight} functions of the \texttt{Embedder} class. + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "latex" +%%% End:

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