SGF.m

function [nmi, label] = SGF(data, truth, knn, beta, gamma, tol, tol2)
% Use similarity graph fusion (SGF) algorithm to perform multi-view clustering.
% Inputs:
%   data - a cell matrix which contains some feature matrices with each row being an instance
%   truth - a column vector, the target label for all instances
%   knn - number of k-nearest neighbors (set knn=0 if using fully connected graph)
%   beta, gamma - hyperparameters for the algorithm
% Optional Inputs:
%   tol, tol2 - the tolerance that determines convergence of algorithm
% Outputs:
%   nmi - normalized mutual information
%   label - label generated by spectral clustering on the learned unified graph
% See "Youwei Liang, Dong Huang, and Chang-Dong Wang. Consistency Meets 
% Inconsistency: A Unified Graph Learning Framework for Multi-view 
% Clustering. 2019 IEEE International Conference on Data Mining(ICDM)."
% for a detailed description of the algorithm.
% Author: Youwei Liang
% 2019/08/31

if nargin < 6
    tol = 1e-4;
    tol2 = 1e-2;
end
self_b = beta; cross_b = gamma;
v = length(data);  % number of views
affinity = cell(1, v);
original_affinity = cell(1, v);
idx = cell(1, v);
n = length(truth);
numClust = length(unique(truth));
ONE = ones(n);
knn_idx = false(n);

for i=1:v
    try
        s = sprintf('kernel%d.mat', i); % try to read the weight matrix (if saved previously)
        load(s)
    catch
        W = make_affinity_matrix(data{i}, 'euclidean');
%         save(s, 'W')  % weight matrix may be saved for repeating experiments
    end
    original_affinity{i} = W;
    if knn ~= 0  % not using fully connected graph
        [W, idx{i}] = kNN(W, knn);
        [~, tp] = extract_from_idx(ONE, idx{i});
        knn_idx = knn_idx | logical(tp);  % common kNN index for all views
    end
    affinity{i} = W;
end

if knn ~= 0
    for i=1:v
        for j=1:v
            if j~=i
                [~, tp] = extract_from_idx(original_affinity{i}, idx{j});
                affinity{i} = affinity{i} + (tp + tp')/2;
            end
        end
    end
end

% make knn index symmetric
if knn~=0
    knn_idx = knn_idx | knn_idx'; %#ok<*BDSCA>
else
    knn_idx = true(n);
end

[com_affinity, E, A] = consistent_graph(affinity, knn_idx, self_b, cross_b, tol, tol2);

% do kNN again
com_a = kNN(com_affinity, knn);

[label] = SpectralClustering(com_a, numClust, 3);  % obtain lable for each instance, label # starts from 1

nmi = NMImax(truth, label);
% [ACC, MIhat, Purity] = ClusteringMeasure(truth, label);
fprintf('knn:%2d, beta:%1.0e, gamma:%1.0e, NMI: %.3f\n', knn, self_b, cross_b, nmi)