Panel_Data_Analysis-Tucker3_Decomposition_Python.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### trying tucker3 decomposition using python\n",
    "\n",
    "define the function of tucker3 decomposition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(19, 31, 4)\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import tensorly as tl\n",
    "from tensorly.decomposition import tucker\n",
    "import ast\n",
    "\n",
    "def load_tensor_from_file(file_path):\n",
    "    with open(file_path, 'r') as file:\n",
    "        contents = file.read()\n",
    "    tensor_data = np.array(ast.literal_eval(contents))\n",
    "    return tensor_data\n",
    "\n",
    "def perform_tucker_decomposition(tensor_data, ranks):\n",
    "    tensor = tl.tensor(tensor_data)\n",
    "    core, factors = tucker(tensor, rank=ranks)\n",
    "    return core, factors\n",
    "\n",
    "file_path = 'tensor.txt'\n",
    "tensor_data = load_tensor_from_file(file_path)\n",
    "print(tensor_data.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 2:\n",
    "### Conduct Tucker3 analysis with $X_{new}(n\\times m \\times r)$ .The component load constraint of the three modes is orthogonal, and the component decomposition dimensions P,Q,S of the model are calculated according to the $\\overline{R}^2$ under the premise of ensuring the interpretability of the model\n",
    "\n",
    "Tucker3 model:\n",
    "$$\n",
    "x_{ijt} = \\sum_{p=1}^{P} \\sum_{q=1}^{Q} \\sum_{s=1}^{S} b_{jq}c_{ts}g_{pqs} + e_{ijt}                \n",
    "$$\n",
    "and in a matrix format:\n",
    "$$\n",
    "X_{a} = AG_{a}(C'\\otimes B') + E_{a} \n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "19\n",
      "31\n",
      "4\n",
      "0.9816127035389068\n",
      "Best core shape: (6, 4, 3)\n",
      "Best factors shapes: [(19, 6), (31, 4), (4, 3)]\n"
     ]
    }
   ],
   "source": [
    "from tensorly import tucker_to_tensor, norm\n",
    "\n",
    "best_fit = None\n",
    "best_percent = -np.inf\n",
    "mean_tensor = tl.mean(tensor_data)\n",
    "\n",
    "n = 31\n",
    "m = 4\n",
    "r = 19\n",
    "\n",
    "print(tensor_data.shape[0])\n",
    "print(tensor_data.shape[1])\n",
    "print(tensor_data.shape[2])\n",
    "\n",
    "\n",
    "for p in range(1, min(n, tensor_data.shape[1])+1):\n",
    "    for q in range(1, min(m, tensor_data.shape[2])+1):\n",
    "        for s in range(1, min(r, tensor_data.shape[0])+1):\n",
    "            tucker_result = tucker(tensor_data, rank=[p, q, s], n_iter_max=25, tol=1e-05)\n",
    "            core = tucker_result.core\n",
    "            factors = tucker_result.factors\n",
    "            reconstruction = tucker_to_tensor(tucker_result)\n",
    "            resid_2 = norm(tensor_data - reconstruction, 2)**2\n",
    "            total_var = norm(tensor_data - mean_tensor, 2)**2\n",
    "            R_2 = 1 - resid_2 / total_var\n",
    "            N = np.prod(tensor_data.shape)\n",
    "            k = sum(factor.shape[0] for factor in factors) + np.prod(core.shape) - 1\n",
    "            R_2_adj = 1 - ((1 - R_2) * (N - 1) / (N - k - 1))\n",
    "            \n",
    "            if isinstance(R_2_adj, np.float64) and not np.isnan(R_2_adj):\n",
    "                if R_2_adj > best_percent:\n",
    "                    best_percent = R_2_adj\n",
    "                    best_fit = tucker_result\n",
    "\n",
    "print(best_percent)\n",
    "if best_fit is not None:\n",
    "    print(\"Best core shape:\", best_fit.core.shape)\n",
    "    print(\"Best factors shapes:\", [factor.shape for factor in best_fit.factors])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 3:\n",
    "\n",
    "### Calculate the combined score of the \"variable-time\" mode on the p-th component of the individual mode $score_{pjt}$\n",
    "\n",
    "$$\n",
    "score_{pjt} = \\sum_{q=1}^{Q} \\sum_{s=1}^{S} b_{jq}c_{ts}g_{pqs}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0. 0. 0. 0.]\n",
      "Score for factor 1: -7.0857057209523955\n",
      "Score for factor 2: 0.51969174417314\n",
      "Score for factor 3: 0.49494826448288065\n",
      "Score for factor 4: 0.11102018475195384\n",
      "Scores: [-7.08570572  0.51969174  0.49494826  0.11102018]\n"
     ]
    }
   ],
   "source": [
    "core = best_fit.core\n",
    "factors = best_fit.factors\n",
    "\n",
    "P = factors[1].shape[1]  \n",
    "Q = factors[2].shape[1]  \n",
    "S = factors[0].shape[1] \n",
    "\n",
    "p = 0  \n",
    "j = 0\n",
    "t = 0\n",
    "score_pjt = np.zeros(P)\n",
    "print(score_pjt)\n",
    "\n",
    "for p in range(P):\n",
    "    for q in range(Q):\n",
    "        for s in range(S):\n",
    "            score_pjt[p] += factors[2][j, q] * factors[0][t, s] * core[s, p, q]    \n",
    "    print(f\"Score for factor {p+1}: {score_pjt[p]}\")\n",
    "print(\"Scores:\", score_pjt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 4:\n",
    "### Calculate the Minkowski distance between two region slices:$X_{i1..} (m \\times r)$ and $X_{i2..} (m \\times r)$\n",
    "\n",
    "Given the panel data $X (n \\times m \\times r)$ where the two horizontal slice matrices are $X_{i1..} (m \\times r)$ and $X_{i2..} (m \\times r)$，$i1, i2 = 1, 2, ..., n$，and both matrices are observations of the same $m$ variables over $r$ periods, the \"individual\" distance $d_{i1i2}^A$ between $i1$ and $i2$ is defined as:\n",
    "\n",
    "$$\n",
    "d_{i1i2}^A = \\left( \\sum_{p=1}^{P} w_p(a_{i1p} - a_{i2p})^h \\right)^{1/h} = \\left( \\sum_{p=1}^{P} \\sum_{q=1}^{Q} \\sum_{s=1}^{S} b_{jq}c_{ts}g_{pqs}(a_{i1p} - a_{i2p})^h \\right)^{1/h}\n",
    "$$\n",
    "\n",
    "Here，$w_p = score_{pjt}$，and in this article $d_{i1i2}^A$  is defined based on a form of Minkowski distance, which can be adjusted according to different research purposes and data types. Furthermore, based on this equation, the distances between \"variable modes\" and \"time modes\" can also be articulated, thus allowing for separate clustering of variables and time.\n",
    "\n",
    "We set h to 3 at this time, and we can change it if we want more experiments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Weighted Minkowski Distance:\n",
      "[[0.         0.0459605  0.3582037  0.47317028 0.47929358 0.29262264\n",
      "  0.07967763 0.12424944 0.0195838  0.17283018 0.10125852 0.21830942\n",
      "  0.0904033  0.20706746 0.20918433 0.07980062 0.02723666 0.02184922\n",
      "  0.09033866 0.13635009 0.02669607 0.04688954 0.31507933 0.13021533\n",
      "  0.09271321 0.07465697 0.21664744 0.05818432 0.37021696 0.17621138\n",
      "  0.09663465]\n",
      " [0.0459605  0.         0.36741024 0.47784118 0.51495987 0.32167672\n",
      "  0.09104495 0.16897486 0.03247726 0.12691364 0.05570891 0.17770015\n",
      "  0.05373663 0.205144   0.19370367 0.05478379 0.04319169 0.02473605\n",
      "  0.045358   0.17949692 0.02783107 0.02953053 0.35923591 0.10717516\n",
      "  0.10060305 0.11798902 0.21560068 0.08484725 0.40468902 0.18035236\n",
      "  0.1402815 ]\n",
      " [0.3582037  0.36741024 0.         0.68012639 0.72283082 0.47177265\n",
      "  0.36753397 0.40494196 0.35830399 0.4124211  0.38518719 0.43302049\n",
      "  0.41277971 0.52961496 0.52667147 0.41855954 0.378267   0.3579192\n",
      "  0.38675477 0.44267801 0.35136899 0.37509958 0.51421319 0.41196133\n",
      "  0.35518923 0.37099016 0.47910886 0.39830538 0.60670953 0.42025055\n",
      "  0.41252192]\n",
      " [0.47317028 0.47784118 0.68012639 0.         0.39875587 0.70885746\n",
      "  0.39443071 0.44394189 0.4596265  0.49502225 0.49946504 0.60281447\n",
      "  0.44840627 0.61709806 0.61530958 0.44257101 0.44986651 0.47841103\n",
      "  0.49777534 0.48132212 0.46641802 0.44831423 0.60630412 0.57744327\n",
      "  0.38455014 0.50692596 0.26824241 0.51571864 0.72583886 0.29861508\n",
      "  0.47469237]\n",
      " [0.47929358 0.51495987 0.72283082 0.39875587 0.         0.57765627\n",
      "  0.44385885 0.37842814 0.48561381 0.62108615 0.56549294 0.68752645\n",
      "  0.52634111 0.53466471 0.55876239 0.50307769 0.47181668 0.49795497\n",
      "  0.55503555 0.39958004 0.49605029 0.50049039 0.45351721 0.59444995\n",
      "  0.46902114 0.45232835 0.50168378 0.47890648 0.57761643 0.45666962\n",
      "  0.41637905]\n",
      " [0.29262264 0.32167672 0.47177265 0.70885746 0.57765627 0.\n",
      "  0.34783227 0.26702314 0.31204423 0.42484273 0.35737527 0.43796139\n",
      "  0.36026482 0.22885981 0.26678543 0.34520375 0.31078598 0.30439273\n",
      "  0.34710835 0.23094337 0.31451804 0.33575241 0.13686542 0.3284818\n",
      "  0.37194754 0.22766002 0.49151396 0.24390612 0.14567081 0.44224024\n",
      "  0.24459265]\n",
      " [0.07967763 0.09104495 0.36753397 0.39443071 0.44385885 0.34783227\n",
      "  0.         0.12456646 0.06690938 0.18668581 0.13363528 0.25983848\n",
      "  0.10798193 0.26573776 0.26762346 0.09959241 0.06182409 0.08592404\n",
      "  0.12700296 0.14766779 0.07404093 0.06849206 0.32918496 0.19759017\n",
      "  0.03381639 0.12141913 0.15128669 0.12757613 0.4096577  0.09849964\n",
      "  0.11310216]\n",
      " [0.12424944 0.16897486 0.40494196 0.44394189 0.37842814 0.26702314\n",
      "  0.12456646 0.         0.14074972 0.29483653 0.22348429 0.33632672\n",
      "  0.20248503 0.23396223 0.2456374  0.17955145 0.1298437  0.14599653\n",
      "  0.21148179 0.06419264 0.15019687 0.16639752 0.21098206 0.23057609\n",
      "  0.15765993 0.07431047 0.24966102 0.10876146 0.30899361 0.19275118\n",
      "  0.05214413]\n",
      " [0.0195838  0.03247726 0.35830399 0.4596265  0.48561381 0.31204423\n",
      "  0.06690938 0.14074972 0.         0.15675795 0.08739477 0.20958944\n",
      "  0.07845237 0.21644823 0.2148443  0.07213613 0.02008811 0.01902892\n",
      "  0.07761541 0.15325309 0.01061675 0.03018021 0.33316623 0.13362549\n",
      "  0.07895865 0.09357633 0.20120237 0.07367976 0.38937602 0.16216098\n",
      "  0.11364602]\n",
      " [0.17283018 0.12691364 0.4124211  0.49502225 0.62108615 0.42484273\n",
      "  0.18668581 0.29483653 0.15675795 0.         0.0723672  0.10855273\n",
      "  0.09674273 0.27502108 0.22514411 0.12209961 0.16527823 0.15123468\n",
      "  0.08431812 0.30276136 0.14911827 0.12978557 0.48421544 0.11054979\n",
      "  0.17095603 0.243926   0.2268164  0.20560871 0.51469164 0.21175587\n",
      "  0.2642357 ]\n",
      " [0.10125852 0.05570891 0.38518719 0.49946504 0.56549294 0.35737527\n",
      "  0.13363528 0.22348429 0.08739477 0.0723672  0.         0.12660925\n",
      "  0.05283583 0.21801819 0.18378782 0.06693304 0.09650621 0.07979711\n",
      "  0.0124758  0.2317761  0.08018844 0.06706593 0.41186989 0.08067234\n",
      "  0.13309605 0.17161459 0.23461162 0.13430657 0.44609193 0.20318385\n",
      "  0.19288032]\n",
      " [0.21830942 0.17770015 0.43302049 0.60281447 0.68752645 0.43796139\n",
      "  0.25983848 0.33632672 0.20958944 0.10855273 0.12660925 0.\n",
      "  0.17150235 0.29093169 0.23305859 0.18939644 0.21910199 0.19795914\n",
      "  0.13520087 0.33636232 0.20114656 0.19361063 0.5143917  0.11404337\n",
      "  0.25413953 0.27829094 0.33485951 0.2378518  0.53115654 0.31507423\n",
      "  0.30048322]\n",
      " [0.0904033  0.05373663 0.41277971 0.44840627 0.52634111 0.36026482\n",
      "  0.10798193 0.20248503 0.07845237 0.09674273 0.05283583 0.17150235\n",
      "  0.         0.21875931 0.19429499 0.02564503 0.07568201 0.07412448\n",
      "  0.05021486 0.20846773 0.07778572 0.04982761 0.39634612 0.1292806\n",
      "  0.11216792 0.15642022 0.184332   0.11918545 0.43864005 0.15628192\n",
      "  0.17029506]\n",
      " [0.20706746 0.205144   0.52961496 0.61709806 0.53466471 0.22885981\n",
      "  0.26573776 0.23396223 0.21644823 0.27502108 0.21801819 0.29093169\n",
      "  0.21875931 0.         0.05995982 0.20814666 0.20870677 0.20533799\n",
      "  0.20886598 0.17258995 0.21827885 0.21882255 0.31437045 0.18439967\n",
      "  0.28523818 0.19871665 0.37080007 0.15188824 0.24632116 0.34192234\n",
      "  0.18469164]\n",
      " [0.20918433 0.19370367 0.52667147 0.61530958 0.55876239 0.26678543\n",
      "  0.26762346 0.2456374  0.2148443  0.22514411 0.18378782 0.23305859\n",
      "  0.19429499 0.05995982 0.         0.19124313 0.20768578 0.20219731\n",
      "  0.1780151  0.18898522 0.21505587 0.20898738 0.35474753 0.13961181\n",
      "  0.28375547 0.20959031 0.35990093 0.1585429  0.30487696 0.33828733\n",
      "  0.19437705]\n",
      " [0.07980062 0.05478379 0.41855954 0.44257101 0.50307769 0.34520375\n",
      "  0.09959241 0.17955145 0.07213613 0.12209961 0.06693304 0.18939644\n",
      "  0.02564503 0.20814666 0.19124313 0.         0.06020561 0.06953159\n",
      "  0.06026766 0.18329284 0.07521311 0.04793224 0.37427906 0.1351233\n",
      "  0.11085797 0.13744478 0.17987187 0.10136049 0.41892226 0.15158895\n",
      "  0.14576618]\n",
      " [0.02723666 0.04319169 0.378267   0.44986651 0.47181668 0.31078598\n",
      "  0.06182409 0.1298437  0.02008811 0.16527823 0.09650621 0.21910199\n",
      "  0.07568201 0.20870677 0.20768578 0.06020561 0.         0.03082157\n",
      "  0.08536823 0.14095663 0.02890479 0.03686688 0.32543212 0.13968993\n",
      "  0.07729728 0.08789808 0.19269766 0.07202408 0.38283736 0.15317469\n",
      "  0.10172614]\n",
      " [0.02184922 0.02473605 0.3579192  0.47841103 0.49795497 0.30439273\n",
      "  0.08592404 0.14599653 0.01902892 0.15123468 0.07979711 0.19795914\n",
      "  0.07412448 0.20533799 0.20219731 0.06953159 0.03082157 0.\n",
      "  0.06938525 0.15728121 0.01385021 0.03447363 0.33581908 0.11660047\n",
      "  0.09762183 0.09486168 0.21847796 0.06675769 0.38572    0.18092806\n",
      "  0.11783024]\n",
      " [0.09033866 0.045358   0.38675477 0.49777534 0.55503555 0.34710835\n",
      "  0.12700296 0.21148179 0.07761541 0.08431812 0.0124758  0.13520087\n",
      "  0.05021486 0.20886598 0.1780151  0.06026766 0.08536823 0.06938525\n",
      "  0.         0.21930572 0.07153585 0.05920731 0.4000762  0.08150767\n",
      "  0.13002868 0.15975629 0.23349073 0.12189442 0.43476536 0.20130524\n",
      "  0.18045557]\n",
      " [0.13635009 0.17949692 0.44267801 0.48132212 0.39958004 0.23094337\n",
      "  0.14766779 0.06419264 0.15325309 0.30276136 0.2317761  0.33636232\n",
      "  0.20846773 0.17258995 0.18898522 0.18329284 0.14095663 0.15728121\n",
      "  0.21930572 0.         0.16274349 0.17763951 0.20697764 0.22425498\n",
      "  0.1805212  0.07386552 0.27622251 0.09925509 0.2697468  0.2241213\n",
      "  0.03992276]\n",
      " [0.02669607 0.02783107 0.35136899 0.46641802 0.49605029 0.31451804\n",
      "  0.07404093 0.15019687 0.01061675 0.14911827 0.08018844 0.20114656\n",
      "  0.07778572 0.21827885 0.21505587 0.07521311 0.02890479 0.01385021\n",
      "  0.07153585 0.16274349 0.         0.03001486 0.34097797 0.12809292\n",
      "  0.08456322 0.10097038 0.20700822 0.07737888 0.39484632 0.16874273\n",
      "  0.12310993]\n",
      " [0.04688954 0.02953053 0.37509958 0.44831423 0.50049039 0.33575241\n",
      "  0.06849206 0.16639752 0.03018021 0.12978557 0.06706593 0.19361063\n",
      "  0.04982761 0.21882255 0.20898738 0.04793224 0.03686688 0.03447363\n",
      "  0.05920731 0.17763951 0.03001486 0.         0.36050664 0.13346882\n",
      "  0.07721697 0.12022384 0.18647612 0.093686   0.41318491 0.15096295\n",
      "  0.13842023]\n",
      " [0.31507933 0.35923591 0.51421319 0.60630412 0.45351721 0.13686542\n",
      "  0.32918496 0.21098206 0.33316623 0.48421544 0.41186989 0.5143917\n",
      "  0.39634612 0.31437045 0.35474753 0.37427906 0.32543212 0.33581908\n",
      "  0.4000762  0.20697764 0.34097797 0.36050664 0.         0.4026289\n",
      "  0.36039747 0.2414293  0.46023336 0.28342369 0.21747137 0.40097043\n",
      "  0.2322792 ]\n",
      " [0.13021533 0.10717516 0.41196133 0.57744327 0.59444995 0.3284818\n",
      "  0.19759017 0.23057609 0.13362549 0.11054979 0.08067234 0.11404337\n",
      "  0.1292806  0.18439967 0.13961181 0.1351233  0.13968993 0.11660047\n",
      "  0.08150767 0.22425498 0.12809292 0.13346882 0.4026289  0.\n",
      "  0.20711104 0.16970961 0.3135557  0.12628719 0.42001334 0.28218801\n",
      "  0.19082813]\n",
      " [0.09271321 0.10060305 0.35518923 0.38455014 0.46902114 0.37194754\n",
      "  0.03381639 0.15765993 0.07895865 0.17095603 0.13309605 0.25413953\n",
      "  0.11216792 0.28523818 0.28375547 0.11085797 0.07729728 0.09762183\n",
      "  0.13002868 0.1805212  0.08456322 0.07721697 0.36039747 0.20711104\n",
      "  0.         0.14432906 0.14029578 0.145235   0.43900672 0.08659202\n",
      "  0.14431417]\n",
      " [0.07465697 0.11798902 0.37099016 0.50692596 0.45232835 0.22766002\n",
      "  0.12141913 0.07431047 0.09357633 0.243926   0.17161459 0.27829094\n",
      "  0.15642022 0.19871665 0.20959031 0.13744478 0.08789808 0.09486168\n",
      "  0.15975629 0.07386552 0.10097038 0.12022384 0.2414293  0.16970961\n",
      "  0.14432906 0.         0.26634353 0.05857638 0.30081842 0.21869182\n",
      "  0.04526612]\n",
      " [0.21664744 0.21560068 0.47910886 0.26824241 0.50168378 0.49151396\n",
      "  0.15128669 0.24966102 0.20120237 0.2268164  0.23461162 0.33485951\n",
      "  0.184332   0.37080007 0.35990093 0.17987187 0.19269766 0.21847796\n",
      "  0.23349073 0.27622251 0.20700822 0.18647612 0.46023336 0.3135557\n",
      "  0.14029578 0.26634353 0.         0.26258969 0.54409371 0.07718899\n",
      "  0.24985828]\n",
      " [0.05818432 0.08484725 0.39830538 0.51571864 0.47890648 0.24390612\n",
      "  0.12757613 0.10876146 0.07367976 0.20560871 0.13430657 0.2378518\n",
      "  0.11918545 0.15188824 0.1585429  0.10136049 0.07202408 0.06675769\n",
      "  0.12189442 0.09925509 0.07737888 0.093686   0.28342369 0.12628719\n",
      "  0.145235   0.05857638 0.26258969 0.         0.32066256 0.22195577\n",
      "  0.06528871]\n",
      " [0.37021696 0.40468902 0.60670953 0.72583886 0.57761643 0.14567081\n",
      "  0.4096577  0.30899361 0.38937602 0.51469164 0.44609193 0.53115654\n",
      "  0.43864005 0.24632116 0.30487696 0.41892226 0.38283736 0.38572\n",
      "  0.43476536 0.2697468  0.39484632 0.41318491 0.21747137 0.42001334\n",
      "  0.43900672 0.30081842 0.54409371 0.32066256 0.         0.49365729\n",
      "  0.29720939]\n",
      " [0.17621138 0.18035236 0.42025055 0.29861508 0.45666962 0.44224024\n",
      "  0.09849964 0.19275118 0.16216098 0.21175587 0.20318385 0.31507423\n",
      "  0.15628192 0.34192234 0.33828733 0.15158895 0.15317469 0.18092806\n",
      "  0.20130524 0.2241213  0.16874273 0.15096295 0.40097043 0.28218801\n",
      "  0.08659202 0.21869182 0.07718899 0.22195577 0.49365729 0.\n",
      "  0.1994343 ]\n",
      " [0.09663465 0.1402815  0.41252192 0.47469237 0.41637905 0.24459265\n",
      "  0.11310216 0.05214413 0.11364602 0.2642357  0.19288032 0.30048322\n",
      "  0.17029506 0.18469164 0.19437705 0.14576618 0.10172614 0.11783024\n",
      "  0.18045557 0.03992276 0.12310993 0.13842023 0.2322792  0.19082813\n",
      "  0.14431417 0.04526612 0.24985828 0.06528871 0.29720939 0.1994343\n",
      "  0.        ]]\n"
     ]
    }
   ],
   "source": [
    "h = 3\n",
    "sum_power_h = 0\n",
    "A = factors[1]\n",
    "n,P = A.shape\n",
    "distance_d_i1_i2_A = np.empty((n,n))\n",
    "\n",
    "for i in range(n): \n",
    "    for j in range(n):\n",
    "        for p in range(P):\n",
    "            sum_power_h += score_pjt[p] * (np.abs(A[i,p] - A[j, p])**h)\n",
    "        distance_d_i1_i2_A[i,j] = sum_power_h**(1/h)  \n",
    "        sum_power_h = 0   \n",
    "print(\"Weighted Minkowski Distance:\")\n",
    "print(distance_d_i1_i2_A)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 5:\n",
    "### Perform traditional two-way data clustering analysis on the three-way \"individual\" distance matrix distance_d_i1_i2_A."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2520x1080 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.cluster.hierarchy import linkage, dendrogram\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.spatial.distance import squareform\n",
    "\n",
    "# Convert the distance matrix into a condensed distance matrix. \n",
    "condensed_distance_d_i1_i2_A = squareform(distance_d_i1_i2_A)\n",
    "\n",
    "#  Use the Ward linkage criterion for hierarchical clustering.\n",
    "Z = linkage(condensed_distance_d_i1_i2_A, method='ward')\n",
    "\n",
    "# Visualize with a dendrogram.\n",
    "plt.figure(figsize=(35, 15))\n",
    "dendrogram(Z)\n",
    "\n",
    "plt.title('Cluster Analysis of Solid Waste Treatment in 31 Provinces and Regions of China from 2003 to 2021 using PCT3 Method; Model - Tucker3(6,4,3), Adjusted R-squared -- 98.16%')\n",
    "plt.xlabel('Sample index')\n",
    "plt.ylabel('Distance')\n",
    "plt.savefig('hierarchical_clustering.png', dpi = 700)  \n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>10</th>\n",
       "      <th>11</th>\n",
       "      <th>12</th>\n",
       "      <th>13</th>\n",
       "      <th>14</th>\n",
       "      <th>15</th>\n",
       "      <th>16</th>\n",
       "      <th>17</th>\n",
       "      <th>18</th>\n",
       "      <th>19</th>\n",
       "      <th>20</th>\n",
       "      <th>21</th>\n",
       "      <th>22</th>\n",
       "      <th>23</th>\n",
       "      <th>24</th>\n",
       "      <th>25</th>\n",
       "      <th>26</th>\n",
       "      <th>27</th>\n",
       "      <th>28</th>\n",
       "      <th>29</th>\n",
       "      <th>30</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Region</th>\n",
       "      <td>Beijing</td>\n",
       "      <td>Tianjin</td>\n",
       "      <td>Hebei</td>\n",
       "      <td>Shanxi</td>\n",
       "      <td>Neimenggu</td>\n",
       "      <td>Liaoning</td>\n",
       "      <td>Jilin</td>\n",
       "      <td>Heilongjiang</td>\n",
       "      <td>Shanghai</td>\n",
       "      <td>Jiangsu</td>\n",
       "      <td>Zhejiang</td>\n",
       "      <td>Anhui</td>\n",
       "      <td>Fujian</td>\n",
       "      <td>Jiangxi</td>\n",
       "      <td>Shandong</td>\n",
       "      <td>Henan</td>\n",
       "      <td>Hubei</td>\n",
       "      <td>Hunan</td>\n",
       "      <td>Guangdong</td>\n",
       "      <td>Guangxi</td>\n",
       "      <td>Hainan</td>\n",
       "      <td>Chongqing</td>\n",
       "      <td>Sichuan</td>\n",
       "      <td>Guizhou</td>\n",
       "      <td>Yunnan</td>\n",
       "      <td>Xizang</td>\n",
       "      <td>Shaanxi</td>\n",
       "      <td>Gansu</td>\n",
       "      <td>Qinghai</td>\n",
       "      <td>Ningxia</td>\n",
       "      <td>Xinjiang</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              0        1      2       3          4         5      6  \\\n",
       "Region  Beijing  Tianjin  Hebei  Shanxi  Neimenggu  Liaoning  Jilin   \n",
       "\n",
       "                   7         8        9        10     11      12       13  \\\n",
       "Region  Heilongjiang  Shanghai  Jiangsu  Zhejiang  Anhui  Fujian  Jiangxi   \n",
       "\n",
       "              14     15     16     17         18       19      20         21  \\\n",
       "Region  Shandong  Henan  Hubei  Hunan  Guangdong  Guangxi  Hainan  Chongqing   \n",
       "\n",
       "             22       23      24      25       26     27       28       29  \\\n",
       "Region  Sichuan  Guizhou  Yunnan  Xizang  Shaanxi  Gansu  Qinghai  Ningxia   \n",
       "\n",
       "              30  \n",
       "Region  Xinjiang  "
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "data = {\n",
    "    'Region': [\n",
    "        'Beijing', 'Tianjin', 'Hebei', 'Shanxi', 'Neimenggu',\n",
    "        'Liaoning', 'Jilin', 'Heilongjiang', 'Shanghai', 'Jiangsu',\n",
    "        'Zhejiang', 'Anhui', 'Fujian', 'Jiangxi', 'Shandong',\n",
    "        'Henan', 'Hubei', 'Hunan', 'Guangdong', 'Guangxi',\n",
    "        'Hainan', 'Chongqing', 'Sichuan', 'Guizhou', 'Yunnan',\n",
    "        'Xizang', 'Shaanxi', 'Gansu', 'Qinghai', 'Ningxia',\n",
    "        'Xinjiang'\n",
    "    ]\n",
    "}\n",
    "pd.set_option('display.max_columns', None)\n",
    "data_1 = pd.DataFrame(data).T\n",
    "data_1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font face = \"Times New Roman\" size = 3 >To study the regional characteristics of solid waste treatment, we have divided the 31 provinces, cities, and autonomous regions of the country into four categories -- in accordance with our tucker3 decomposition results, based on the results shown in the figure above, which are:<br>\n",
    "First category: {4, 3, 26, 29}, that is {Inner Mongolia, Shanxi, Shaanxi, Ningxia}<br>\n",
    "Second category: {28, 5, 22}, that is {Qinghai, Liaoning, Sichuan}<br>\n",
    "<font face = \"Times New Roman\" size = 3 color = darkorange>Third category: {2}, that is {Hebei}</font><br>\n",
    "Fourth category: {23, 9, 11, 10, 18, 12, 15, 6, 24, 1, 21, 16, 0, 17, 8, 20, 13, 14, 25, 27, 7, 19, 30}, that is {Guizhou, Jiangsu, Anhui, Zhejiang, Guangdong, Fujian, Henan, Jilin, Yunnan, Tianjin, Chongqing, Hubei, Beijing, Hunan, Shanghai, Hainan, Jiangxi, Shandong, Tibet, Gansu, Heilongjiang, Guangxi, Xinjiang}<br></font>\n",
    "\n",
    "<font face = \"Times New Roman\" size = 3 >Additionally, if the 31 provinces, cities, and autonomous regions of the country are further subdivided into five categories, then:<br>\n",
    "First category: {4, 3, 26, 29}, that is {Inner Mongolia, Shanxi, Shaanxi, Ningxia}<br>\n",
    "Second category: {28, 5, 22}, that is {Qinghai, Liaoning, Sichuan}<br>\n",
    "Third category: {2}, that is {Hebei}<br>\n",
    "Fourth category: {23, 9, 11, 10, 18, 12, 15, 6, 24, 1, 21, 16, 0, 17, 8, 20}, that is {Guizhou, Jiangsu, Anhui, Zhejiang, Guangdong, Fujian, Henan, Jilin, Yunnan, Tianjin, Chongqing, Hubei, Beijing, Hunan, Shanghai, Hainan}<br>\n",
    "Fifth category: {13, 14, 25, 27, 7, 19, 30}, that is {Jiangxi, Shandong, Tibet, Gansu, Heilongjiang, Guangxi, Xinjiang}</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We could see that Hebei is the only one in its group, fairly unique, perfectly matches our initail motivation for this analysis towards three-dimensional data. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We could also do the clustering for years and indexes, which is one of the reasons why we chose Tucker3 instead of Tucker1 or Tucker2. The results suggested that the years can be devided into six groups, a great chance for us to explore dynamic development of all regions and indexes. However, I've decided not to go further into this right now, for the last three steps are almost the same. The same goes for index clustering. Nevertheless, the change in the index number may indicate that there might be some improvement in index-collecting process."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There's just one problem waiting to be solved. Since they use the same estimation procedure--Higher-Order Orthogonal Iteration (HOOI), why there's obvious disparity between results from R and python ? I hope I could find out the answer in the future study."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### References:\n",
    "* [1]X. Ao and E. Wei, \"Review of Panel Data Clustering Methods and Applications,\" 2022 5th International Conference on Artificial Intelligence and Big Data (ICAIBD), Chengdu, China, 2022, pp. 369-374, doi: 10.1109/ICAIBD55127.2022.9820005.\n",
    "* [2] Dang Y G, Hou D Q (2016). Multi-index panel data clustering method based on feature extraction . Statistics and Decision, vol 19, pp.68-72.\n",
    "* [3] Li Y G, He X Q, Li X C (2016). Three-way data clustering method based on Tucker3 decomposition. Mathematical statistics and management, vol35 no1, pp.71-80."
   ]
  }
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