The structure is the message - preserving experimental context through tensor decomposition.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "9f14ce43",
   "metadata": {},
   "source": [
    "# The structure is the message: preserving experimental context through tensor decomposition"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5156358e",
   "metadata": {},
   "source": [
    "<h4 style=\"text-align: center;\">Z. Cyrillus Tan, Aaron S. Meyer</h4>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "72c2e80c",
   "metadata": {},
   "source": [
    "In this demonstration, we provide an example of how to apply tensor methods to a synthetic example dataset. We will walk through all the analyses described in the text in order to provide a more comprehensive tutorial."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "813b8acc",
   "metadata": {},
   "source": [
    "## 1. Import data and structure it to a tensor format"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4404df27",
   "metadata": {},
   "source": [
    "Throughout this work, we consider a synthetic dataset that records an experiment that profiles cells from seven organs responding to six candidate drugs over five time points.\n",
    "First, we import the example dataset. Traditionally, a multivariate dataset like this is recorded as a spreadsheet, with some dimensions merged. For example, here, the drugs and time points are merged, so that each column represents a pair of drug-time point combinations. This is called MultiIndex in the `pandas` package."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "fde375bf",
   "metadata": {},
   "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 tr th {\n",
       "        text-align: left;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"5\" halign=\"left\">Alfazumab</th>\n",
       "      <th colspan=\"5\" halign=\"left\">Bravociclib</th>\n",
       "      <th>...</th>\n",
       "      <th colspan=\"5\" halign=\"left\">Echoxacin</th>\n",
       "      <th colspan=\"5\" halign=\"left\">Foxtrotolol</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>1 hr</th>\n",
       "      <th>3 hr</th>\n",
       "      <th>6 hr</th>\n",
       "      <th>12 hr</th>\n",
       "      <th>24 hr</th>\n",
       "      <th>1 hr</th>\n",
       "      <th>3 hr</th>\n",
       "      <th>6 hr</th>\n",
       "      <th>12 hr</th>\n",
       "      <th>24 hr</th>\n",
       "      <th>...</th>\n",
       "      <th>1 hr</th>\n",
       "      <th>3 hr</th>\n",
       "      <th>6 hr</th>\n",
       "      <th>12 hr</th>\n",
       "      <th>24 hr</th>\n",
       "      <th>1 hr</th>\n",
       "      <th>3 hr</th>\n",
       "      <th>6 hr</th>\n",
       "      <th>12 hr</th>\n",
       "      <th>24 hr</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Thymus</th>\n",
       "      <td>7.5931</td>\n",
       "      <td>-74.0560</td>\n",
       "      <td>-156.3267</td>\n",
       "      <td>-152.0899</td>\n",
       "      <td>-129.2603</td>\n",
       "      <td>69.7114</td>\n",
       "      <td>111.0545</td>\n",
       "      <td>177.4723</td>\n",
       "      <td>161.4991</td>\n",
       "      <td>157.9950</td>\n",
       "      <td>...</td>\n",
       "      <td>87.7958</td>\n",
       "      <td>200.3265</td>\n",
       "      <td>353.3183</td>\n",
       "      <td>317.5187</td>\n",
       "      <td>283.2818</td>\n",
       "      <td>-28.2758</td>\n",
       "      <td>-22.8253</td>\n",
       "      <td>-26.9893</td>\n",
       "      <td>-20.9940</td>\n",
       "      <td>-24.8508</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Skin</th>\n",
       "      <td>96.4908</td>\n",
       "      <td>97.6188</td>\n",
       "      <td>135.4522</td>\n",
       "      <td>106.3627</td>\n",
       "      <td>107.4902</td>\n",
       "      <td>84.3421</td>\n",
       "      <td>68.4413</td>\n",
       "      <td>80.3329</td>\n",
       "      <td>67.1187</td>\n",
       "      <td>80.8065</td>\n",
       "      <td>...</td>\n",
       "      <td>58.7727</td>\n",
       "      <td>19.6130</td>\n",
       "      <td>9.9165</td>\n",
       "      <td>-1.6546</td>\n",
       "      <td>-5.6995</td>\n",
       "      <td>-61.4324</td>\n",
       "      <td>-59.4331</td>\n",
       "      <td>-72.4681</td>\n",
       "      <td>-62.6582</td>\n",
       "      <td>-80.3741</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Pancreas</th>\n",
       "      <td>82.8958</td>\n",
       "      <td>41.7587</td>\n",
       "      <td>43.6539</td>\n",
       "      <td>9.7820</td>\n",
       "      <td>-3.6321</td>\n",
       "      <td>116.1266</td>\n",
       "      <td>123.8453</td>\n",
       "      <td>163.5675</td>\n",
       "      <td>149.8666</td>\n",
       "      <td>175.2404</td>\n",
       "      <td>...</td>\n",
       "      <td>120.0887</td>\n",
       "      <td>172.2481</td>\n",
       "      <td>215.8126</td>\n",
       "      <td>226.1064</td>\n",
       "      <td>323.9284</td>\n",
       "      <td>-57.6145</td>\n",
       "      <td>-32.3156</td>\n",
       "      <td>-51.3740</td>\n",
       "      <td>-23.2484</td>\n",
       "      <td>13.8744</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Liver</th>\n",
       "      <td>54.0536</td>\n",
       "      <td>-2.0641</td>\n",
       "      <td>-29.5443</td>\n",
       "      <td>-51.6633</td>\n",
       "      <td>-55.9508</td>\n",
       "      <td>102.3161</td>\n",
       "      <td>122.6016</td>\n",
       "      <td>172.1183</td>\n",
       "      <td>158.7541</td>\n",
       "      <td>176.4939</td>\n",
       "      <td>...</td>\n",
       "      <td>112.8466</td>\n",
       "      <td>189.4797</td>\n",
       "      <td>269.7720</td>\n",
       "      <td>268.1009</td>\n",
       "      <td>331.7243</td>\n",
       "      <td>-46.3147</td>\n",
       "      <td>-26.0519</td>\n",
       "      <td>-40.3760</td>\n",
       "      <td>-18.4811</td>\n",
       "      <td>9.3109</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Heart</th>\n",
       "      <td>176.2525</td>\n",
       "      <td>118.8718</td>\n",
       "      <td>117.1203</td>\n",
       "      <td>95.2692</td>\n",
       "      <td>133.7000</td>\n",
       "      <td>126.5419</td>\n",
       "      <td>127.0990</td>\n",
       "      <td>179.5757</td>\n",
       "      <td>136.0497</td>\n",
       "      <td>130.0312</td>\n",
       "      <td>...</td>\n",
       "      <td>121.8980</td>\n",
       "      <td>182.4849</td>\n",
       "      <td>279.9835</td>\n",
       "      <td>239.0031</td>\n",
       "      <td>246.0975</td>\n",
       "      <td>-97.8848</td>\n",
       "      <td>-77.1348</td>\n",
       "      <td>-101.4701</td>\n",
       "      <td>-73.2257</td>\n",
       "      <td>-64.2342</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Colon</th>\n",
       "      <td>45.5757</td>\n",
       "      <td>-33.6277</td>\n",
       "      <td>-102.2309</td>\n",
       "      <td>-101.4290</td>\n",
       "      <td>-71.5326</td>\n",
       "      <td>80.1902</td>\n",
       "      <td>113.8835</td>\n",
       "      <td>178.9411</td>\n",
       "      <td>155.4155</td>\n",
       "      <td>148.6795</td>\n",
       "      <td>...</td>\n",
       "      <td>94.3906</td>\n",
       "      <td>200.4200</td>\n",
       "      <td>348.5009</td>\n",
       "      <td>308.1313</td>\n",
       "      <td>276.5570</td>\n",
       "      <td>-43.5885</td>\n",
       "      <td>-35.1011</td>\n",
       "      <td>-43.4352</td>\n",
       "      <td>-32.9590</td>\n",
       "      <td>-35.0784</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Kidney</th>\n",
       "      <td>90.7719</td>\n",
       "      <td>82.5750</td>\n",
       "      <td>116.1591</td>\n",
       "      <td>86.8304</td>\n",
       "      <td>76.0428</td>\n",
       "      <td>77.3614</td>\n",
       "      <td>66.4917</td>\n",
       "      <td>78.0255</td>\n",
       "      <td>65.8033</td>\n",
       "      <td>83.3234</td>\n",
       "      <td>...</td>\n",
       "      <td>73.4567</td>\n",
       "      <td>80.2512</td>\n",
       "      <td>69.3572</td>\n",
       "      <td>83.7880</td>\n",
       "      <td>172.3019</td>\n",
       "      <td>-47.7500</td>\n",
       "      <td>-26.8817</td>\n",
       "      <td>-43.6549</td>\n",
       "      <td>-19.8480</td>\n",
       "      <td>12.6196</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>7 rows × 30 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         Alfazumab                                         Bravociclib  \\\n",
       "              1 hr      3 hr      6 hr     12 hr     24 hr        1 hr   \n",
       "Thymus      7.5931  -74.0560 -156.3267 -152.0899 -129.2603     69.7114   \n",
       "Skin       96.4908   97.6188  135.4522  106.3627  107.4902     84.3421   \n",
       "Pancreas   82.8958   41.7587   43.6539    9.7820   -3.6321    116.1266   \n",
       "Liver      54.0536   -2.0641  -29.5443  -51.6633  -55.9508    102.3161   \n",
       "Heart     176.2525  118.8718  117.1203   95.2692  133.7000    126.5419   \n",
       "Colon      45.5757  -33.6277 -102.2309 -101.4290  -71.5326     80.1902   \n",
       "Kidney     90.7719   82.5750  116.1591   86.8304   76.0428     77.3614   \n",
       "\n",
       "                                                  ... Echoxacin            \\\n",
       "              3 hr      6 hr     12 hr     24 hr  ...      1 hr      3 hr   \n",
       "Thymus    111.0545  177.4723  161.4991  157.9950  ...   87.7958  200.3265   \n",
       "Skin       68.4413   80.3329   67.1187   80.8065  ...   58.7727   19.6130   \n",
       "Pancreas  123.8453  163.5675  149.8666  175.2404  ...  120.0887  172.2481   \n",
       "Liver     122.6016  172.1183  158.7541  176.4939  ...  112.8466  189.4797   \n",
       "Heart     127.0990  179.5757  136.0497  130.0312  ...  121.8980  182.4849   \n",
       "Colon     113.8835  178.9411  155.4155  148.6795  ...   94.3906  200.4200   \n",
       "Kidney     66.4917   78.0255   65.8033   83.3234  ...   73.4567   80.2512   \n",
       "\n",
       "                                       Foxtrotolol                     \\\n",
       "              6 hr     12 hr     24 hr        1 hr     3 hr      6 hr   \n",
       "Thymus    353.3183  317.5187  283.2818    -28.2758 -22.8253  -26.9893   \n",
       "Skin        9.9165   -1.6546   -5.6995    -61.4324 -59.4331  -72.4681   \n",
       "Pancreas  215.8126  226.1064  323.9284    -57.6145 -32.3156  -51.3740   \n",
       "Liver     269.7720  268.1009  331.7243    -46.3147 -26.0519  -40.3760   \n",
       "Heart     279.9835  239.0031  246.0975    -97.8848 -77.1348 -101.4701   \n",
       "Colon     348.5009  308.1313  276.5570    -43.5885 -35.1011  -43.4352   \n",
       "Kidney     69.3572   83.7880  172.3019    -47.7500 -26.8817  -43.6549   \n",
       "\n",
       "                            \n",
       "            12 hr    24 hr  \n",
       "Thymus   -20.9940 -24.8508  \n",
       "Skin     -62.6582 -80.3741  \n",
       "Pancreas -23.2484  13.8744  \n",
       "Liver    -18.4811   9.3109  \n",
       "Heart    -73.2257 -64.2342  \n",
       "Colon    -32.9590 -35.0784  \n",
       "Kidney   -19.8480  12.6196  \n",
       "\n",
       "[7 rows x 30 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from os.path import join, dirname\n",
    "\n",
    "data = pd.read_csv(\"example_drug_data.csv\", \n",
    "                   delimiter=\",\", comment=\"#\", index_col=0, header=[0, 1])\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "454cd521",
   "metadata": {},
   "source": [
    "Although this MultiIndex format can represent the data faithfully, analyzing them as a spreadsheet/matrix muddles the relationship between drugs and time points. The columns are not equally related: some share drugs, some share time points, but many more have nothing in common. We sometimes call this spreadsheet a \"flattened\" version of the original dataset.\n",
    "\n",
    "To make the structure reflect the right message, we convert the dataset into a tensor format. The original data has three modes: Organs, Drugs, and Time points, each having 7, 6, and 5 entries. Therefore, the tensor should be $7 \\times 6 \\times 5$. We print these out to have a more intuitive understanding of the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "5cdf658e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[['Thymus', 'Skin', 'Pancreas', 'Liver', 'Heart', 'Colon', 'Kidney'], ['Alfazumab', 'Bravociclib', 'Charlivir', 'Deltatinib', 'Echoxacin', 'Foxtrotolol'], ['1 hr', '3 hr', '6 hr', '12 hr', '24 hr']]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[[   7.5931,  -74.056 , -156.3267, -152.0899, -129.2603],\n",
       "        [  69.7114,  111.0545,  177.4723,  161.4991,  157.995 ],\n",
       "        [  68.0527,  130.6083,  210.7125,  206.7382,  213.4184],\n",
       "        [   0.5923,   80.0086,  179.5254,  144.0355,   87.8173],\n",
       "        [  87.7958,  200.3265,  353.3183,  317.5187,  283.2818],\n",
       "        [ -28.2758,  -22.8253,  -26.9893,  -20.994 ,  -24.8508]],\n",
       "\n",
       "       [[  96.4908,   97.6188,  135.4522,  106.3627,  107.4902],\n",
       "        [  84.3421,   68.4413,   80.3329,   67.1187,   80.8065],\n",
       "        [  47.7073,   56.7609,   56.444 ,   71.3942,  124.8541],\n",
       "        [ -41.5447,  -85.8681, -117.5078, -127.2689, -174.8336],\n",
       "        [  58.7727,   19.613 ,    9.9165,   -1.6546,   -5.6995],\n",
       "        [ -61.4324,  -59.4331,  -72.4681,  -62.6582,  -80.3741]],\n",
       "\n",
       "       [[  82.8958,   41.7587,   43.6539,    9.782 ,   -3.6321],\n",
       "        [ 116.1266,  123.8453,  163.5675,  149.8666,  175.2404],\n",
       "        [  58.2814,   41.5263,   94.9442,   68.5988,  -16.8659],\n",
       "        [  -8.7859,   53.0051,   36.7611,   70.6833,  200.4127],\n",
       "        [ 120.0887,  172.2481,  215.8126,  226.1064,  323.9284],\n",
       "        [ -57.6145,  -32.3156,  -51.374 ,  -23.2484,   13.8744]],\n",
       "\n",
       "       [[  54.0536,   -2.0641,  -29.5443,  -51.6633,  -55.9508],\n",
       "        [ 102.3161,  122.6016,  172.1183,  158.7541,  176.4939],\n",
       "        [  64.5437,   72.2617,  138.3943,  117.8525,   54.8836],\n",
       "        [  -6.0798,   65.9478,   84.9613,   99.2392,  180.454 ],\n",
       "        [ 112.8466,  189.4797,  269.772 ,  268.1009,  331.7243],\n",
       "        [ -46.3147,  -26.0519,  -40.376 ,  -18.4811,    9.3109]],\n",
       "\n",
       "       [[ 176.2525,  118.8718,  117.1203,   95.2692,  133.7   ],\n",
       "        [ 126.5419,  127.099 ,  179.5757,  136.0497,  130.0312],\n",
       "        [  -8.5867,  -24.2365,    1.7063,  -45.3029, -131.5577],\n",
       "        [  49.661 ,  148.8044,  225.5783,  242.1085,  304.1596],\n",
       "        [ 121.898 ,  182.4849,  279.9835,  239.0031,  246.0975],\n",
       "        [ -97.8848,  -77.1348, -101.4701,  -73.2257,  -64.2342]],\n",
       "\n",
       "       [[  45.5757,  -33.6277, -102.2309, -101.429 ,  -71.5326],\n",
       "        [  80.1902,  113.8835,  178.9411,  155.4155,  148.6795],\n",
       "        [  46.5094,   93.1496,  161.5269,  146.1838,  130.4188],\n",
       "        [  16.8095,  106.5628,  210.598 ,  184.945 ,  151.0049],\n",
       "        [  94.3906,  200.42  ,  348.5009,  308.1313,  276.557 ],\n",
       "        [ -43.5885,  -35.1011,  -43.4352,  -32.959 ,  -35.0784]],\n",
       "\n",
       "       [[  90.7719,   82.575 ,  116.1591,   86.8304,   76.0428],\n",
       "        [  77.3614,   66.4917,   78.0255,   65.8033,   83.3234],\n",
       "        [   6.9782,  -36.9686,  -26.5928,  -56.4948, -146.8149],\n",
       "        [   8.5349,   46.3207,   11.8956,   56.8941,  194.9679],\n",
       "        [  73.4567,   80.2512,   69.3572,   83.788 ,  172.3019],\n",
       "        [ -47.75  ,  -26.8817,  -43.6549,  -19.848 ,   12.6196]]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Retrieve mode axes information\n",
    "shape = (7, 6, 5)\n",
    "axes_names = [\"Organs\", \"Drugs\", \"Times\"]\n",
    "organs = data.index.tolist()\n",
    "drugs = data.columns.get_level_values(0).unique().tolist()\n",
    "times = data.columns.get_level_values(1).unique().tolist()\n",
    "entry_names = [organs, drugs, times]\n",
    "print(entry_names)\n",
    "\n",
    "# Now convert the data into a three mode tensor\n",
    "tensor = data.to_numpy().reshape(*shape)\n",
    "tensor"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "50e63316",
   "metadata": {},
   "source": [
    "## 2. Perform CP decomposition on the data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "25e9ce3f",
   "metadata": {},
   "source": [
    "Let's assume this tensor is already properly proprocessed. Now, we perform a CP (also called PARAFAC or CANDECOMP) decomposition on it. Here, we tentatively choose 4 components. Throughout this demonstration, we use `TensorLy`, a commonly used Python tensor package. To see alternative options, check Tbl. 2 in the text."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "458e8553",
   "metadata": {},
   "outputs": [],
   "source": [
    "from tensorly.decomposition import parafac\n",
    "\n",
    "cp = parafac(tensor, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d6a31d03",
   "metadata": {},
   "source": [
    "In the `TensorLy` package, the CP results are stored as two sets of values: weights and factors. Weights are vectors of values, and factors are sets of factor matrices. Unnormalized weights are all 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "04c5059d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 1., 1.])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cp[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d9bef82-4f47-47e3-b5b4-f0a7e3b652c3",
   "metadata": {},
   "source": [
    "Since our data is a 3-mode tensor, there should be three factor matrices. For a 3-component decomposition, these matrices should have sizes $7 \\times 3$, $6 \\times 3$, and $5 \\times 3$, respectively. They are the factor matrices of organ, drug, and time modes, as drawn in Fig. 2b, right."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "1285c4f2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([[ 274.64169957,  -14.79200921, -149.12287797],\n",
       "        [ 503.59685754,  -27.51843979,   16.10666417],\n",
       "        [ 632.18068065,   33.92925401,  -68.2982001 ],\n",
       "        [ 513.90114321,   19.42504466, -100.37113855],\n",
       "        [ 859.91732879,   86.79388985,  -41.93656738],\n",
       "        [ 397.76813848,   11.43466963, -128.20282009],\n",
       "        [ 503.36243637,   54.0652088 ,    3.66731937]]),\n",
       " array([[ 0.43901696,  0.00722143, -1.38734364],\n",
       "        [ 0.38562811, -0.15236277,  0.82226257],\n",
       "        [ 0.19256511, -1.589673  ,  1.08228365],\n",
       "        [-0.18231082,  2.11621792,  1.34270882],\n",
       "        [ 0.27626033,  0.69444713,  2.08236156],\n",
       "        [-0.26303276,  0.34441116,  0.12923539]]),\n",
       " array([[ 0.41914428,  0.45568069, -0.19249686],\n",
       "        [ 0.37305043,  0.82617892, -0.58293319],\n",
       "        [ 0.47631714,  0.89684467, -1.03346475],\n",
       "        [ 0.38817167,  1.09352939, -0.96188274],\n",
       "        [ 0.42631597,  1.94450497, -0.91325084]])]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cp[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6277d326-402d-4b88-bf86-3604000e380f",
   "metadata": {},
   "source": [
    "Each component can be represented as three factor vectors. For example, Component 1 can be represented as the first vectors across three modes. They are:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "bb1ac7c9-401d-490b-8c6c-d5589a5711fd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[274.64169957 503.59685754 632.18068065 513.90114321 859.91732879\n",
      " 397.76813848 503.36243637]\n",
      "[ 0.43901696  0.38562811  0.19256511 -0.18231082  0.27626033 -0.26303276]\n",
      "[0.41914428 0.37305043 0.47631714 0.38817167 0.42631597]\n"
     ]
    }
   ],
   "source": [
    "print(cp[1][0][:, 0])\n",
    "print(cp[1][1][:, 0])\n",
    "print(cp[1][2][:, 0])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d2afb47-22a6-41af-99c4-808636d41c7c",
   "metadata": {},
   "source": [
    "These three vectors exactly correspond to the blue, orange, and green vectors shown in Fig. 2b, shaded box in the middle. Although represented as three vectors, Component 1 is in fact a rank-one tensor of $7 \\times 6 \\times 5$ dimension, which is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "2090531f-cb89-49b2-935b-15f7057091c7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[  50.53721762,   44.97957306,   57.43068344,   46.80277657,\n",
       "           51.40192438],\n",
       "        [  44.39138602,   39.50960668,   50.44653738,   41.11109039,\n",
       "           45.15093578],\n",
       "        [  22.16703631,   19.72929805,   25.1907031 ,   20.52900607,\n",
       "           22.54632086],\n",
       "        [ -20.98661831,  -18.67869218,  -23.84927167,  -19.43581491,\n",
       "          -21.34570557],\n",
       "        [  31.80156939,   28.30430881,   36.13942259,   29.4515966 ,\n",
       "           32.34570366],\n",
       "        [ -30.2788845 ,  -26.94907559,  -34.40903778,  -28.04143031,\n",
       "          -30.79696518]],\n",
       "\n",
       "       [[  92.66758844,   82.47681136,  105.30779466,   85.81992917,\n",
       "           94.25315831],\n",
       "        [  81.39828197,   72.44680541,   92.50131257,   75.38336662,\n",
       "           82.79103067],\n",
       "        [  40.64659461,   36.17663492,   46.19094238,   37.64301984,\n",
       "           41.34206987],\n",
       "        [ -38.4821207 ,  -34.25019107,  -43.73122613,  -35.63848945,\n",
       "          -39.14056118],\n",
       "        [  58.31295988,   51.90020668,   66.26706607,   54.00393138,\n",
       "           59.31071189],\n",
       "        [ -55.52088815,  -49.41518276,  -63.0941453 ,  -51.41817942,\n",
       "          -56.47086699]],\n",
       "\n",
       "       [[ 116.32848429,  103.53568725,  132.19612536,  107.73240623,\n",
       "          118.31889909],\n",
       "        [ 102.18177601,   90.94471117,  116.11975307,   94.6310671 ,\n",
       "          103.93013645],\n",
       "        [  51.02492492,   45.41364654,   57.98491583,   47.25444479,\n",
       "           51.89797649],\n",
       "        [ -48.30779401,  -42.99532211,  -54.89715809,  -44.73809592,\n",
       "          -49.13435467],\n",
       "        [  73.20205859,   65.15193154,   83.18709362,   67.79280209,\n",
       "           74.45456748],\n",
       "        [ -69.69708476,  -62.03240431,  -79.20402823,  -64.54682784,\n",
       "          -70.88962251]],\n",
       "\n",
       "       [[  94.56369499,   84.16440058,  107.46253726,   87.57592318,\n",
       "           96.18170781],\n",
       "        [  83.06380299,   73.92916688,   94.3940169 ,   76.92581418,\n",
       "           84.48504924],\n",
       "        [  41.47827994,   36.91685872,   47.13607272,   38.4132479 ,\n",
       "           42.18798559],\n",
       "        [ -39.26951792,  -34.95099718,  -44.62602728,  -36.36770206,\n",
       "          -39.941431  ],\n",
       "        [  59.5061234 ,   52.96215643,   67.62298156,   55.10892623,\n",
       "           60.52429079],\n",
       "        [ -56.65692204,  -50.4262855 ,  -64.38513846,  -52.47026623,\n",
       "          -57.62633874]],\n",
       "\n",
       "       [[ 158.23463535,  140.83336353,  179.81843241,  146.54190776,\n",
       "          160.9420768 ],\n",
       "        [ 138.99171957,  123.70661662,  157.95071082,  128.72094472,\n",
       "          141.36990903],\n",
       "        [  69.40613416,   61.77344993,   78.87339088,   64.277377  ,\n",
       "           70.59369366],\n",
       "        [ -65.71018454,  -58.48394877,  -74.67329988,  -60.85453909,\n",
       "          -66.83450525],\n",
       "        [  99.57235425,   88.62225096,  113.1543964 ,   92.21446822,\n",
       "          101.27606671],\n",
       "        [ -94.80474931,  -84.37894583, -107.73647229,  -87.79916482,\n",
       "          -96.42688664]],\n",
       "\n",
       "       [[  73.19389229,   65.1446633 ,   83.17781341,   67.78523924,\n",
       "           74.44626146],\n",
       "        [  64.29278223,   57.22242006,   73.06255859,   59.54187554,\n",
       "           65.39285077],\n",
       "        [  32.10488713,   28.5742703 ,   36.48411401,   29.73250072,\n",
       "           32.65421125],\n",
       "        [ -30.39526813,  -27.05266036,  -34.54129658,  -28.14921379,\n",
       "          -30.91534017],\n",
       "        [  46.05874154,   40.99360091,   52.34132644,   42.65523689,\n",
       "           46.84682024],\n",
       "        [ -43.85341171,  -39.03079411,  -49.83518135,  -40.61286961,\n",
       "          -44.60375656]],\n",
       "\n",
       "       [[  92.62445226,   82.43841892,  105.25877455,   85.77998053,\n",
       "           94.20928405],\n",
       "        [  81.36039158,   72.41308187,   92.45825379,   75.34827614,\n",
       "           82.75249196],\n",
       "        [  40.62767387,   36.15979492,   46.16944079,   37.62549725,\n",
       "           41.3228254 ],\n",
       "        [ -38.46420752,  -34.23424782,  -43.71086952,  -35.62189996,\n",
       "          -39.12234149],\n",
       "        [  58.28581557,   51.87604746,   66.23621917,   53.97879289,\n",
       "           59.28310313],\n",
       "        [ -55.49504353,  -49.39218031,  -63.06477537,  -51.39424458,\n",
       "          -56.44458015]]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from tensorly.tenalg import outer\n",
    "outer([cp[1][0][:, 0], cp[1][1][:, 0], cp[1][2][:, 0]])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "209cf8d1-d155-4e43-b5d4-5dda4fecca35",
   "metadata": {},
   "source": [
    "This is called a rank-one 3-mode tensor because it can be computed exactly as the outer product of three vectors (therefore recovers a 3-mode tensor). See Figs. 1e-1g to see how this works. \n",
    "In CP decomposition, we write our original data tensor as the sum of 3 rank-one tensors (because we earlier chose the number of components to be 3, not because it has 3 modes). We can say that we break our original data down into three separate signals. Since rank-one tensors are easier to interpret, by reading into each component, we get to understand what information is contained in the data."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c5f49eb3",
   "metadata": {},
   "source": [
    "## 3. Choosing the number of components\n",
    "How do we choose the number of components for CP decomposition? The most basic method involves comparing the fitting error of each option. The reconstruction error is defined as the sum of squared differences between the original tensor and the reconstructed tensor, normalized (i.e. divided by) the sum of squares of the original data. This is equivalent to $1 - R^2$. We write a function to compute this value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "ee57cb5b",
   "metadata": {},
   "outputs": [],
   "source": [
    "import seaborn as sns\n",
    "from tensorly.cp_tensor import CPTensor\n",
    "from tensorly.tucker_tensor import TuckerTensor, tucker_to_tensor\n",
    "from tensorly.tenalg import multi_mode_dot\n",
    "\n",
    "def error(original, res):\n",
    "    # res is in CP\n",
    "    if isinstance(res, CPTensor):\n",
    "        res = res.to_tensor()\n",
    "    \n",
    "    # deal with cases when res is Tucker\n",
    "    if isinstance(res, TuckerTensor):\n",
    "        res = tucker_to_tensor(res)\n",
    "        \n",
    "    assert original.shape == res.shape\n",
    "    return np.sum((original - res)**2) / np.sum(original**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1dabd53d-6dc0-44e2-8deb-f640079e8734",
   "metadata": {},
   "source": [
    "To choose the optimal number of components, we need to first experiment with a range of numbers and find their fitting errors (Fig. 2c):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "f2cf8bff-f7e4-42f5-b672-434a63cf948e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='Num of Comps.', ylabel='Error'>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "errors = pd.DataFrame(columns=[\"Num of Comps.\", \"Error\"])\n",
    "for rr in np.arange(1, 7):\n",
    "    errors.loc[len(errors)+1] = [rr, error(tensor, parafac(tensor, rr))]\n",
    "\n",
    "sns.pointplot(data=errors, x=\"Num of Comps.\", y=\"Error\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e64b083-41c5-4ff2-9df5-865eb9a74d37",
   "metadata": {},
   "source": [
    "The fitting error consistently decreases with a greater number of components. We do not want a perfect fit; instead, we identify where the benefit of adding more components diminishes. This can be found as the elbow point (or kink) on the plot above. Here, we can see that it is at the 3rd component. Therefore, from now on, we can confidently choose 3 components for our dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "0a969033",
   "metadata": {},
   "outputs": [],
   "source": [
    "rank = 3\n",
    "cp = parafac(tensor, rank)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f2878bbc",
   "metadata": {},
   "source": [
    "### Compare CP and PCA performance\n",
    "\n",
    "The number of components chosen directly relates to the data compression efficiency and fidelity trade-off. Basically, when we choose more components, the reconstructed tensor has lower error, but with the cost of needing more parameters. We compare this relationship between CP and principal component analysis (PCA) performed on the original flattened matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "aad18187",
   "metadata": {},
   "outputs": [],
   "source": [
    "reduction = pd.DataFrame(columns=[\"Size\", \"Error\", \"Method\", \"Data\"])\n",
    "\n",
    "# Add CP reduction\n",
    "for rr in np.arange(1, 10):\n",
    "    reduction.loc[len(reduction)+1] = [rr * np.sum(tensor.shape),\n",
    "                                 error(tensor, parafac(tensor, rr, tol=1e-09)),\n",
    "                                 \"CP\",\n",
    "                                 \"Original data\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a3d2a08c-f22c-4a18-9ab8-caa9ce2beed9",
   "metadata": {},
   "source": [
    "A n-component CP decomposition needs $n \\times (7+6+5)$ parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "2581ae4d",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "\n",
    "flatten = tensor.reshape(tensor.shape[0], -1)\n",
    "pca = PCA(n_components=flatten.shape[0])\n",
    "pca.fit(flatten)\n",
    "pca_errors = 1 - np.cumsum(pca.explained_variance_ratio_)\n",
    "pca_sizes = np.sum(flatten.shape) * np.arange(1, flatten.shape[0] + 1)\n",
    "for rr in range(flatten.shape[0]-1):\n",
    "\n",
    "    reduction.loc[len(reduction)+1] = [pca_sizes[rr],\n",
    "                                pca_errors[rr],\n",
    "                                 \"PCA\",\n",
    "                                 \"Original data\",]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0c1e260-a7c4-44d4-84a5-32eba5591de3",
   "metadata": {},
   "source": [
    "A n-component PCA on a flattened matrix needs $n \\times (7+6 \\times 5)$ parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "aed5b0eb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='Size', ylabel='Error'>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lineplot(data=reduction, x=\"Size\", y=\"Error\", style=\"Method\", markers=[\"o\", \"o\"], color=\"#CFAD00\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2ca8d834",
   "metadata": {},
   "source": [
    "As we can see here, CP compresses the data more efficiently than PCA. Note that in this case, we cannot compare an n-component CP and an n-component PCA directly, as they are different in both parameters needed and fitting errors.\n",
    "\n",
    "Nonetheless, CP decomposition is not always better than PCA; it depends on the underlying data structure. Here, we can do an experiment to demonstrate this (Fig). First, we create two new datasets by randomly shuffling the chords (defined in Fig. 2a) and all numbers in the original datasets. This will break the underlying low-rank structure in the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "61282596",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Shuffle the chords / columns\n",
    "col_tensor = tensor.reshape(tensor.shape[0], -1)\n",
    "col_tensor = col_tensor[:, np.random.permutation(col_tensor.shape[1])]\n",
    "col_tensor = col_tensor.reshape(*tensor.shape)\n",
    "\n",
    "# Shuffle all numbers\n",
    "rng = np.random.default_rng(123)\n",
    "rand_tensor = rng.permutation(tensor.flatten()).reshape(*tensor.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8e5e542b-17a4-4572-a8c3-0f7fbc28ecd0",
   "metadata": {},
   "source": [
    "We now compare the CP and PCA errors when run on the original datasets and these two new datasets. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "c0c06c0e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='Size', ylabel='Error'>"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for rr in np.arange(1, 13):\n",
    "    reduction = pd.concat([reduction, pd.DataFrame([{\n",
    "                        'Size': rr * np.sum(col_tensor.shape),\n",
    "                        'Error': error(col_tensor, parafac(col_tensor, rr, tol=1e-09)),\n",
    "                        'Method': \"CP\",\n",
    "                        'Data': 'Chord shuffled',\n",
    "                    }])], ignore_index=True)\n",
    "    reduction = pd.concat([reduction, pd.DataFrame([{\n",
    "                        'Size': rr * np.sum(rand_tensor.shape),\n",
    "                        'Error': error(rand_tensor, parafac(rand_tensor, rr, tol=1e-09)),\n",
    "                        'Method': \"CP\",\n",
    "                        'Data': 'All number shuffled',\n",
    "                    }])], ignore_index=True)\n",
    "    \n",
    "# Find PCA data reduction\n",
    "# Chords shuffled\n",
    "col_flatten = col_tensor.reshape(col_tensor.shape[0], -1)\n",
    "col_pca = PCA(n_components=col_flatten.shape[0])\n",
    "col_pca.fit(col_flatten)\n",
    "col_pca_errors = 1 - np.cumsum(col_pca.explained_variance_ratio_)\n",
    "col_pca_sizes = np.sum(col_flatten.shape) * np.arange(1, col_flatten.shape[0] + 1)\n",
    "\n",
    "# All number shuffled\n",
    "rand_flatten = rand_tensor.reshape(rand_tensor.shape[0], -1)\n",
    "rand_pca = PCA(n_components=rand_flatten.shape[0])\n",
    "rand_pca.fit(rand_flatten)\n",
    "rand_pca_errors = 1 - np.cumsum(rand_pca.explained_variance_ratio_)\n",
    "rand_pca_sizes = np.sum(rand_flatten.shape) * np.arange(1, rand_flatten.shape[0] + 1)\n",
    "for rr in range(rand_flatten.shape[0]-1):\n",
    "    reduction = pd.concat([reduction, pd.DataFrame([{\n",
    "                    'Size': col_pca_sizes[rr],\n",
    "                    'Error': col_pca_errors[rr],\n",
    "                    'Method': \"PCA\",\n",
    "                    'Data': 'Chord shuffled',\n",
    "                }])], ignore_index=True)\n",
    "    \n",
    "    reduction = pd.concat([reduction, pd.DataFrame([{\n",
    "                    'Size': rand_pca_sizes[rr],\n",
    "                    'Error': rand_pca_errors[rr],\n",
    "                    'Method': \"PCA\",\n",
    "                    'Data': 'All number shuffled',\n",
    "            }])], ignore_index=True)\n",
    "\n",
    "sns.lineplot(data=reduction, x=\"Size\", y=\"Error\", hue=\"Data\", style=\"Method\", marker=\"o\", \n",
    "             palette=[\"#CFAD00\", \"#9A24D1\", \"#FF5956\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a007e606-c69b-4cd9-92af-cb53060c4a3d",
   "metadata": {},
   "source": [
    "As we can see here, the chord shuffle harms the fitting of CP, and all number shuffle even worsens it. Permuting chords in a tensor is equivalent to shuffling the columns in its flattened matrix, which does not impact the performance of PCA at all. Therefore, the PCA curves for the original data and the chord-shuffled version perfectly overlap. However, PCA performs much worse on the all-number-shuffled datasets."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18fa3877",
   "metadata": {},
   "source": [
    "## 4. Visualize the results with heatmaps"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b6ba2f9",
   "metadata": {},
   "source": [
    "We now visualize the decomposition results. To visualize these factor matrices, we plot heatmaps for each of them, one for each mode."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "51d95389",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib\n",
    "from matplotlib import gridspec, pyplot as plt\n",
    "\n",
    "def plot_factors(res):\n",
    "    ddims = len(res[1])\n",
    "    f = plt.figure(figsize=(5*ddims, 6))\n",
    "    gs = gridspec.GridSpec(1, ddims, wspace=0.5)\n",
    "    axes = [plt.subplot(gs[rr]) for rr in range(ddims)]\n",
    "    \n",
    "    factors = [pd.DataFrame(res[1][rr],\n",
    "                        columns=[f\"Cmp. {i}\" for i in np.arange(1, res[1][rr].shape[1]+1)],\n",
    "                        index=[organs, drugs, times][rr])\n",
    "               for rr in range(ddims)]\n",
    "    \n",
    "    for rr in range(ddims):\n",
    "        sns.heatmap(factors[rr], cmap=\"vlag\", center=0, \n",
    "                    xticklabels=[str(ii+1) for ii in range(res[1][rr].shape[1])], \n",
    "                    yticklabels=factors[rr].index,\n",
    "                    cbar=True, vmin=-1.0, vmax=1.0, ax=axes[rr])\n",
    "        axes[rr].set_xlabel(\"Components\")\n",
    "        axes[rr].set_title(axes_names[rr])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "6dfc91b8",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1500x600 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_factors(cp)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "28d3e5ea",
   "metadata": {},
   "source": [
    "By default setting of the `parafac` function, the weights are all 1, and the factor matrices are unnormalized. Therefore, the colors in some blocks are at the strongest ends because these weights are far beyond +1 and -1, making them hard to compare directly. To better visualize the results, we perform two additional steps to normalize the results:\n",
    "1. We scale the factor matrix columns so that the largest weight in each column is 1. The weights are shifted to the weights, `cp[0]`. We then sort the components by their weights. These operations will give us an equivalent decomposition."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "cbcbf45a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def factor_scaling(res: CPTensor):\n",
    "    \"\"\" Scale the factor matrices so that they are in plottable scales. \"\"\"\n",
    "    for i, factor in enumerate(res.factors):\n",
    "        scales = np.linalg.norm(factor, ord=np.inf, axis=0)\n",
    "        res.weights *= scales\n",
    "        res.factors[i] /= scales\n",
    "\n",
    "    comp_order = np.flip(np.argsort(res.weights))\n",
    "    res.weights = res.weights[comp_order]\n",
    "    for i, factor in enumerate(res.factors):\n",
    "        res.factors[i] = factor[:, comp_order]\n",
    "    return res\n",
    "\n",
    "cp = factor_scaling(cp)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7040de84",
   "metadata": {},
   "source": [
    "2. We invert the signs of the factor weights of any component that have negative weights on two modes. This will ensure that at most one mode contains strong negative weights."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "8604eb55",
   "metadata": {},
   "outputs": [],
   "source": [
    "def sign_indeterminacy(res: CPTensor):\n",
    "    \"\"\" Fix CP decomposition sign indeterminacy by flipping signs in pairs of modes. \"\"\"\n",
    "    ddims = len(res[1])\n",
    "    for rr in range(ddims-1):\n",
    "        mmeans = np.sign(np.mean(res.factors[rr], axis=0))\n",
    "        res.factors[rr] *= mmeans[np.newaxis, :]\n",
    "        res.factors[rr+1] *= mmeans[np.newaxis, :]\n",
    "    return res\n",
    "\n",
    "cp = sign_indeterminacy(cp)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ea785453",
   "metadata": {},
   "source": [
    "Check out Fig. 2i to learn more about factors' scale indeterminacy and why these two operations above will give us equivalent decomposition results.\n",
    "Now we plot the factor matrices again (Fig. 2f)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "49113317",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1500x600 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_factors(cp) "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c77c9135-b01f-4340-a1f2-14522cbd8352",
   "metadata": {},
   "source": [
    "Now all values in the heatmaps are in reasonable ranges, easing the interpretation process."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4be92fc6",
   "metadata": {},
   "source": [
    "## 5. Other options for visualizing the results"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "81cd4fef",
   "metadata": {},
   "source": [
    "Heatmaps are sometimes not the most intuitive way of visualizing factors. Therefore, here we show a few other options to demonstrate the tensor decomposition results.\n",
    "\n",
    "### Looking into one component\n",
    "To inspect one component, we can make a bar plot for each factor of the three modes (Fig. 2e):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "8c2f12e1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1500x300 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_one_component(res, i_comp=1):\n",
    "    ddims = len(res[1])\n",
    "    f = plt.figure(figsize=(5*ddims, 3))\n",
    "    gs = gridspec.GridSpec(1, ddims, wspace=0.5)\n",
    "    axes = [plt.subplot(gs[rr]) for rr in range(ddims)]\n",
    "    \n",
    "    bar_colors = [\"#3177FF\", \"#FF644F\", \"#00AD01\"]\n",
    "    \n",
    "    for rr in range(ddims):\n",
    "        sns.barplot(data = pd.DataFrame(data={\"Entry\": entry_names[rr], \"Weight\": cp[1][rr][:, i_comp-1]}),\n",
    "                    x='Entry', y='Weight', color=bar_colors[rr], ax=axes[rr])\n",
    "        \n",
    "        axes[rr].set_title(axes_names[rr])\n",
    "        axes[rr].tick_params(axis='x', rotation=90)\n",
    "        \n",
    "    f.suptitle(f\"Component {i_comp}\")\n",
    "\n",
    "plot_one_component(cp, i_comp=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "87b28358",
   "metadata": {},
   "source": [
    "### Looking into one mode\n",
    "Alternatively, we can also compare the factors across components within one mode. Depending on the nature of the mode, one can either choose a barplot or a lineplot.\n",
    "Bar plot usually works well for discrete labels such as samples or treatments. In our case, organs and drugs are discrete labels. Here is a bar plot for drug factors (Fig. 2g)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "25f50431",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Drug factors')"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "drug_factors = pd.DataFrame(cp[1][1], columns=[f\"Comp. {rr}\" for rr in np.arange(1, rank+1)], index=drugs)\n",
    "drug_factors.index.name = \"Drug\"\n",
    "drug_factors = drug_factors.reset_index().melt(id_vars=['Drug'], \n",
    "                                               value_vars=[f\"Comp. {rr}\" for rr in np.arange(1, rank+1)],\n",
    "                                               var_name=\"Component\", value_name='Weight')\n",
    "\n",
    "sns.barplot(data=drug_factors, x=\"Drug\", y=\"Weight\", hue=\"Component\", \n",
    "            palette= [\"#E1812C\", \"#3A923A\", \"#C03D3E\"]).set_title(\"Drug factors\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "34d5a7a7-ded3-45cf-b35f-13e967ffe41f",
   "metadata": {},
   "source": [
    "Line plot usually works better for continuous labels, such as time or concentration. Here is a line plot for time factors (Fig. 2h)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "b1138191",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Time point factors')"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "time_factors = pd.DataFrame(cp[1][2], columns=[f\"Comp. {rr}\" for rr in np.arange(1, rank+1)], index=times)\n",
    "time_factors.index.name = \"Time\"\n",
    "time_factors = time_factors.reset_index().melt(id_vars=['Time'], \n",
    "                                               value_vars=[f\"Comp. {rr}\" for rr in np.arange(1, rank+1)],\n",
    "                                               var_name=\"Component\", value_name='Weight')\n",
    "\n",
    "sns.lineplot(data=time_factors, x=\"Time\", y=\"Weight\", hue=\"Component\", \n",
    "             palette=[\"#E1812C\", \"#3A923A\", \"#C03D3E\"]).set_title(\"Time point factors\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f1d02509",
   "metadata": {},
   "source": [
    "## 6. Use factor matrix to find associations among organs\n",
    "\n",
    "A factor matrix can serve as reduced and summarized data for its mode. For example, we can run hierarchical clustering to the factor matrix to reveal the association among the mode entries (Fig. 2j)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "2a939109",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.matrix.ClusterGrid at 0x143c5ac30>"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAe8AAAH0CAYAAAAUmKWVAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8fJSN1AAAACXBIWXMAAA9hAAAPYQGoP6dpAAAtv0lEQVR4nO3df1hUZf7/8dcgMCigVhJqgWZaiRv+IvuYiWIJpGuamqZuRmZZmSaoGVsJWDpm9rF0k/3sVtCWv7Ja86Ot1bphuWqmRpaS+TO20lgzZaUPA8L5/tHXuZpAHRBm5sbn47rOdTH3uc993odz5av7njODzbIsSwAAwBgBvi4AAADUDOENAIBhCG8AAAxDeAMAYBjCGwAAwxDeAAAYhvAGAMAwhDcAAIYhvAEAMAzhDQCAYYwN7w8//FCDBg1S69atZbPZtGrVKl+XBACAVxgb3iUlJercubP+8Ic/+LoUAAC8KtDXBdTWLbfcoltuucXXZQAA4HV+Fd5Op1NOp9OtzW63y263+6giAAD8j8fh/foNveuzDknS7sSblJWV5daWkZGhzMzMej83AACm8Di8GwXV/yQ9PT1daWlpbm3MugEAcOdxIgcE1n94s0QOAMC5eZzItsBG9VkHAADwkOfL5l6YedfEyZMntW/fPtfrgwcPKj8/XxdffLGio6N9WBkAAPXL82VzL7znXRPbtm1TQkKC6/Xp98rvuusu5ebm+qgqAADqn7Hh3bdvX1mW5esyAADwOr96YA0AAJxbDWbeQfVZBwAA8BAzbwAADON5eDfio2IAAPgDYx9YAwDgQlWDL2khvAEA8AfMvAEAMEwNHljjaXMAAPwBM28AAAzj+XvePG0OAIBf4HPeAAAYhm9YAwDAMMy8AQAwDE+bAwBgGJ42BwDAMDxtDgCAYXhgDQAAw/DAGgAAhmHmDQCAYWrwV8UIbwAA/AFPmwMAYBg+5w0AgGH4qBgAAIbhgTUAAAxDeAMAYBg+5w0AgGGYeQMAYBiPw7sR4Q0AgF/gaXMAAAzDsjkAAIYhvAEAMAzveQMAYBi+HhUAAMOwbA4AgGECPO4YFFjvW20sXrxYV1xxhUJCQtS9e3d99NFHtRoHAABTeBzetoBG9b7V1IoVKzRlyhQ99thj+vTTT9W7d2/dcsstKiwsrPFYAACYwmZZluVJx/KT/6nvWhQUFl6j/tdff726deum7OxsV1vHjh01ZMgQORyOui4PAAC/4PladYDHk/Raczqdcjqdbm12u112u71K37KyMm3fvl2PPvqoW3tiYqI2bdpUr3UCAOBLNUhkW71vDodDzZo1c9vONIM+evSoKioqFBkZ6dYeGRmpI0eOeH5ZAAAYxuOZd6VHi+vnJz09XWlpaW5t1c26f8lms7m9tiyrShsAAA2Jx+Fd4YX0bnKGJfLqtGjRQo0aNaoyyy4qKqoyGwcAoCHxeNm8orKy3reaCA4OVvfu3fX++++7tb///vu64YYbajQWAAAm8XjmfaqiZuHqDWlpabrzzjsVFxennj176k9/+pMKCwt1//33+7o0AADqjcfhXX6qoj7rqJWRI0fqhx9+0KxZs3T48GH95je/0TvvvKM2bdr4ujQAAOqNx5/z/va7o/Vdiy5r3aLezwEAgOmMnnkDAHAhIrwBADBMDcLb/x5YAwDgQlSDz3kT3gAA+ANm3gAAGIbwBgDAMDywBgCAYYz+hjUAAC5ELJsDAGAYv/qrYgAA4NyYeQMAYBjPw5v3vAEA8AvMvAEAMAwzbwAADOP5R8VO8cAaAAD+wPPw5mlzAAD8Al/SAgCAYWrwwBozbwAA/AEPrAEAYJgahDczbwAA/AHL5gAAGIZlcwAADFODP0xSn2UAAABP8Z43AACGIbwBADAMD6wBAGAYZt4AABiG8AYAwDA1+MMk9VkGAADwVA1m3vVZBgAA8JTH4V3GsjkAAH6BmTcAAIbxfOZ9qj7LAAAAnqrBsnl9lgEAADzlcXg7DQ7v2bNna+3atcrPz1dwcLCOHz/u65IAAKg1z9/zNvijYmVlZbr99tvVs2dPvfTSS74uBwCA83JBzLyzsrIkSbm5ub4tBACAOuBxeP/fKVt91iFJcjqdcjqdbm12u112u73ezw0AgCk8Du89L/SrzzokSZmZma5Z8mkZGRnKzMys93MDAGCKAF8X8Evp6ek6ceKE25aenl5t38zMTNlstrNu27Zt8/IVAABQ/zyeeXtDTZbIH3roId1xxx1n7dO2bds6qAoAAP/iV+FdEy1atFCLFi18XQYAAF5nbHjXRGFhoY4dO6bCwkJVVFQoPz9fktS+fXuFhYX5rK4NW7/y2bnhud+0u9TXJcADX7+02NclwAPdZvze1yU0CBdEeM+cOVOvvPKK63XXrl0lSR988IH69u3ro6oAAKgdv3pgrb7k5ubKsqwqG8ENADDRBRHeAAA0JIQ3AACGIbwBADAM4Q0AgGEIbwAADEN4AwBgGMIbAADDEN4AABiG8AYAwDCENwAAhiG8AQAwDOENAIBhCG8AAAxDeAMAYBjCGwAAwxDeAAAYhvAGAMAwhDcAAIYhvAEARrLZbFq1atUZ97dt21bPPfec1+rxJsIbAOCXioqKNGHCBEVHR8tut6tly5ZKSkrS5s2bPTr+k08+0X333VfPVfpGoK8LAACgOsOGDVN5ebleeeUVtWvXTt9//73Wr1+vY8eOeXR8REREPVfoO8y8AQB+5/jx49q4caOefvppJSQkqE2bNurRo4fS09M1cODAao+ZNWuWIiMjlZ+fL6nqsrnNZtOLL76o2267TU2aNFGHDh20evVqL1xN3SO8AQBe43Q6VVxc7LY5nc4q/cLCwhQWFqZVq1ZVu/+XLMvSww8/rJdeekkbN25Uly5dztg3KytLI0aM0M6dOzVgwACNGTPG45m8P6nTZfP09HSVlpbW5ZAN1oIFC3xdAgB4ncPhUFZWlltbRkaGMjMz3doCAwOVm5ure++9V3/84x/VrVs39enTR3fccYdiY2Nd/U6dOqWxY8dq27Zt+uc//6nLL7/8rOdPSUnRqFGjJElz5szRokWLtHXrViUnJ9fNBXpJnYZ3aWkpoQQAOKP09HSlpaW5tdnt9mr7Dhs2TAMHDtRHH32kzZs3a926dZo3b55efPFFpaSkSJJSU1Nlt9u1ZcsWtWjR4pzn/2Xwh4aGKjw8XEVFRbW/IB9h2RwA4DV2u11NmzZ1284U3pIUEhKi/v37a+bMmdq0aZNSUlKUkZHh2t+/f399++23evfddz06f1BQkNtrm82mysrK2l2MDxHeAABjxMTEqKSkxPX61ltv1dKlSzV+/HgtX77ch5V5Fx8VAwD4nR9++EG33367xo0bp9jYWIWHh2vbtm2aN2+eBg8e7Nb3tttu06uvvqo777xTgYGBGj58uI+q9h7CGwDgd8LCwnT99ddrwYIF2r9/v8rLyxUVFaV7771Xv//976v0Hz58uCorK3XnnXcqICBAQ4cO9UHV3kN4AwD8jt1ul8PhkMPhOGMfy7LcXo8YMUIjRoxwvT506NBZ+0s/f57cRLznDQCAYQhvAAAMQ3gDAGAYwhsAAMMQ3gAAGIbwBgDAMIQ3AACGIbwBADAM4Q0AgGEIbwAADEN4AwBgGMIbAADDEN4AABiG8AYAwDCENwAAhiG8AQAwDOENAIBhCG8AAAwT6OsCLmRtWjbzdQnwwPrf/tbXJcADPWfP9HUJgNcw8wYAwDCENwAAhiG8AQAwDOENAIBhCG8AAAxDeAMAYBjCGwAAwxDeAAAYhvAGAMAwhDcAAIYhvAEAMAzhDQCAYQhvAAAMQ3gDAGAYwhsAAMMQ3gAAGIbwBgDAMIQ3AACGIbwBADAM4Q0AgGEIbwCAcQ4dOiSbzab8/Hxfl+IThDcAwK/YbLazbikpKb4u0ecCfV0AAAC/dPjwYdfPK1as0MyZM7Vnzx5XW+PGjfXjjz/6ojS/wcwbAOBXWrZs6dqaNWsmm81Wpe20AwcOKCEhQU2aNFHnzp21efNmSVJJSYmaNm2qN954w23s//3f/1VoaKj+85//uJbeX3/9dfXu3VuNGzfWddddp6+++kqffPKJ4uLiFBYWpuTkZP373/92jdG3b19NmTLFbdwhQ4a4rQgsXrxYHTp0UEhIiCIjIzV8+PA6/R0R3gAAr3E6nSouLnbbnE5nrcd77LHHNG3aNOXn5+uqq67SqFGjdOrUKYWGhuqOO+5QTk6OW/+cnBwNHz5c4eHhrraMjAw9/vjj2rFjhwIDAzVq1Cg98sgjev755/XRRx9p//79mjlzpsc1bdu2TZMnT9asWbO0Z88erVu3TvHx8bW+xuo0uGXz9PR0lZaW+rqMc1qwYIGvSwAAr3M4HMrKynJry8jIUGZmZq3GmzZtmgYOHChJysrKUqdOnbRv3z5dc801Gj9+vG644QZ99913at26tY4ePao1a9bo/fffrzJGUlKSJOnhhx/WqFGjtH79evXq1UuSdM899yg3N9fjmgoLCxUaGqrf/va3Cg8PV5s2bdS1a9daXd+ZNLjwLi0tJRgBwE+lp6crLS3Nrc1ut9d6vNjYWNfPrVq1kiQVFRXpmmuuUY8ePdSpUyf95S9/0aOPPqpXX31V0dHRVWbBvxwjMjJSknTttde6tRUVFXlcU//+/dWmTRu1a9dOycnJSk5O1m233aYmTZrU6hqrw7I5AMBr7Ha7mjZt6radT3gHBQW5frbZbJKkyspKV9v48eNdS+c5OTm6++67Xf3ONsav2345ZkBAgCzLchujvLzc9XN4eLh27NihZcuWqVWrVpo5c6Y6d+6s48eP1/YyqyC8AQAN1u9+9zsVFhZq4cKF2rVrl+66667zHjMiIsLtifiKigp98cUXbn0CAwN18803a968edq5c6cOHTqkf/zjH+d9btf4dTYSAAB+5qKLLtLQoUM1ffp0JSYm6vLLLz/vMfv166e0tDStXbtWV155pRYsWOA2q16zZo0OHDig+Ph4XXTRRXrnnXdUWVmpq6+++rzPfRozbwBAg3bPPfeorKxM48aNq5Pxxo0bp7vuuktjx45Vnz59dMUVVyghIcG1v3nz5nrrrbfUr18/dezYUX/84x+1bNkyderUqU7OL0k269cL9+chNTXV5w+L+UMNnjpU+L2vS4AHto4Y5usS4IGesz3/KA98J+qmRK+fc8mSJXr44Yf13XffKTg42Ovnrw8smwMAGqSffvpJBw8elMPh0IQJExpMcEssmwMAGqh58+apS5cuioyMVHp6uq/LqVOENwCgQcrMzFR5ebnWr1+vsLAwX5dTpwhvAAAMQ3gDAGAYwhsAAMMQ3gAAGIbwBgDAMIQ3AACGIbwBADAM4Q0AgGEIbwAADEN4AwBgGMIbAADDEN4AABiG8AYAwDCENwAAhiG8AQAwTKCvC7iQVXzyoa9LgAdiHxjn6xLggQNv/dXXJcADUTcl+rqEBoGZNwAAhiG8AQAwDOENAIBhCG8AAAxDeAMAYBjCGwAAwxDeAAAYhvAGAMAwhDcAAIYhvAEAMAzhDQCAYQhvAAAMQ3gDAGAYwhsAAMMQ3gAAGIbwBgDAMIQ3AACGIbwBADAM4Q0AgGEC6/sE6enpKi0tre/TuBQVFXntXAAA+EK9h3dpaakWLFhQ36dxSU1N9dq5AADwBZbNAQB+KSUlRTabTTabTUFBQWrXrp2mTZumkpISX5fmc/U+8wYAoLaSk5OVk5Oj8vJyffTRRxo/frxKSkqUnZ3t9VrKysoUHBzs9fNWh5k3AMBv2e12tWzZUlFRURo9erTGjBmjVatW6bXXXlNcXJzCw8PVsmVLjR492u2Zp7y8PNlsNq1fv15xcXFq0qSJbrjhBu3Zs8dt/NWrVysuLk4hISFq0aKFhg4d6trXtm1bPfXUU0pJSVGzZs107733SpI2bdqk+Ph4NW7cWFFRUZo8ebLbasC5avvxxx81ZswYRUREqHHjxurQoYNycnJq9HshvAEAXuN0OlVcXOy2OZ1Oj49v3LixysvLVVZWpieffFKfffaZVq1apYMHDyolJaVK/8cee0zPPvustm3bpsDAQI0bN861b+3atRo6dKgGDhyoTz/91BX0v/TMM8/oN7/5jbZv364nnnhCn3/+uZKSkjR06FDt3LlTK1as0MaNG/XQQw+5jjlXbU888YR2796tv/3tbyooKFB2drZatGjh+S9RLJt7/Wn407z5EB8A+AuHw6GsrCy3toyMDGVmZp7z2K1bt2rp0qW66aab3EK4Xbt2WrhwoXr06KGTJ08qLCzMtW/27Nnq06ePJOnRRx/VwIEDVVpaqpCQEM2ePVt33HGHWz2dO3d2O2e/fv00bdo01+uxY8dq9OjRmjJliiSpQ4cOWrhwofr06aPs7GyFhIScs7bCwkJ17drV9T8Kbdu2Pee1/9oFH97efhoeAC5k6enpSktLc2uz2+1n7L9mzRqFhYXp1KlTKi8v1+DBg7Vo0SJ9+umnyszMVH5+vo4dO6bKykpJUmFhoWJiYlzHx8bGun5u1aqVpJ8/UhwdHa38/HzXUviZ/Homvn37du3bt09LlixxtVmWpcrKSh08eFAdO3Y8Z20PPPCAhg0bph07digxMVFDhgzRDTfccNY6fu2CD28AgPfY7fazhvWvJSQkKDs7W0FBQWrdurWCgoJUUlKixMREJSYm6rXXXlNERIQKCwuVlJSksrIyt+ODgoJcP9tsNklyhWnjxo3Pef7Q0FC315WVlZowYYImT55cpW90dLRHtd1yyy36+uuvtXbtWv3973/XTTfdpIkTJ2r+/Pke/14IbwCA3woNDVX79u3d2r788ksdPXpUc+fOVVRUlCRp27ZtNR47NjZW69ev19133+3xMd26ddOuXbuq1HTa559/7lFtERERSklJUUpKinr37q3p06fXKLx5YA0AYJTo6GgFBwdr0aJFOnDggFavXq0nn3yyxuNkZGRo2bJlysjIUEFBgT7//HPNmzfvrMfMmDFDmzdv1sSJE5Wfn6+9e/dq9erVmjRpkse1zZw5U2+//bb27dunXbt2ac2aNerYsWONaie8AQBGiYiIUG5urlauXKmYmBjNnTu3RrPW0/r27auVK1dq9erV6tKli/r166ePP/74rMfExsZqw4YN2rt3r3r37q2uXbvqiSeecL2f7kltwcHBSk9PV2xsrOLj49WoUSMtX768RrXbLMuyana5Z5aamlrl4a/q2upTTc/n7fp+af+bK31yXtRM+cn/+LoEeOD7rZ/4ugR4oM8L3v9ylYaImTcAAIYhvAEAMAzhDQCAYQhvAAAMQ3gDAGAYwhsAAMMQ3gAAGIbwBgDAMIQ3AACGIbwBADAM4Q0AgGEIbwAADEN4AwBgGMIbAADDEN4AABiG8AYAwDCENwAAhiG8AQAwTKCvC7iQNb3ySl+XAA/sXbbM1yXAA2GXtfZ1CYDXMPMGAMAwhDcAAIYhvAEAMAzhDQCAYQhvAAAMQ3gDAGAYwhsAAMMQ3gAAGIbwBgDAMIQ3AACGIbwBADAM4Q0AgGEa3B8mCQkJUWpqqsf9i4qK6rEaAADqXoMLb4fDUaP+NQl6AAD8AcvmAAAYhvAGAMAwhDcAAIYhvAEAMAzhDQCAYQhvAAAMQ3gDAIxjs9m0atUqX5fhMw3uc94AgIYhJSVFx48frzakDx8+rIsuusj7RfkJwhsAYJyWLVvW6/gVFRWy2WwKCPDPBWr/rAoAgLP45bJ5z5499eijj7rt//e//62goCB98MEHkqSysjI98sgjuuyyyxQaGqrrr79eeXl5rv65ublq3ry51qxZo5iYGNntdn399dfeupwaI7wBAF7jdDpVXFzstjmdzvMac8yYMVq2bJksy3K1rVixQpGRkerTp48k6e6779Y///lPLV++XDt37tTtt9+u5ORk7d2713XMTz/9JIfDoRdffFG7du3SpZdeel511SeWzWshPT1dpaWl5zXGggUL6qgaADCHw+FQVlaWW1tGRoYyMzNrPebIkSOVmpqqjRs3qnfv3pKkpUuXavTo0QoICND+/fu1bNkyffPNN2rdurUkadq0aVq3bp1ycnI0Z84cSVJ5ebkWL16szp0717oWbyG8a6G0tJTwBYBaSE9PV1pamlub3W4/rzEjIiLUv39/LVmyRL1799bBgwe1efNmZWdnS5J27Nghy7J01VVXuR3ndDp1ySWXuF4HBwcrNjb2vGrxFsIbAOA1drv9vMO6OmPGjNHDDz+sRYsWaenSperUqZNrBl1ZWalGjRpp+/btatSokdtxYWFhrp8bN24sm81W57XVB8IbAGC8IUOGaMKECVq3bp2WLl2qO++807Wva9euqqioUFFRkWtZ3XSENwDAb504cUL5+flubRdffHGVfqGhoRo8eLCeeOIJFRQUaPTo0a59V111lcaMGaOxY8fq2WefVdeuXXX06FH94x//0LXXXqsBAwbU92XUOcIbAOC38vLy1LVrV7e2u+66q9q+Y8aM0cCBAxUfH6/o6Gi3fTk5OXrqqac0depUffvtt7rkkkvUs2dPI4NbIrwBAH4qNzdXubm5Z9z3awMGDHD7uNgvBQUFKSsrq8qT7qelpKQoJSWllpV6H5/zBgDAMIQ3AACGIbwBADAM4Q0AgGEIbwAADEN4AwBgGMIbAADDEN4AABiG8AYAwDCENwAAhiG8AQAwDOENAIBhCG8AAAxDeAMAYBjCGwAAwxDeAAAYhvAGAMAwhDcAAIYJ9HUBvhYSEqLU1NQaHVNUVFQn5258ySV1Mg7q1/F9B3xdAjxwxaABvi4B8JoLPrwdDkeNj6lp2AMAUJdYNgcAwDCENwAAhiG8AQAwDOENAIBhCG8AAAxDeAMAYBjCGwAAwxDeAAAYpk6/pKW6byurq28jAwAAP6vT8K7u28r4NjIAAOoWy+YAABiG8AYAwDCENwAAhiG8AQAwDOENAIBhCG8AAAxDeAMAYBjCGwAAwxDeAAAYhvAGADRYmZmZ6tKli6/LqHOENwDAbx05ckSTJk1Su3btZLfbFRUVpUGDBmn9+vW+Ls2n6vS7zQEAqCuHDh1Sr1691Lx5c82bN0+xsbEqLy/Xu+++q4kTJ+rLL7/0dYk+w8wbAOCXHnzwQdlsNm3dulXDhw/XVVddpU6dOiktLU1btmyRJBUWFmrw4MEKCwtT06ZNNWLECH3//fdnHLOyslKzZs3S5ZdfLrvdri5dumjdunWu/YcOHZLNZtNbb72lhIQENWnSRJ07d9bmzZvr/XprgvAGAHiN0+lUcXGx2+Z0Oqv0O3bsmNatW6eJEycqNDS0yv7mzZvLsiwNGTJEx44d04YNG/T+++9r//79Gjly5BnP//zzz+vZZ5/V/PnztXPnTiUlJenWW2/V3r173fo99thjmjZtmvLz83XVVVdp1KhROnXq1Pn/AuoIy+a1UN3fLa+pBQsW1FE1AGAOh8OhrKwst7aMjAxlZma6te3bt0+WZemaa64541h///vftXPnTh08eFBRUVGSpFdffVWdOnXSJ598ouuuu67KMfPnz9eMGTN0xx13SJKefvppffDBB3ruuef0wgsvuPpNmzZNAwcOlCRlZWWpU6dO2rdv31nr8SbCuxaq+7vlAIBzS09PV1pamlub3W6v0s+yLEmSzWY741gFBQWKiopyBbckxcTEqHnz5iooKKgS3sXFxfruu+/Uq1cvt/ZevXrps88+c2uLjY11/dyqVStJUlFRkd+EN8vmAACvsdvtatq0qdtWXXh36NBBNptNBQUFZxzLsqxqw/1M7af9el91/YOCgqr0r6ysPOOY3kZ4AwD8zsUXX6ykpCS98MILKikpqbL/+PHjiomJUWFhof71r3+52nfv3q0TJ06oY8eOVY5p2rSpWrdurY0bN7q1b9q0qdr+/oxlcwCAX1q8eLFuuOEG9ejRQ7NmzVJsbKxOnTql999/X9nZ2dq9e7diY2M1ZswYPffcczp16pQefPBB9enTR3FxcdWOOX36dGVkZOjKK69Uly5dlJOTo/z8fC1ZssTLV3d+CG8AgF+64oortGPHDs2ePVtTp07V4cOHFRERoe7duys7O1s2m02rVq3SpEmTFB8fr4CAACUnJ2vRokVnHHPy5MkqLi7W1KlTVVRUpJiYGK1evVodOnTw4pWdP5t1+qmAepKamsqT1Wdw8l9f+7oEeODDKWnn7gSfu2LQAF+XAA90TLnH1yU0CLznDQCAYQhvAAAMQ3gDAGAYwhsAAMMQ3gAAGIbwBgDAMIQ3AACGIbwBADAM4Q0AgGEIbwAADEN4AwBgGMIbAADDEN4AABiG8AYAwDCENwAAhiG8AQAwDOENAIBhCG8AAAwT6OsCLmTv3D7G1yXAAzfOn+PrEuCBjdN+7+sS4IGOKff4uoQGgZk3AACGIbwBADAM4Q0AgGEIbwAADEN4AwBgGMIbAADDEN4AABiG8AYAwDCENwAAhiG8AQAwDOENAIBhCG8AAAxDeAMAYBjCGwAAwxDeAAAYhvAGAMAwhDcAAIYhvAEAMAzhDQCAYQhvAAAMQ3gDAGAYwhsA4JdSUlI0ZMiQKu15eXmy2Ww6fvx4vZ4/MzNTXbp0qddz1FagrwsAAMCfWJaliooKX5dxVsy8AQBG27Rpk+Lj49W4cWNFRUVp8uTJKikpce1/7bXXFBcXp/DwcLVs2VKjR49WUVGRa//pmfy7776ruLg42e12vfrqq8rKytJnn30mm80mm82m3NxcH1xd9QhvAIDXOJ1OFRcXu21Op7PW433++edKSkrS0KFDtXPnTq1YsUIbN27UQw895OpTVlamJ598Up999plWrVqlgwcPKiUlpcpYjzzyiBwOhwoKCpSYmKipU6eqU6dOOnz4sA4fPqyRI0fWus661mCWzdPT01VaWurrMjy2YMECX5cAAF7ncDiUlZXl1paRkaHMzMxq+69Zs0ZhYWFubb9c0n7mmWc0evRoTZkyRZLUoUMHLVy4UH369FF2drZCQkI0btw4V/927dpp4cKF6tGjh06ePOk29qxZs9S/f3/X67CwMAUGBqply5a1vdx602DCu7S0lEAEAD+Xnp6utLQ0tza73X7G/gkJCcrOznZr+/jjj/W73/1OkrR9+3bt27dPS5Ysce23LEuVlZU6ePCgOnbsqE8//VSZmZnKz8/XsWPHVFlZKUkqLCxUTEyM67i4uLjzvj5vaTDhDQDwf3a7/axh/WuhoaFq3769W9s333zj+rmyslITJkzQ5MmTqxwbHR2tkpISJSYmKjExUa+99poiIiJUWFiopKQklZWVVTmXKQhvAICxunXrpl27dlUJ+NM+//xzHT16VHPnzlVUVJQkadu2bR6NHRwc7LdPnfPAGgDAWDNmzNDmzZs1ceJE5efna+/evVq9erUmTZok6efZd3BwsBYtWqQDBw5o9erVevLJJz0au23btjp48KDy8/N19OjR83qwrq4R3gAAY8XGxmrDhg3au3evevfura5du+qJJ55Qq1atJEkRERHKzc3VypUrFRMTo7lz52r+/PkejT1s2DAlJycrISFBERERWrZsWX1eSo2wbA4A8Etn+lx13759ZVmW6/V1112n995774zjjBo1SqNGjXJr++Xxvx7vNLvdrjfeeKOGVXsHM28AAAxDeAMAYBjCGwAAwxDeAAAYhvAGAMAwhDcAAIYhvAEAMAzhDQCAYQhvAAAMQ3gDAGAYwhsAAMMQ3gAAGIbwBgDAMIQ3AACGIbwBADAM4Q0AgGEIbwAADEN4AwBgmMD6PkFISIhSU1Pr+zQqKiqq93PUtSsG3OTrEuCBFt3ifF0CPND+tgG+LgHwmnoPb4fDUd+nkCSv/A8CAAD+gGVzAAAMQ3gDAGAYwhsAAMMQ3gAAGIbwBgDAMIQ3AACGIbwBADAM4Q0AgGEIbwAADEN4AwBgGMIbAADDEN4AABiG8AYAwDCENwAAhiG8AQAwDOENAIBhCG8AAAxDeAMAYBjCGwAAwxDeAAAjpaSkaMiQIWft07dvX02ZMsUr9XgT4Q0A8EvVhfMbb7yhkJAQzZs3T88//7xyc3N9UpuvBfq6AAAAPPHiiy9q4sSJeuGFFzR+/Hhfl+NTzLwBAH5v3rx5euihh7R06VJXcP96Zl5SUqKxY8cqLCxMrVq10rPPPltlnLZt22rOnDkaN26cwsPDFR0drT/96U9ufb799luNHDlSF110kS655BINHjxYhw4dkiR9+OGHCgoK0pEjR9yOmTp1quLj4+v2os+C8AYAeI3T6VRxcbHb5nQ6z3rMo48+qieffFJr1qzRsGHDzthv+vTp+uCDD/TXv/5V7733nvLy8rR9+/Yq/Z599lnFxcXp008/1YMPPqgHHnhAX375pSTpp59+UkJCgsLCwvThhx9q48aNCgsLU3JyssrKyhQfH6927drp1VdfdY136tQpvfbaa7r77rtr+VupuQazbB4SEqLU1FRfl+GxBQsW+LoEAPA6h8OhrKwst7aMjAxlZmZW2/9vf/ub3n77ba1fv179+vU747gnT57USy+9pL/85S/q37+/JOmVV17R5ZdfXqXvgAED9OCDD0qSZsyYoQULFigvL0/XXHONli9froCAAL344ouy2WySpJycHDVv3lx5eXlKTEzUPffco5ycHE2fPl2StHbtWv30008aMWJEjX8ftdVgwtvhcPi6BADAOaSnpystLc2tzW63n7F/bGysjh49qpkzZ+q6665TeHh4tf3279+vsrIy9ezZ09V28cUX6+qrr652zNNsNptatmypoqIiSdL27du1b9++KucpLS3V/v37Jf28XP/4449ry5Yt+q//+i+9/PLLGjFihEJDQ89x9XWnwYQ3AMD/2e32s4b1r1122WV68803lZCQoOTkZK1bt67aALcsy+Mxg4KC3F7bbDZVVlZKkiorK9W9e3ctWbKkynERERGSpEsvvVSDBg1STk6O2rVrp3feeUd5eXken78u8J43AMCvRUdHa8OGDSoqKlJiYqKKi4ur9Gnfvr2CgoK0ZcsWV9uPP/6or776qkbn6tatm/bu3atLL71U7du3d9uaNWvm6jd+/HgtX75c//M//6Mrr7xSvXr1qv0F1gLhDQDwe5dffrny8vL0ww8/KDExUSdOnHDbHxYWpnvuuUfTp0/X+vXr9cUXXyglJUUBATWLuTFjxqhFixYaPHiwPvroIx08eFAbNmzQww8/rG+++cbVLykpSc2aNdNTTz3l1QfVTiO8AQBGuOyyy7RhwwYdP35c/fv31/Hjx932P/PMM4qPj9ett96qm2++WTfeeKO6d+9eo3M0adJEH374oaKjozV06FB17NhR48aN0//93/+padOmrn4BAQFKSUlRRUWFxo4dWxeXVyM2qyZvFKBOfTIrw9clwAOdp83wdQnwwBeLnvN1CfBAtxm/93UJdebee+/V999/r9WrV3v93DywBgBADZw4cUKffPKJlixZorffftsnNRDeAADUwODBg7V161ZNmDDB9ZlybyO8AQCoAW9/LKw6PLAGAIBhCG8AAAxDeAMAYBjCGwAAwxDeAAAYhvAGAMAwhDcAAIYhvAEAMAzhDQCAYQhvAAAMQ3gDAGAYwhsAAMMQ3gAAGIbwBgDAMIQ3AACGsVmWZfm6CDQMTqdTDodD6enpstvtvi4HZ8B9MgP3CWdDeKPOFBcXq1mzZjpx4oSaNm3q63JwBtwnM3CfcDYsmwMAYBjCGwAAwxDeAAAYhvBGnbHb7crIyODhGj/HfTID9wlnwwNrAAAYhpk3AACGIbwBADAM4Q0AgGEIbwAADEN4XwCOHDmiSZMmqV27drLb7YqKitKgQYO0fv16X5fmkdLSUqWkpOjaa69VYGCghgwZ4uuS6oXp9ykvL0+DBw9Wq1atFBoaqi5dumjJkiW+LqvOmX6f9uzZo4SEBEVGRiokJETt2rXT448/rvLycl+XhhoI9HUBqF+HDh1Sr1691Lx5c82bN0+xsbEqLy/Xu+++q4kTJ+rLL7/0dYnnVFFRocaNG2vy5Ml68803fV1OvWgI92nTpk2KjY3VjBkzFBkZqbVr12rs2LFq2rSpBg0a5Ovy6kRDuE9BQUEaO3asunXrpubNm+uzzz7Tvffeq8rKSs2ZM8fX5cFTFhq0W265xbrsssuskydPVtn3448/un7++uuvrVtvvdUKDQ21wsPDrdtvv906cuSIa39GRobVuXNn66WXXrKioqKs0NBQ6/7777dOnTplPf3001ZkZKQVERFhPfXUU27nkGQtXrzYSk5OtkJCQqy2bdtar7/+eq2v56677rIGDx5c6+P9VUO7T6cNGDDAuvvuu897HH/RUO9TamqqdeONN573OPAewrsB++GHHyybzWbNmTPnrP0qKyutrl27WjfeeKO1bds2a8uWLVa3bt2sPn36uPpkZGRYYWFh1vDhw61du3ZZq1evtoKDg62kpCRr0qRJ1pdffmm9/PLLliRr8+bNruMkWZdccon15z//2dqzZ4/1+OOPW40aNbJ2795dq2tqiOHdEO/Tab169bKmTp16XmP4i4Z6n/bu3Wt17NjReuyxx2o9BryP8G7APv74Y0uS9dZbb52133vvvWc1atTIKiwsdLXt2rXLkmRt3brVsqyf/7Fp0qSJVVxc7OqTlJRktW3b1qqoqHC1XX311ZbD4XC9lmTdf//9bue7/vrrrQceeKBW19QQw7sh3ifLsqyVK1dawcHB1hdffFHrMfxJQ7tPPXv2tOx2uyXJuu+++9zOC//HA2sNmPX/vzzPZrOdtV9BQYGioqIUFRXlaouJiVHz5s1VUFDgamvbtq3Cw8NdryMjIxUTE6OAgAC3tqKiIrfxe/bsWeX1L8e90DXE+5SXl6eUlBT9+c9/VqdOnWo1hr9paPdpxYoV2rFjh5YuXaq1a9dq/vz5NR4DvkN4N2AdOnSQzWY753/YlmVV+w/Sr9uDgoLc9ttstmrbKisrz1nbuf4BvJA0tPu0YcMGDRo0SP/93/+tsWPH1vh4f9XQ7lNUVJRiYmI0atQozZ07V5mZmaqoqKjxOPANwrsBu/jii5WUlKQXXnhBJSUlVfYfP35c0s+zgsLCQv3rX/9y7du9e7dOnDihjh07nncdW7ZsqfL6mmuuOe9xG4qGdJ/y8vI0cOBAzZ07V/fdd9951+RPGtJ9+jXLslReXu5aXYD/I7wbuMWLF6uiokI9evTQm2++qb1796qgoEALFy50Lb/dfPPNio2N1ZgxY7Rjxw5t3bpVY8eOVZ8+fRQXF3feNaxcuVIvv/yyvvrqK2VkZGjr1q166KGHXPtvuukm/eEPfzjrGLt371Z+fr6OHTumEydOKD8/X/n5+eddm79oCPfpdHBPnjxZw4YN05EjR3TkyBEdO3bsvGvzFw3hPi1ZskSvv/66CgoKdODAAa1cuVLp6ekaOXKkAgP59LApuFMN3BVXXKEdO3Zo9uzZmjp1qg4fPqyIiAh1795d2dnZkn5eclu1apUmTZqk+Ph4BQQEKDk5WYsWLaqTGrKysrR8+XI9+OCDatmypZYsWaKYmBjX/v379+vo0aNnHWPAgAH6+uuvXa+7du0qSQ1mptAQ7lNubq5++uknORwOORwOV3ufPn2Ul5dXJzX6WkO4T4GBgXr66af11VdfybIstWnTRhMnTlRqamqd1Afv4E+Col7ZbDb99a9/bbDfitZQcJ/MwH3CaSybAwBgGMIbAADDsGwOAIBhmHkDAGAYwhsAAMMQ3gAAGIbwBgDAMIQ3AACGIbwBADAM4Q0AgGEIbwAADEN4AwBgmP8H703kzvDHzK0AAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 500x500 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_organ = pd.DataFrame(data=cp[1][0], columns=[f\"Comp. {rr}\" for rr in np.arange(1, rank+1)], index=organs)\n",
    "sns.clustermap(df_organ, col_cluster=False, method='average', \n",
    "               cmap=\"vlag\", vmin=-1.0, vmax=1.0, figsize=(5, 5)) "
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "ee97e928",
   "metadata": {},
   "source": [
    "## 7. Missing value and imputation test\n",
    "\n",
    "Many tensor factorization methods allow the data to contain missing values. Some factorization algorithms have quite high tolerance for missing values (for example, some prefilled value methods can theoretically allow 100% missing values). However, the factorization results with a lot of missing values would deviate from what the factors would have been if there was no missingness. Here, we experiment with adding random missing values to our drug response dataset and see how the proportion of missingness relates to the recontruction errors (Fig. 3d)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "f03798a5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='Missing proportion', ylabel='Error'>"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "missing_value_errors = []\n",
    "missing_value_proportions = [0.0, 0.05, 0.1, 0.3, 0.5, 0.7, 0.9, 0.95]\n",
    "np.random.seed(1234)\n",
    "\n",
    "for miss_ratio in missing_value_proportions:\n",
    "    # for each proportion, we try 40 random missingness.\n",
    "    for rep in range(40):\n",
    "        unmask = np.random.rand(*tensor.shape) < 1 - miss_ratio\n",
    "        masked_tensor = np.copy(tensor)\n",
    "        masked_tensor[~unmask] = 1.0\n",
    "        cp_masked = parafac(masked_tensor, 3, mask=unmask)\n",
    "        recon_error = error(tensor, cp_masked.to_tensor())\n",
    "        missing_value_errors.append((miss_ratio, recon_error))\n",
    "\n",
    "missing_value_df = pd.DataFrame(missing_value_errors, columns=[\"Missing proportion\", \"Error\"])\n",
    "\n",
    "sns.stripplot(data=missing_value_df, x=\"Missing proportion\", y=\"Error\", color=\"gray\")\n",
    "sns.pointplot(data=missing_value_df, x=\"Missing proportion\", y=\"Error\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b5419e8c-cc59-42dd-9728-08e77431b3ea",
   "metadata": {},
   "source": [
    "As we can see here, more missingness comes with worse reconstruction errors.\n",
    "\n",
    "The imputation test has adopted the idea of artificially introducing missing values to test the decomposition (Fig. 3e). Basically, the imputation test randomly removes a portion of the data and sees if the reconstructed tensor can impute the removed data. A low imputation error indicates that the decomposition can even fit the unseen data well, which is a strong signal that the decomposition works. This can also be used to determine the number of components."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "b56d3509",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='Components', ylabel='Value'>"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "imputation_test = []\n",
    "np.random.seed(1234)\n",
    "\n",
    "for rep in range(30):\n",
    "    unmask = np.random.rand(*tensor.shape) < 0.7\n",
    "    # this is equivalent to masking 30% of values to be missing\n",
    "    for rr in np.arange(1, 13):\n",
    "        masked_tensor = np.copy(tensor)\n",
    "        masked_tensor[~unmask] = 0.0\n",
    "        cp_masked = parafac(masked_tensor, rr, mask=unmask)\n",
    "        fitting_error = error(tensor[unmask], cp_masked.to_tensor()[unmask])\n",
    "        imputation_error = error(tensor[~unmask], cp_masked.to_tensor()[~unmask])\n",
    "        imputation_test.append((rr, \"Fitting\", fitting_error))\n",
    "        imputation_test.append((rr, \"Imputation\", imputation_error))\n",
    "\n",
    "imputation_df = pd.DataFrame(imputation_test, columns=[\"Components\", \"Error Type\", \"Value\"])\n",
    "\n",
    "sns.pointplot(data=imputation_df, x=\"Components\", y=\"Value\", hue=\"Error Type\", \n",
    "              linestyle=\"none\", palette=[\"#E1812C\", \"#0173B2\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2af4ccb6-540c-4b12-8e43-eae123269091",
   "metadata": {},
   "source": [
    "The result shows that while the fitting errors monotonically decrease with more components, the imputation errors can increase with too many components. Sometimes, the imputation errors can be very off. From this plot, it seems like a 5-component model best imputes unseen data."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e2d3ef9",
   "metadata": {},
   "source": [
    "## 8. Factor sparsity\n",
    "\n",
    "Sparsity means that most elements in an array are zero. A sparse factor can be easier to interpret as the association is clearer. The following code uses Lasso, a regularization method, to achieve sparsity. It simulates one step in the alternating least squares scheme. Here, we show the first factors of the organ mode under three different levels of sparsity (Fig. 3f)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "884dfd28-d295-41f4-b72a-c6687ece4b08",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from tensorly.tenalg import khatri_rao\n",
    "from sklearn.linear_model import Lasso\n",
    "\n",
    "lasso_alphas = [1.0, 8, 15]\n",
    "sparse_factors = np.zeros((tensor.shape[0], len(lasso_alphas)))\n",
    "\n",
    "for ii, alpha in enumerate(lasso_alphas):\n",
    "    lasso = Lasso(alpha=alpha, fit_intercept=False)\n",
    "    # This step simulates one step in ALS solving. Its rationale is beyond the scope of this review.\n",
    "    lasso.fit(khatri_rao([cp[1][1], cp[1][2]]), tensor.reshape(tensor.shape[0], -1).T)\n",
    "    # We can visualize any factor of any mode, but here we just show Factor 1 of Organ as examples.\n",
    "    sparse_factors[:, ii] = lasso.coef_[:, 0] / np.linalg.norm(lasso.coef_[:, 0], ord=np.inf)\n",
    "\n",
    "sns.heatmap(sparse_factors, cmap=\"vlag\", center=0, \n",
    "            xticklabels=[\"Low sparsity\", \"Medium sparsity\", \"High sparsity\"], yticklabels=organs,\n",
    "            cbar=True, vmin=-1.0, vmax=1.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d82bc6c-4f0c-4f40-982c-0415e5672c19",
   "metadata": {},
   "source": [
    "While the low sparsity factor has nonzero weights on all organs, the high sparsity factor is only associated with two organs. This can improve the interpretation of tensor factors."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "711f21b4",
   "metadata": {},
   "source": [
    "## 9. Logistic regression on the organs\n",
    "\n",
    "The decomposed factors can be used for classification when combined with logistic regression. For example, we try to identify the association between the drug response measurements and a simulated dataset of organ effect, the \"Y\" to be predicted."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "8b73928c-0fa7-420a-9918-c449e3e33c83",
   "metadata": {},
   "outputs": [],
   "source": [
    "organ_effect = np.array([0, 0, 1, 0, 1, 0, 1])\n",
    "\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "lr = LogisticRegression().fit(cp[1][0], organ_effect)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ea106ef2",
   "metadata": {},
   "source": [
    "Logistic regression assigns linear weights to each component, therefore the previous normalization on the organ factor matrix, such as scaling and sign flipping, does not alter the results.\n",
    "The fitting score of the logistic regression is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "ce527fc7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8571428571428571"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.score(cp[1][0], organ_effect)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e68b73e0-8a0e-4dd0-ba40-557f0e50a0f8",
   "metadata": {},
   "source": [
    "with the coefficients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "9566d043",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.88194697, -0.44151518,  0.33957457]])"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35d1a664",
   "metadata": {},
   "source": [
    "To estimate the variations of the coefficient, we perform a jackknife resampling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "302e6082",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import LeaveOneOut\n",
    "from tensorly.metrics.factors import congruence_coefficient\n",
    "\n",
    "lr_jackknife = []\n",
    "\n",
    "for ii in range(tensor.shape[0]):\n",
    "    # get jackknife indices\n",
    "    jk = np.delete(np.arange(tensor.shape[0]), [ii])\n",
    "    jcp = parafac(tensor[jk], 3)\n",
    "    jcp = factor_scaling(jcp)\n",
    "    \n",
    "    # align jackknifed factors with original for comparison    \n",
    "    jcp = sign_indeterminacy(jcp)\n",
    "    congru_perm = congruence_coefficient(cp[1][0][jk, :], jcp[1][0])[1]\n",
    "    jcp.weights = jcp[0][congru_perm]\n",
    "    for i, factor in enumerate(jcp.factors):\n",
    "        jcp.factors[i] = factor[:, congru_perm]\n",
    "    \n",
    "    # run logistic regression\n",
    "    lr = LogisticRegression().fit(jcp[1][0], organ_effect[jk])\n",
    "    lr_jackknife.append(lr.coef_)\n",
    "\n",
    "lr_coef = pd.DataFrame(np.concatenate(lr_jackknife), columns=[f\"Comp. {r}\" for r in np.arange(1, rank+1)])\n",
    "lr_coef = pd.melt(lr_coef, var_name=\"Factor\", value_name=\"Coefficient\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1fa11df1-d604-4438-87ce-2d3d5b618f7e",
   "metadata": {},
   "source": [
    "We now visualize the coefficient assigned to each factor with a jackknife confidence interval (Fig. 3g)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "23516fe3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='Coefficient', ylabel='Factor'>"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.barplot(data=lr_coef, x=\"Coefficient\", y=\"Factor\", orient=\"h\", color=\"gray\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "226841a3-490d-49e5-b243-1a0258c6e160",
   "metadata": {},
   "source": [
    "Since not all factors relate to the effect we try to predict, the model may be reduced to using a subset of the factors. Here, we explore a few options for reducing the model (Fig. 3h)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "76e42bac-253d-4056-9652-04c1cb6ea645",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='Models', ylabel='Fitting score'>"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "reduced_names = [\"All Factors\", \"Factors 1+2\", \"Factors 2+3\"]\n",
    "reduced_columns = [[0,1,2], [0,1], [1,2]]\n",
    "reduced_pred = [0] * len(reduced_columns)\n",
    "\n",
    "for ri, reduced_col in enumerate(reduced_columns):\n",
    "    reduced_lr = LogisticRegression().fit(cp[1][0][:, reduced_col], organ_effect)\n",
    "    reduced_pred[ri] = reduced_lr.score(cp[1][0][:, reduced_col], organ_effect)\n",
    "\n",
    "sns.barplot(data=pd.DataFrame({\"Models\": reduced_names, \"Fitting score\": reduced_pred}),\n",
    "            x=\"Models\",\n",
    "            y=\"Fitting score\",\n",
    "            color=\"#7349C0\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "07e11796",
   "metadata": {},
   "source": [
    "## 10. Tucker decomposition\n",
    "\n",
    "Tucker decomposition is a more flexible tensor factorization scheme. It allows each mode to have different factor numbers, and explicitly models how they interact. See Fig. 4a to learn about how it works. Here, we perform a (4,3,2)-rank Tucker decomposition on our drug response $7 \\times 6 \\times 5$ tensor. This means the organ mode has 4 factors, drug 3, and time 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "3736a3ec",
   "metadata": {},
   "outputs": [],
   "source": [
    "from tensorly.decomposition import tucker\n",
    "\n",
    "tres = tucker(tensor, (4, 3, 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a3265a12-7ff7-4494-aa71-0e0757375259",
   "metadata": {},
   "source": [
    "The result of a Tucker decomposition consists of to part: the core tensor and the factor matrices. The factor matrices can be plotted similarly as in Fig. 2f. The shape of these three factor matrices should be"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "399e592b-6c78-4c66-8689-2a5918093581",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(7, 4) (6, 3) (5, 2)\n"
     ]
    }
   ],
   "source": [
    "print(tres[1][0].shape, tres[1][1].shape, tres[1][2].shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a596f03d-9a6a-48c8-9552-ac8298a941fd",
   "metadata": {},
   "source": [
    "The core tensor is a new part of Tucker. It represents the interactions across these factors. It has dimension $4 \\times 3 \\times 2$. We can visualize it as (Fig. 4b, left)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "684aa660-0fb1-4e19-8d8d-8bd4053a36b1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1400x400 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f = plt.figure(figsize=(14, 4))\n",
    "gs = gridspec.GridSpec(1, 2, wspace=0.5)\n",
    "axes = [plt.subplot(gs[rr]) for rr in range(2)]\n",
    "\n",
    "sns.heatmap(tres[0][:, :, 0].T, ax=axes[0], vmin=-1500, vmax=1700, cmap=\"vlag\", annot=True,\n",
    "            xticklabels=[f\"O Fac. {i}\" for i in np.arange(1, tres[0].shape[0]+1)], \n",
    "            yticklabels=[f\"D Fac. {i}\" for i in np.arange(1, tres[0].shape[1]+1)],)\n",
    "sns.heatmap(tres[0][:, :, 1].T, ax=axes[1], vmin=-1500, vmax=1700, cmap=\"vlag\", annot=True,\n",
    "            xticklabels=[f\"O Fac. {i}\" for i in np.arange(1, tres[0].shape[0]+1)], \n",
    "            yticklabels=[f\"D Fac. {i}\" for i in np.arange(1, tres[0].shape[1]+1)],)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4388966b-c9df-425a-8aef-6e1af2954153",
   "metadata": {},
   "source": [
    "### Find the most significant interactions\n",
    "\n",
    "We define the significance of an interaction as the proportion of its squared weight over the sum of all squared weights in the core tensor. To interpret the results, we first find the significance of all interactions, then sort them in decreasing order."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "ecaf85c8-3a2d-4807-ab6f-cf5fa5ea734b",
   "metadata": {},
   "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>Index</th>\n",
       "      <th>Weight</th>\n",
       "      <th>Fraction</th>\n",
       "      <th>Sign</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>(1, 1, 1)</td>\n",
       "      <td>1631.393536</td>\n",
       "      <td>0.781533</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>(2, 2, 1)</td>\n",
       "      <td>-632.485523</td>\n",
       "      <td>0.117471</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>(3, 3, 1)</td>\n",
       "      <td>-456.732019</td>\n",
       "      <td>0.061257</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>(1, 3, 2)</td>\n",
       "      <td>243.787831</td>\n",
       "      <td>0.017452</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>(2, 3, 2)</td>\n",
       "      <td>173.713752</td>\n",
       "      <td>0.008861</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>(4, 3, 2)</td>\n",
       "      <td>105.895351</td>\n",
       "      <td>0.003293</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>(4, 1, 2)</td>\n",
       "      <td>105.725373</td>\n",
       "      <td>0.003282</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>(2, 3, 1)</td>\n",
       "      <td>-68.055514</td>\n",
       "      <td>0.001360</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>(4, 2, 2)</td>\n",
       "      <td>-63.160668</td>\n",
       "      <td>0.001171</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>(2, 2, 2)</td>\n",
       "      <td>-60.768254</td>\n",
       "      <td>0.001084</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>(3, 2, 2)</td>\n",
       "      <td>59.898667</td>\n",
       "      <td>0.001054</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>(3, 2, 1)</td>\n",
       "      <td>47.961471</td>\n",
       "      <td>0.000675</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>(3, 1, 2)</td>\n",
       "      <td>-39.525881</td>\n",
       "      <td>0.000459</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>(4, 2, 1)</td>\n",
       "      <td>38.197014</td>\n",
       "      <td>0.000428</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>(2, 1, 1)</td>\n",
       "      <td>-28.906291</td>\n",
       "      <td>0.000245</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>(1, 2, 2)</td>\n",
       "      <td>-19.065667</td>\n",
       "      <td>0.000107</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>(3, 3, 2)</td>\n",
       "      <td>17.726220</td>\n",
       "      <td>0.000092</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>(4, 1, 1)</td>\n",
       "      <td>-15.926474</td>\n",
       "      <td>0.000074</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>(4, 3, 1)</td>\n",
       "      <td>-9.158988</td>\n",
       "      <td>0.000025</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>(1, 1, 2)</td>\n",
       "      <td>-8.759414</td>\n",
       "      <td>0.000023</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>(1, 3, 1)</td>\n",
       "      <td>-8.497257</td>\n",
       "      <td>0.000021</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>(2, 1, 2)</td>\n",
       "      <td>7.959040</td>\n",
       "      <td>0.000019</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>(1, 2, 1)</td>\n",
       "      <td>-4.966199</td>\n",
       "      <td>0.000007</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>(3, 1, 1)</td>\n",
       "      <td>-4.394055</td>\n",
       "      <td>0.000006</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Index       Weight  Fraction  Sign\n",
       "0   (1, 1, 1)  1631.393536  0.781533   1.0\n",
       "8   (2, 2, 1)  -632.485523  0.117471  -1.0\n",
       "16  (3, 3, 1)  -456.732019  0.061257  -1.0\n",
       "5   (1, 3, 2)   243.787831  0.017452   1.0\n",
       "11  (2, 3, 2)   173.713752  0.008861   1.0\n",
       "23  (4, 3, 2)   105.895351  0.003293   1.0\n",
       "19  (4, 1, 2)   105.725373  0.003282   1.0\n",
       "10  (2, 3, 1)   -68.055514  0.001360  -1.0\n",
       "21  (4, 2, 2)   -63.160668  0.001171  -1.0\n",
       "9   (2, 2, 2)   -60.768254  0.001084  -1.0\n",
       "15  (3, 2, 2)    59.898667  0.001054   1.0\n",
       "14  (3, 2, 1)    47.961471  0.000675   1.0\n",
       "13  (3, 1, 2)   -39.525881  0.000459  -1.0\n",
       "20  (4, 2, 1)    38.197014  0.000428   1.0\n",
       "6   (2, 1, 1)   -28.906291  0.000245  -1.0\n",
       "3   (1, 2, 2)   -19.065667  0.000107  -1.0\n",
       "17  (3, 3, 2)    17.726220  0.000092   1.0\n",
       "18  (4, 1, 1)   -15.926474  0.000074  -1.0\n",
       "22  (4, 3, 1)    -9.158988  0.000025  -1.0\n",
       "1   (1, 1, 2)    -8.759414  0.000023  -1.0\n",
       "4   (1, 3, 1)    -8.497257  0.000021  -1.0\n",
       "7   (2, 1, 2)     7.959040  0.000019   1.0\n",
       "2   (1, 2, 1)    -4.966199  0.000007  -1.0\n",
       "12  (3, 1, 1)    -4.394055  0.000006  -1.0"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from itertools import product\n",
    "\n",
    "core_tensor = pd.DataFrame({\n",
    "                       \"Index\": product(*[np.arange(1, si+1) for si in tres[0].shape]),\n",
    "                        \"Weight\": tres[0].flatten(),\n",
    "                        \"Fraction\": tres[0].flatten()**2,\n",
    "                        \"Sign\": np.sign(tres[0].flatten()),\n",
    "                    })\n",
    "\n",
    "core_tensor = core_tensor.sort_values(\"Fraction\", ascending=False)\n",
    "core_tensor[\"Index\"] = core_tensor[\"Index\"].astype(str)\n",
    "core_tensor[\"Fraction\"] = core_tensor[\"Fraction\"] / np.sum(core_tensor[\"Fraction\"])\n",
    "core_tensor"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4b88d652-9090-4301-b943-12a8886b474e",
   "metadata": {},
   "source": [
    "We can use a barplot to visualize these fractions (Fig. 4b, right). While all significance are positive, we use different colors to annotate the sign of the original weights."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "b322890c-9070-47d5-b6fb-b835f4426f93",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='Index', ylabel='Fraction'>"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.barplot(core_tensor.iloc[:8, :], x=\"Index\", y=\"Fraction\", hue=\"Sign\", \n",
    "            palette=[\"#2369BD\", \"#A9393C\"], legend=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd314eeb-8ee9-4d62-b661-cc7d688ead2b",
   "metadata": {},
   "source": [
    "The result shows that 78% of the variance in the data can be explained by the interaction of the first factors of organ, drug, and time. Combined with the factor plots below, we get to know that it represents a time-consistent effect mostly from echoxacin on most cells except those from the skin and the kidney. The top three interactions together explain almost 96% of the variance, and they are all related to time Factor 1 which is relatively constant over time. This example shows that Tucker can summarize the modes better without redundancy, as a factor can be reused."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "81f2ffcc-63c4-478e-bb2e-999afca8ef3a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1500x600 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_factors([tres[0], tres[1]])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d69e4d5c-83a2-4bfe-b8ae-7a4ebd6c58a8",
   "metadata": {},
   "source": [
    "### Compare the data reduction of Tucker and CP\n",
    "\n",
    "We here plot the size of reduced data of a few selected Tucker ranks along with CP decompositions to see if Tucker provides a concise data representation (Fig. 4d)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "f8363466-a0be-4265-a9ea-026cc4814628",
   "metadata": {},
   "outputs": [],
   "source": [
    "reduction = pd.DataFrame()\n",
    "\n",
    "tucker_rank = list(np.ones(tensor.ndim, dtype=int))\n",
    "reduction = pd.concat([reduction, pd.DataFrame([{\n",
    "                'Size': np.sum(tensor.shape * np.array(tucker_rank)) + np.prod(tucker_rank),\n",
    "                'Error': error(tensor, tucker(tensor, tucker_rank)),\n",
    "                'Method': \"Tucker\",\n",
    "                'Rank': tucker_rank,\n",
    "        }])], ignore_index=True)\n",
    "\n",
    "for tr in range(10):\n",
    "    for add_r in range(tensor.ndim):\n",
    "        new_tucker_rank = tucker_rank.copy()\n",
    "        new_tucker_rank[add_r] += 1\n",
    "        reduction = pd.concat([reduction, pd.DataFrame([{\n",
    "                    'Size': np.sum(tensor.shape * np.array(new_tucker_rank)),\n",
    "                    'Error': error(tensor, tucker(tensor, new_tucker_rank)),\n",
    "                    'Method': \"Tucker\",\n",
    "                    'Rank': new_tucker_rank,\n",
    "            }])], ignore_index=True)\n",
    "        \n",
    "    # selection the lowest error rank and continue\n",
    "    min_rank = np.argmin(reduction.iloc[-3:, 1])\n",
    "    tucker_rank = reduction.iloc[-(tensor.ndim-min_rank), 3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "1308cee0-54a1-4464-bdfc-416fed42c12f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Add CP reduction\n",
    "for rr in np.arange(1, 7):\n",
    "    reduction = pd.concat([reduction, pd.DataFrame([{\n",
    "                'Size': rr * np.sum(tensor.shape),\n",
    "                'Error': error(tensor, parafac(tensor, rr, tol=1e-09)),\n",
    "                'Method': \"CP\",\n",
    "                'Rank': rr,\n",
    "        }])], ignore_index=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "1ff9a0f7-9224-4f94-acc5-67f4f2ff932a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='Size', ylabel='Error'>"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lineplot(data=reduction, x=\"Size\", y=\"Error\", hue=\"Method\", marker=\"o\", \n",
    "                    linestyle=\"\", palette=[\"#B41F64\", \"#CFAD00\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "507c4bdc-ccce-490d-8763-28bf8a2c4285",
   "metadata": {},
   "source": [
    "As we can see here, not all Tucker rank yields a more parsimonious model. The rank selection for Tucker decomposition is more complicated."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b8cf9845-2456-47e0-be2c-11731c29c548",
   "metadata": {},
   "source": [
    "## 11. Coupled tensor decomposition\n",
    "\n",
    "A coupled decomposition can jointly factorize multiple coupled tensors. See Fig. 4e to learn how it works. Here, we use a variant of coupled decomposition, coupled matrix and tensor decomposition (CMTF) (see Fig. 4g, left), to explore how the relative scale between two coupled tensor can impact the goodness of fit. First, we generate a synthetic Tensor B (the matrix):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "2f705d6d-c1cd-4f89-b6f5-c6a78d3265ff",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(234)\n",
    "mat = np.random.gamma(1, 5, size=(7, 6)) * 100"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c21ea1f-a2ef-4116-90c2-44b134bdf9ca",
   "metadata": {},
   "source": [
    "Now we perform CMTF with different scaling of Tensor B, and plot the errors for both tensors and the total errors (Fig. 4f)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "830d1310-f0fc-44ed-ad95-0857e0618723",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/envs/tensor_review/lib/python3.12/site-packages/tensorly/backend/__init__.py:195: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
      "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
      "  return getattr(\n",
      "/opt/anaconda3/envs/tensor_review/lib/python3.12/site-packages/tensorly/decomposition/_cmtf_als.py:128: UserWarning: Reached maximum iteration number without convergence.\n",
      "  warnings.warn(\"Reached maximum iteration number without convergence.\")\n"
     ]
    }
   ],
   "source": [
    "from tensorly.decomposition._cmtf_als import coupled_matrix_tensor_3d_factorization\n",
    "\n",
    "coupled = pd.DataFrame()\n",
    "\n",
    "for scale in np.logspace(-2.5, 2.5, num=30, endpoint=True, base=2):\n",
    "    cmtf = coupled_matrix_tensor_3d_factorization(tensor, mat*scale, 4, normalize_factors=False)\n",
    "\n",
    "    total_recon = np.concatenate([cmtf[0].to_tensor().flatten(), cmtf[1].to_tensor().flatten()])\n",
    "    total_original = np.concatenate([tensor.flatten(), (mat*scale).flatten()])\n",
    "    coupled = pd.concat([coupled, pd.DataFrame([{\n",
    "            'Scale': scale,\n",
    "            'Total': error(total_original, total_recon),\n",
    "            'Tensor A': error(tensor, cmtf[0]),\n",
    "            'Tensor B': error(mat*scale, cmtf[1]),\n",
    "        }])], ignore_index=True)\n",
    "\n",
    "coupled = pd.melt(coupled, id_vars=\"Scale\", var_name=\"Tensor\", value_name=\"Error\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "272fce34-d621-42ce-9212-6807e2e166ab",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[None,\n",
       " [<matplotlib.axis.XTick at 0x143b810d0>,\n",
       "  <matplotlib.axis.XTick at 0x1439da090>,\n",
       "  <matplotlib.axis.XTick at 0x143e6e390>,\n",
       "  <matplotlib.axis.XTick at 0x143af1940>,\n",
       "  <matplotlib.axis.XTick at 0x143a467e0>]]"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = sns.lineplot(data=coupled, x=\"Scale\", y=\"Error\", hue=\"Tensor\", \n",
    "                  palette=[\"#004381\", \"#A13800\", \"#148964\"])\n",
    "ax.set(xscale=\"log\", xticks=[0.25, 0.5, 1, 2, 4])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "991855dd-146d-4432-b1af-900d931b59b9",
   "metadata": {},
   "source": [
    "The results shows that the fitting error of Tensor A increase a lot when Tensor B is scaled much higher, and the fitting error of Tensor B increase when Tensor B is scaled much lower. The relative scale of coupled tensors is a hyperparameter to tune when implementing a coupled decomposition."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2ac36848-9c9c-4e17-8f89-ca99a152255a",
   "metadata": {},
   "source": [
    "## 12. Tensor partial least squares\n",
    "\n",
    "Tensor partial least squares also deal with more than one tensors, but here instead of optimizing the joint variance of Tensors A and B, we aims to discover the cause and effect embedded in Tensors X and Y. Therefore, tensor partial least sqaures prioritize the covariance between X and Y. See Fig. 4h to see how it works\n",
    "To demonstrate tensor partial least squares, we first generate a simulated Y matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "id": "47cc92a3-171c-4601-b0a7-9ad78d7b0fa5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate a simulated predictor, Y\n",
    "np.random.seed(1234)\n",
    "Y = cp[1][0][:, [0]] @ np.random.gamma(1, 5, size=(1,4)) * 0.6 + \\\n",
    "    cp[1][0][:, [2]] @ np.random.gamma(3, 1, size=(1,4)) * 0.4\n",
    "Y *= np.random.lognormal(0, 0.1, size=Y.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "74d4ac6e-3276-415c-9434-9383a63a74ab",
   "metadata": {},
   "source": [
    "To assess the performance of tensor partial least squares, we find the fitting errors of X and Y. Also, through a leave-one-out cross-validation, we evaluate the prediction error of Y. In a leave-one-out cross-validation, we hide one sample from the model at a time, and use the rest of samples to fit the model so that the left-out sample is unseen to the model can serve as a fair estimation of the prediction performance (Fig. 4i)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "id": "ed1a6983-64a1-4493-b802-e220ef7512f2",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/envs/tensor_review/lib/python3.12/site-packages/tensorly/backend/__init__.py:195: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
      "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
      "  return getattr(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(-0.05, 0.8)"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from tensorly.regression.cp_plsr import CP_PLSR\n",
    "from tensorly.cp_tensor import cp_to_tensor\n",
    "\n",
    "plsr_r2 = pd.DataFrame()\n",
    "\n",
    "for rr in range(1, 11):\n",
    "    plsr = CP_PLSR(rr)\n",
    "    plsr.fit(tensor, Y)\n",
    "\n",
    "    # Calculate fitting error of X and Y\n",
    "    plsr_r2 = pd.concat([plsr_r2, pd.DataFrame([{\n",
    "            'Component': rr,\n",
    "            'Error': error(tensor-plsr.X_mean_, CPTensor((None, plsr.X_factors))),\n",
    "            'Type': \"Fitting error of X\",\n",
    "        }])], ignore_index=True)\n",
    "    plsr_r2 = pd.concat([plsr_r2, pd.DataFrame([{\n",
    "                'Component': rr,\n",
    "                'Error': error(Y-plsr.Y_mean_, plsr.predict(tensor)-plsr.Y_mean_),\n",
    "                'Type': \"Fitting error of Y\",\n",
    "            }])], ignore_index=True)\n",
    "\n",
    "    # Leave one out prediction on Y\n",
    "    Y_loo = np.zeros_like(Y)\n",
    "    for ii in range(tensor.shape[0]):\n",
    "        idx = np.delete(np.arange(tensor.shape[0]), ii)\n",
    "        plsr.fit(tensor[idx], Y[idx])\n",
    "        Y_loo[ii] = plsr.predict(tensor[[ii]])\n",
    "    plsr_r2 = pd.concat([plsr_r2, pd.DataFrame([{\n",
    "                'Component': rr,\n",
    "                'Error': error(Y- plsr.Y_mean_, Y_loo- plsr.Y_mean_),\n",
    "                'Type': \"Prediction error of Y\",\n",
    "            }])], ignore_index=True)\n",
    "\n",
    "ax_plsr = sns.pointplot(data=plsr_r2, x=\"Component\", y=\"Error\", hue=\"Type\")\n",
    "ax_plsr.set_ylim(-0.05, 0.8)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2b7a743a-c9b7-4be8-a54a-a2877f35a65d",
   "metadata": {},
   "source": [
    "For a correctly performed tensor partial least squares, the fitting errors of both X and Y should monotonically decrease with more components. However, the prediction error of Y will increase after passing its optimal number of components. This is because having too many components will lead to the model overfitting the data, which means the model fits the data too closely that it loses generality and cannot predict unseen samples well anymore. In our example, overfitting happens when the model has more than 3 components. Cross-validation is needed when choosing the number of components for tensor partial least squares."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "tensor_review",
   "language": "python",
   "name": "tensor_review"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}