A03_svd_applied_to_slightly_bigger_word_document_matrix.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# SVD Applied to a Word-Document Matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook applies the SVD to a simple word-document matrix. The aim is to see what the reconstructed reduced dimension matrix looks like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#import pandas for conviently labelled arrays\n",
    "import pandas\n",
    "# import numpy for SVD function\n",
    "import numpy\n",
    "# import matplotlib.pyplot for visualising arrays\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## A Slightly Bigger Word-Document Matrix\n",
    "The example word-document matrix is taken from http://makeyourowntextminingtoolkit.blogspot.co.uk/2016/11/so-many-dimensions-and-how-to-reduce.html but expanded to cover a 3rd topic related to a home or house"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['wheel', ' seat', ' engine', ' slice', ' oven', ' boil', 'door', 'kitchen', 'roof']\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>doc1</th>\n",
       "      <th>doc2</th>\n",
       "      <th>doc3</th>\n",
       "      <th>doc4</th>\n",
       "      <th>doc5</th>\n",
       "      <th>doc6</th>\n",
       "      <th>doc7</th>\n",
       "      <th>doc8</th>\n",
       "      <th>doc9</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>wheel</th>\n",
       "      <td>0.50</td>\n",
       "      <td>0.3333</td>\n",
       "      <td>0.25</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>seat</th>\n",
       "      <td>0.25</td>\n",
       "      <td>0.3333</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.25</td>\n",
       "      <td>0.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>engine</th>\n",
       "      <td>0.25</td>\n",
       "      <td>0.3333</td>\n",
       "      <td>0.75</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>slice</th>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.5000</td>\n",
       "      <td>0.5000</td>\n",
       "      <td>0.6</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>oven</th>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.3333</td>\n",
       "      <td>0.1667</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>boil</th>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.1667</td>\n",
       "      <td>0.3333</td>\n",
       "      <td>0.4</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>door</th>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.25</td>\n",
       "      <td>0.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>kitchen</th>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.25</td>\n",
       "      <td>0.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>roof</th>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.25</td>\n",
       "      <td>0.50</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         doc1    doc2  doc3    doc4    doc5  doc6  doc7  doc8  doc9\n",
       "wheel    0.50  0.3333  0.25  0.0000  0.0000   0.0   0.0  0.00  0.00\n",
       " seat    0.25  0.3333  0.00  0.0000  0.0000   0.0   0.0  0.25  0.00\n",
       " engine  0.25  0.3333  0.75  0.0000  0.0000   0.0   0.0  0.00  0.00\n",
       " slice   0.00  0.0000  0.00  0.5000  0.5000   0.6   0.0  0.00  0.00\n",
       " oven    0.00  0.0000  0.00  0.3333  0.1667   0.0   0.5  0.00  0.00\n",
       " boil    0.00  0.0000  0.00  0.1667  0.3333   0.4   0.0  0.00  0.00\n",
       "door     0.00  0.0000  0.00  0.0000  0.0000   0.0   0.0  0.25  0.25\n",
       "kitchen  0.00  0.0000  0.00  0.0000  0.0000   0.0   0.5  0.25  0.25\n",
       "roof     0.00  0.0000  0.00  0.0000  0.0000   0.0   0.0  0.25  0.50"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create a simple word-document matrix as a pandas dataframe, the content values have been normalised\n",
    "words = ['wheel', ' seat', ' engine', ' slice', ' oven', ' boil', 'door', 'kitchen', 'roof']\n",
    "print(words)\n",
    "documents = ['doc1', 'doc2', 'doc3', 'doc4', 'doc5', 'doc6', 'doc7', 'doc8', 'doc9']\n",
    "word_doc = pandas.DataFrame([[0.5,0.3333, 0.25, 0, 0, 0, 0, 0, 0],\n",
    "                      [0.25, 0.3333, 0, 0, 0, 0, 0, 0.25, 0],\n",
    "                      [0.25, 0.3333, 0.75, 0, 0, 0, 0, 0, 0],\n",
    "                      [0, 0, 0, 0.5, 0.5, 0.6, 0, 0, 0],\n",
    "                      [0, 0, 0, 0.3333, 0.1667, 0, 0.5, 0, 0],\n",
    "                      [0, 0, 0, 0.1667, 0.3333, 0.4, 0, 0, 0],\n",
    "                      [0, 0, 0, 0, 0, 0, 0, 0.25, 0.25],\n",
    "                      [0, 0, 0, 0, 0, 0, 0.5, 0.25, 0.25],\n",
    "                      [0, 0, 0, 0, 0, 0, 0, 0.25, 0.5]], index=words, columns=documents)\n",
    "# and show it\n",
    "word_doc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Word-Document Matrix is A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# create a numpy array from the pandas dataframe\n",
    "A = word_doc.values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Now Take the SVD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# break it down into an SVD\n",
    "U, s, VT = numpy.linalg.svd(A, full_matrices=False)\n",
    "S = numpy.diag(s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "U =\n",
      " [[-0.01  0.57 -0.05  0.01 -0.45 -0.49 -0.43  0.2   0.07]\n",
      " [-0.01  0.31  0.13  0.19 -0.64  0.43  0.42 -0.26 -0.1 ]\n",
      " [-0.02  0.76 -0.11 -0.11  0.58  0.2   0.15 -0.06 -0.02]\n",
      " [-0.81 -0.03 -0.18  0.17  0.01 -0.07  0.16  0.31 -0.39]\n",
      " [-0.33  0.    0.35 -0.64 -0.06 -0.32  0.35 -0.2   0.29]\n",
      " [-0.46 -0.02 -0.12  0.16  0.02  0.28 -0.44 -0.43  0.53]\n",
      " [-0.02  0.03  0.32  0.35  0.07  0.08  0.24  0.59  0.6 ]\n",
      " [-0.1   0.04  0.68 -0.22  0.02  0.39 -0.45  0.19 -0.3 ]\n",
      " [-0.03  0.04  0.49  0.56  0.23 -0.43  0.05 -0.42 -0.16]] \n",
      "\n",
      "S =\n",
      " [[ 1.11  0.    0.    0.    0.    0.    0.    0.    0.  ]\n",
      " [ 0.    1.06  0.    0.    0.    0.    0.    0.    0.  ]\n",
      " [ 0.    0.    0.84  0.    0.    0.    0.    0.    0.  ]\n",
      " [ 0.    0.    0.    0.62  0.    0.    0.    0.    0.  ]\n",
      " [ 0.    0.    0.    0.    0.46  0.    0.    0.    0.  ]\n",
      " [ 0.    0.    0.    0.    0.    0.22  0.    0.    0.  ]\n",
      " [ 0.    0.    0.    0.    0.    0.    0.19  0.    0.  ]\n",
      " [ 0.    0.    0.    0.    0.    0.    0.    0.06  0.  ]\n",
      " [ 0.    0.    0.    0.    0.    0.    0.    0.    0.04]] \n",
      "\n",
      "V^T =\n",
      " [[-0.01 -0.01 -0.01 -0.53 -0.55 -0.61 -0.2  -0.04 -0.04]\n",
      " [ 0.52  0.51  0.67 -0.01 -0.02 -0.02  0.02  0.1   0.04]\n",
      " [-0.02 -0.01 -0.11  0.01 -0.09 -0.19  0.61  0.48  0.59]\n",
      " [ 0.04  0.05 -0.13 -0.17  0.05  0.27 -0.7   0.36  0.51]\n",
      " [-0.52 -0.37  0.69 -0.03  0.    0.03 -0.04 -0.17  0.3 ]\n",
      " [-0.41  0.2   0.1  -0.43  0.02  0.32  0.14  0.52 -0.45]\n",
      " [-0.36  0.26  0.04  0.63 -0.06 -0.43 -0.27  0.34 -0.15]\n",
      " [ 0.36 -0.62  0.15  0.24 -0.4   0.17 -0.05  0.4  -0.25]\n",
      " [ 0.18 -0.33  0.08 -0.21  0.72 -0.46 -0.08  0.24 -0.13]] \n",
      "\n"
     ]
    }
   ],
   "source": [
    "# what are U, S and V\n",
    "print(\"U =\\n\", numpy.round(U, decimals=2), \"\\n\")\n",
    "print(\"S =\\n\", numpy.round(S, decimals=2), \"\\n\")\n",
    "print(\"V^T =\\n\", numpy.round(VT, decimals=2), \"\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see above that the values in the diagonal **S** matrix are ordered by magnitide. There is a significant different between the biggest value 1.1, and the smallest 0.05. The halfway value of 0.28 is still much smaller than the largest."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Check U, S and V Do Actually Reconstruct A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A2 =\n",
      " [[ 0.5   0.33  0.25  0.    0.   -0.    0.   -0.   -0.  ]\n",
      " [ 0.25  0.33  0.   -0.    0.    0.    0.    0.25  0.  ]\n",
      " [ 0.25  0.33  0.75  0.    0.   -0.    0.    0.    0.  ]\n",
      " [-0.    0.   -0.    0.5   0.5   0.6  -0.    0.   -0.  ]\n",
      " [ 0.    0.   -0.    0.33  0.17 -0.    0.5   0.    0.  ]\n",
      " [-0.    0.   -0.    0.17  0.33  0.4  -0.    0.   -0.  ]\n",
      " [-0.   -0.    0.   -0.   -0.   -0.    0.    0.25  0.25]\n",
      " [ 0.    0.   -0.   -0.   -0.   -0.    0.5   0.25  0.25]\n",
      " [-0.   -0.    0.   -0.   -0.   -0.    0.    0.25  0.5 ]]\n"
     ]
    }
   ],
   "source": [
    "# rebuild A2 from U.S.V\n",
    "A2 = numpy.dot(U,numpy.dot(S,VT))\n",
    "print(\"A2 =\\n\", numpy.round(A2, decimals=2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Yes, that worked .. the reconstructed A2 is the same as the original A (within the bounds of small floating point accuracy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Now Reduce Dimensions, Extract Topics\n",
    "Here we use only the top 3 values of the **S** singular value matrix, pretty brutal reduction in dimensions!\n",
    "\n",
    "Why 3, and not 2?\n",
    "\n",
    "We'll only plot 2 dimensions for the document cluster view, and later we'll use 3 dimensions for the topic word view"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "S_reduced =\n",
      " [[ 1.11  0.    0.    0.    0.    0.    0.    0.    0.  ]\n",
      " [ 0.    1.06  0.    0.    0.    0.    0.    0.    0.  ]\n",
      " [ 0.    0.    0.84  0.    0.    0.    0.    0.    0.  ]\n",
      " [ 0.    0.    0.    0.    0.    0.    0.    0.    0.  ]\n",
      " [ 0.    0.    0.    0.    0.    0.    0.    0.    0.  ]\n",
      " [ 0.    0.    0.    0.    0.    0.    0.    0.    0.  ]\n",
      " [ 0.    0.    0.    0.    0.    0.    0.    0.    0.  ]\n",
      " [ 0.    0.    0.    0.    0.    0.    0.    0.    0.  ]\n",
      " [ 0.    0.    0.    0.    0.    0.    0.    0.    0.  ]]\n"
     ]
    }
   ],
   "source": [
    "# S_reduced is the same as S but with only the top 3 elements kept\n",
    "S_reduced = numpy.zeros_like(S)\n",
    "# only keep top two eigenvalues\n",
    "l = 3\n",
    "S_reduced[:l, :l] = S[:l,:l]\n",
    "# show S_rediced which has less info than original S\n",
    "print(\"S_reduced =\\n\", numpy.round(S_reduced, decimals=2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## New View Of Documents"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "S_reduced_VT = \n",
      " [[-0.01 -0.01 -0.01 -0.59 -0.62 -0.67 -0.22 -0.04 -0.04]\n",
      " [ 0.55  0.55  0.71 -0.02 -0.02 -0.02  0.02  0.11  0.04]\n",
      " [-0.02 -0.01 -0.09  0.01 -0.07 -0.16  0.51  0.4   0.49]\n",
      " [ 0.03  0.03 -0.08 -0.1   0.03  0.17 -0.43  0.22  0.31]\n",
      " [-0.24 -0.17  0.32 -0.01  0.    0.01 -0.02 -0.08  0.14]\n",
      " [-0.09  0.04  0.02 -0.1   0.    0.07  0.03  0.12 -0.1 ]\n",
      " [-0.07  0.05  0.01  0.12 -0.01 -0.08 -0.05  0.07 -0.03]\n",
      " [ 0.02 -0.04  0.01  0.01 -0.02  0.01 -0.    0.02 -0.02]\n",
      " [ 0.01 -0.01  0.   -0.01  0.03 -0.02 -0.    0.01 -0.01]]\n"
     ]
    }
   ],
   "source": [
    "# what is the document matrix now?\n",
    "S_reduced_VT = numpy.dot(S_reduced, VT)\n",
    "print(\"S_reduced_VT = \\n\", numpy.round(S_reduced_VT, decimals=2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11552e518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the array\n",
    "p = plt.subplot(111)\n",
    "p.axis('scaled'); p.axis([-2, 2, -2, 2]); p.axhline(y=0, color='lightgrey'); p.axvline(x=0, color='lightgrey')\n",
    "p.set_yticklabels([]); p.set_xticklabels([])\n",
    "\n",
    "p.set_title(\"S_reduced_VT\")\n",
    "p.plot(S_reduced_VT[0,],S_reduced_VT[1,],'ro')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above shows that there are indeed 3 **clusters** of documents. That matches our expectations as we constructed the example data set that way."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Topics from New View of Words"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "            \n",
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       "            \n",
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       "            \n",
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       "            \n",
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       "            \n",
       "                background-color:  #f7fbff;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow5_col7 {\n",
       "            \n",
       "                background-color:  #f7fbff;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow5_col8 {\n",
       "            \n",
       "                background-color:  #f7fbff;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow6_col0 {\n",
       "            \n",
       "                background-color:  #add0e6;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow6_col1 {\n",
       "            \n",
       "                background-color:  #f2f8fd;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow6_col2 {\n",
       "            \n",
       "                background-color:  #d1e2f3;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow6_col3 {\n",
       "            \n",
       "                background-color:  #f7fbff;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow6_col4 {\n",
       "            \n",
       "                background-color:  #f7fbff;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow6_col5 {\n",
       "            \n",
       "                background-color:  #f7fbff;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow6_col6 {\n",
       "            \n",
       "                background-color:  #f7fbff;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow6_col7 {\n",
       "            \n",
       "                background-color:  #f7fbff;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow6_col8 {\n",
       "            \n",
       "                background-color:  #f7fbff;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow7_col0 {\n",
       "            \n",
       "                background-color:  #b9d6ea;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow7_col1 {\n",
       "            \n",
       "                background-color:  #f2f7fd;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow7_col2 {\n",
       "            \n",
       "                background-color:  #abd0e6;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow7_col3 {\n",
       "            \n",
       "                background-color:  #f7fbff;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow7_col4 {\n",
       "            \n",
       "                background-color:  #f7fbff;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow7_col5 {\n",
       "            \n",
       "                background-color:  #f7fbff;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow7_col6 {\n",
       "            \n",
       "                background-color:  #f7fbff;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow7_col7 {\n",
       "            \n",
       "                background-color:  #f7fbff;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow7_col8 {\n",
       "            \n",
       "                background-color:  #f7fbff;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow8_col0 {\n",
       "            \n",
       "                background-color:  #aed1e7;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow8_col1 {\n",
       "            \n",
       "                background-color:  #f2f7fd;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow8_col2 {\n",
       "            \n",
       "                background-color:  #c3daee;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow8_col3 {\n",
       "            \n",
       "                background-color:  #f7fbff;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow8_col4 {\n",
       "            \n",
       "                background-color:  #f7fbff;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow8_col5 {\n",
       "            \n",
       "                background-color:  #f7fbff;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow8_col6 {\n",
       "            \n",
       "                background-color:  #f7fbff;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow8_col7 {\n",
       "            \n",
       "                background-color:  #f7fbff;\n",
       "            \n",
       "            }\n",
       "        \n",
       "            #T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow8_col8 {\n",
       "            \n",
       "                background-color:  #f7fbff;\n",
       "            \n",
       "            }\n",
       "        \n",
       "        </style>\n",
       "\n",
       "        <table id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4b\" None>\n",
       "        \n",
       "\n",
       "        <thead>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                \n",
       "                <th class=\"blank level0\" >\n",
       "                  \n",
       "                \n",
       "                \n",
       "                \n",
       "                <th class=\"col_heading level0 col0\" colspan=1>\n",
       "                  0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <th class=\"col_heading level0 col1\" colspan=1>\n",
       "                  1\n",
       "                \n",
       "                \n",
       "                \n",
       "                <th class=\"col_heading level0 col2\" colspan=1>\n",
       "                  2\n",
       "                \n",
       "                \n",
       "                \n",
       "                <th class=\"col_heading level0 col3\" colspan=1>\n",
       "                  3\n",
       "                \n",
       "                \n",
       "                \n",
       "                <th class=\"col_heading level0 col4\" colspan=1>\n",
       "                  4\n",
       "                \n",
       "                \n",
       "                \n",
       "                <th class=\"col_heading level0 col5\" colspan=1>\n",
       "                  5\n",
       "                \n",
       "                \n",
       "                \n",
       "                <th class=\"col_heading level0 col6\" colspan=1>\n",
       "                  6\n",
       "                \n",
       "                \n",
       "                \n",
       "                <th class=\"col_heading level0 col7\" colspan=1>\n",
       "                  7\n",
       "                \n",
       "                \n",
       "                \n",
       "                <th class=\"col_heading level0 col8\" colspan=1>\n",
       "                  8\n",
       "                \n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "        </thead>\n",
       "        <tbody>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                \n",
       "                <th id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4b\"\n",
       "                 class=\"row_heading level0 row0\" rowspan=1>\n",
       "                    wheel\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow0_col0\"\n",
       "                 class=\"data row0 col0\" >\n",
       "                    -0.01\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow0_col1\"\n",
       "                 class=\"data row0 col1\" >\n",
       "                    0.6\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow0_col2\"\n",
       "                 class=\"data row0 col2\" >\n",
       "                    -0.04\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow0_col3\"\n",
       "                 class=\"data row0 col3\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow0_col4\"\n",
       "                 class=\"data row0 col4\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow0_col5\"\n",
       "                 class=\"data row0 col5\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow0_col6\"\n",
       "                 class=\"data row0 col6\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow0_col7\"\n",
       "                 class=\"data row0 col7\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow0_col8\"\n",
       "                 class=\"data row0 col8\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                \n",
       "                <th id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4b\"\n",
       "                 class=\"row_heading level0 row1\" rowspan=1>\n",
       "                     seat\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow1_col0\"\n",
       "                 class=\"data row1 col0\" >\n",
       "                    -0.02\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow1_col1\"\n",
       "                 class=\"data row1 col1\" >\n",
       "                    0.33\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow1_col2\"\n",
       "                 class=\"data row1 col2\" >\n",
       "                    0.11\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow1_col3\"\n",
       "                 class=\"data row1 col3\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow1_col4\"\n",
       "                 class=\"data row1 col4\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow1_col5\"\n",
       "                 class=\"data row1 col5\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow1_col6\"\n",
       "                 class=\"data row1 col6\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow1_col7\"\n",
       "                 class=\"data row1 col7\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow1_col8\"\n",
       "                 class=\"data row1 col8\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                \n",
       "                <th id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4b\"\n",
       "                 class=\"row_heading level0 row2\" rowspan=1>\n",
       "                     engine\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow2_col0\"\n",
       "                 class=\"data row2 col0\" >\n",
       "                    -0.02\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow2_col1\"\n",
       "                 class=\"data row2 col1\" >\n",
       "                    0.81\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow2_col2\"\n",
       "                 class=\"data row2 col2\" >\n",
       "                    -0.09\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow2_col3\"\n",
       "                 class=\"data row2 col3\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow2_col4\"\n",
       "                 class=\"data row2 col4\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow2_col5\"\n",
       "                 class=\"data row2 col5\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow2_col6\"\n",
       "                 class=\"data row2 col6\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow2_col7\"\n",
       "                 class=\"data row2 col7\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow2_col8\"\n",
       "                 class=\"data row2 col8\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                \n",
       "                <th id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4b\"\n",
       "                 class=\"row_heading level0 row3\" rowspan=1>\n",
       "                     slice\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow3_col0\"\n",
       "                 class=\"data row3 col0\" >\n",
       "                    -0.91\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow3_col1\"\n",
       "                 class=\"data row3 col1\" >\n",
       "                    -0.03\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow3_col2\"\n",
       "                 class=\"data row3 col2\" >\n",
       "                    -0.15\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow3_col3\"\n",
       "                 class=\"data row3 col3\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow3_col4\"\n",
       "                 class=\"data row3 col4\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow3_col5\"\n",
       "                 class=\"data row3 col5\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow3_col6\"\n",
       "                 class=\"data row3 col6\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow3_col7\"\n",
       "                 class=\"data row3 col7\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow3_col8\"\n",
       "                 class=\"data row3 col8\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                \n",
       "                <th id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4b\"\n",
       "                 class=\"row_heading level0 row4\" rowspan=1>\n",
       "                     oven\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow4_col0\"\n",
       "                 class=\"data row4 col0\" >\n",
       "                    -0.37\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow4_col1\"\n",
       "                 class=\"data row4 col1\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow4_col2\"\n",
       "                 class=\"data row4 col2\" >\n",
       "                    0.29\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow4_col3\"\n",
       "                 class=\"data row4 col3\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow4_col4\"\n",
       "                 class=\"data row4 col4\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow4_col5\"\n",
       "                 class=\"data row4 col5\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow4_col6\"\n",
       "                 class=\"data row4 col6\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow4_col7\"\n",
       "                 class=\"data row4 col7\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow4_col8\"\n",
       "                 class=\"data row4 col8\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                \n",
       "                <th id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4b\"\n",
       "                 class=\"row_heading level0 row5\" rowspan=1>\n",
       "                     boil\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow5_col0\"\n",
       "                 class=\"data row5 col0\" >\n",
       "                    -0.52\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow5_col1\"\n",
       "                 class=\"data row5 col1\" >\n",
       "                    -0.02\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow5_col2\"\n",
       "                 class=\"data row5 col2\" >\n",
       "                    -0.1\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow5_col3\"\n",
       "                 class=\"data row5 col3\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow5_col4\"\n",
       "                 class=\"data row5 col4\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow5_col5\"\n",
       "                 class=\"data row5 col5\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow5_col6\"\n",
       "                 class=\"data row5 col6\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow5_col7\"\n",
       "                 class=\"data row5 col7\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow5_col8\"\n",
       "                 class=\"data row5 col8\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                \n",
       "                <th id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4b\"\n",
       "                 class=\"row_heading level0 row6\" rowspan=1>\n",
       "                    door\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow6_col0\"\n",
       "                 class=\"data row6 col0\" >\n",
       "                    -0.02\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow6_col1\"\n",
       "                 class=\"data row6 col1\" >\n",
       "                    0.03\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow6_col2\"\n",
       "                 class=\"data row6 col2\" >\n",
       "                    0.27\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow6_col3\"\n",
       "                 class=\"data row6 col3\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow6_col4\"\n",
       "                 class=\"data row6 col4\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow6_col5\"\n",
       "                 class=\"data row6 col5\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow6_col6\"\n",
       "                 class=\"data row6 col6\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow6_col7\"\n",
       "                 class=\"data row6 col7\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow6_col8\"\n",
       "                 class=\"data row6 col8\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                \n",
       "                <th id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4b\"\n",
       "                 class=\"row_heading level0 row7\" rowspan=1>\n",
       "                    kitchen\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow7_col0\"\n",
       "                 class=\"data row7 col0\" >\n",
       "                    -0.12\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow7_col1\"\n",
       "                 class=\"data row7 col1\" >\n",
       "                    0.04\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow7_col2\"\n",
       "                 class=\"data row7 col2\" >\n",
       "                    0.57\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow7_col3\"\n",
       "                 class=\"data row7 col3\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow7_col4\"\n",
       "                 class=\"data row7 col4\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow7_col5\"\n",
       "                 class=\"data row7 col5\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow7_col6\"\n",
       "                 class=\"data row7 col6\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow7_col7\"\n",
       "                 class=\"data row7 col7\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow7_col8\"\n",
       "                 class=\"data row7 col8\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "            <tr>\n",
       "                \n",
       "                \n",
       "                <th id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4b\"\n",
       "                 class=\"row_heading level0 row8\" rowspan=1>\n",
       "                    roof\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow8_col0\"\n",
       "                 class=\"data row8 col0\" >\n",
       "                    -0.03\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow8_col1\"\n",
       "                 class=\"data row8 col1\" >\n",
       "                    0.04\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow8_col2\"\n",
       "                 class=\"data row8 col2\" >\n",
       "                    0.41\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow8_col3\"\n",
       "                 class=\"data row8 col3\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow8_col4\"\n",
       "                 class=\"data row8 col4\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow8_col5\"\n",
       "                 class=\"data row8 col5\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow8_col6\"\n",
       "                 class=\"data row8 col6\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow8_col7\"\n",
       "                 class=\"data row8 col7\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "                \n",
       "                <td id=\"T_8e9bafca_efe2_11e6_aedb_a45e60e5dd4brow8_col8\"\n",
       "                 class=\"data row8 col8\" >\n",
       "                    0\n",
       "                \n",
       "                \n",
       "            </tr>\n",
       "            \n",
       "        </tbody>\n",
       "        </table>\n",
       "        "
      ],
      "text/plain": [
       "<pandas.formats.style.Styler at 0x115624710>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# topics are a linear combination of original words\n",
    "U_S_reduced = numpy.dot(U, S_reduced)\n",
    "df = pandas.DataFrame(numpy.round(U_S_reduced, decimals=2), index=words)\n",
    "\n",
    "# show colour coded so it is easier to see significant word contributions to a topic\n",
    "df.style.background_gradient(cmap=plt.get_cmap('Blues'), low=0, high=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above shows that the 3 topics are linear combinations of existing words:\n",
    "* topic 1 is mostly **slice** and some **boil**\n",
    "* topic 2 is mostly **engine** and some **wheel**\n",
    "* topic 3 is mostly **kitchen** and some **roof**"
   ]
  }
 ],
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