11_semantic_spaces.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Semantic Spaces"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from sklearn.feature_extraction.text import TfidfVectorizer\n",
    "from sklearn.datasets import fetch_20newsgroups\n",
    "import numpy.linalg as la\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'text9': 11, 'txt': 12, 'text8': 10, 'text6': 8, 'text7': 9, 'text5': 7, 'text4': 6, 'text12': 3, 'text1': 0, 'text11': 2, 'text3': 5, 'text2': 4, 'text10': 1}\n",
      "['text1', 'text10', 'text11', 'text12', 'text2', 'text3', 'text4', 'text5', 'text6', 'text7', 'text8', 'text9', 'txt']\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_features = 2000\n",
    "t_v2 = TfidfVectorizer( max_features=n_features,\n",
    "                                   stop_words='english', sublinear_tf=True)\n",
    "import os\n",
    "directory = './docs/'\n",
    "flist = [fname for fname in os.listdir(directory)]\n",
    "books = t_v2.fit_transform(flist)\n",
    "books.shape\n",
    "books_d=books.todense()\n",
    "plt.imshow(books_d)\n",
    "plt.colorbar(); plt.savefig(\"./images/books_matrix.png\");\n",
    "print(t_v2.vocabulary_)\n",
    "print(t_v2.get_feature_names())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.94 0.33]\n",
      " [0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.94 0.   0.33]\n",
      " [0.   0.   0.   0.   0.   0.   0.   0.   0.94 0.   0.   0.   0.33]\n",
      " [0.   0.   0.   0.   0.   0.   0.   0.   0.   0.94 0.   0.   0.33]\n",
      " [0.   0.   0.   0.   0.   0.   0.   0.94 0.   0.   0.   0.   0.33]\n",
      " [0.   0.   0.   0.   0.   0.   0.94 0.   0.   0.   0.   0.   0.33]\n",
      " [0.   0.   0.   0.94 0.   0.   0.   0.   0.   0.   0.   0.   0.33]\n",
      " [0.94 0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.33]\n",
      " [0.   0.   0.94 0.   0.   0.   0.   0.   0.   0.   0.   0.   0.33]\n",
      " [0.   0.   0.   0.   0.   0.94 0.   0.   0.   0.   0.   0.   0.33]\n",
      " [0.   0.   0.   0.   0.94 0.   0.   0.   0.   0.   0.   0.   0.33]\n",
      " [0.   0.94 0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.33]]\n"
     ]
    }
   ],
   "source": [
    "print(books_d.round(2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.47971049 0.94438325 0.94438325 0.94438325 0.94438325 0.94438325\n",
      " 0.94438325 0.94438325 0.94438325 0.94438325 0.94438325 0.94438325]\n"
     ]
    }
   ],
   "source": [
    "U, sig, V = la.svd(books_d)\n",
    "print(sig)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "strings = [\"Human machine interface for ABC computer applications\",\n",
    "\"A survey of user opinion of computer system response time\",\n",
    "\"The EPS user interface management system\",\n",
    "\"System and human system engineering testing of EPS\",\n",
    "\"Relation of user perceived response time to error measurement\",\n",
    "\"The generation of random, binary, ordered trees\",\n",
    "\"The intersection graph of paths in trees\",\n",
    "\"Graph minors IV: Widths of trees and well-quasi-ordering\",\n",
    "\"Graph minors: A survey\"]\n",
    "string_short = [\"m1\",\"m2\", \"m3\", \"m4\", \"m5\", \"g1\", \"g2\", 'g3', \"g4\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'human': 3, 'interface': 4, 'computer': 0, 'survey': 8, 'user': 11, 'response': 7, 'time': 9, 'eps': 1, 'perceived': 6, 'trees': 10, 'graph': 2, 'minors': 5}\n",
      "['computer', 'eps', 'graph', 'human', 'interface', 'minors', 'perceived', 'response', 'survey', 'time', 'trees', 'user']\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t_v3 = TfidfVectorizer( max_features=12,\n",
    "                                   stop_words='english', sublinear_tf=True)\n",
    "\n",
    "titles = t_v3.fit_transform(strings)\n",
    "titles_d=titles.todense()\n",
    "plt.imshow(titles_d)\n",
    "plt.colorbar(); plt.savefig(\"./images/books_matrix.png\");\n",
    "print(t_v3.vocabulary_)\n",
    "print(t_v3.get_feature_names())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.58 0.   0.   0.58 0.58 0.   0.   0.   0.   0.   0.   0.  ]\n",
      " [0.46 0.   0.   0.   0.   0.   0.   0.46 0.46 0.46 0.   0.4 ]\n",
      " [0.   0.6  0.   0.   0.6  0.   0.   0.   0.   0.   0.   0.52]\n",
      " [0.   0.71 0.   0.71 0.   0.   0.   0.   0.   0.   0.   0.  ]\n",
      " [0.   0.   0.   0.   0.   0.   0.58 0.49 0.   0.49 0.   0.43]\n",
      " [0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   1.   0.  ]\n",
      " [0.   0.   0.71 0.   0.   0.   0.   0.   0.   0.   0.71 0.  ]\n",
      " [0.   0.   0.55 0.   0.   0.63 0.   0.   0.   0.   0.55 0.  ]\n",
      " [0.   0.   0.52 0.   0.   0.6  0.   0.   0.6  0.   0.   0.  ]]\n"
     ]
    }
   ],
   "source": [
    "print(titles_d.round(2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "im = ax.imshow(titles_d.T, cmap=plt.cm.Oranges)\n",
    "\n",
    "# We want to show all ticks...\n",
    "ax.set_yticks(np.arange(len(t_v3.get_feature_names())))\n",
    "ax.set_xticks(np.arange(len(strings)))\n",
    "# ... and label them with the respective list entries\n",
    "ax.set_yticklabels(t_v3.get_feature_names());\n",
    "ax.set_xticklabels(string_short); plt.savefig(\"./images/titles_matrix.png\", bbox_inches='tight');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\\begin{bmatrix}\n",
      "  0.58 & 0.46 & 0. & 0. & 0. & 0. & 0. & 0. & 0.\\\\\n",
      "  0. & 0. & 0.6 & 0.71 & 0. & 0. & 0. & 0. & 0.\\\\\n",
      "  0. & 0. & 0. & 0. & 0. & 0. & 0.71 & 0.55 & 0.52\\\\\n",
      "  0.58 & 0. & 0. & 0.71 & 0. & 0. & 0. & 0. & 0.\\\\\n",
      "  0.58 & 0. & 0.6 & 0. & 0. & 0. & 0. & 0. & 0.\\\\\n",
      "  0. & 0. & 0. & 0. & 0. & 0. & 0. & 0.63 & 0.6\\\\\n",
      "  0. & 0. & 0. & 0. & 0.58 & 0. & 0. & 0. & 0.\\\\\n",
      "  0. & 0.46 & 0. & 0. & 0.49 & 0. & 0. & 0. & 0.\\\\\n",
      "  0. & 0.46 & 0. & 0. & 0. & 0. & 0. & 0. & 0.6\\\\\n",
      "  0. & 0.46 & 0. & 0. & 0.49 & 0. & 0. & 0. & 0.\\\\\n",
      "  0. & 0. & 0. & 0. & 0. & 1. & 0.71 & 0.55 & 0.\\\\\n",
      "  0. & 0.4 & 0.52 & 0. & 0.43 & 0. & 0. & 0. & 0.\\\\\n",
      "\\end{bmatrix}\n"
     ]
    }
   ],
   "source": [
    "def bmatrix(a):\n",
    "    lines = str(a).replace('[', '').replace(']', '').splitlines()\n",
    "    rv = [r'\\begin{bmatrix}']\n",
    "    rv += ['  ' + ' & '.join(l.split()) + r'\\\\' for l in lines]\n",
    "    rv +=  [r'\\end{bmatrix}']\n",
    "    return '\\n'.join(rv)\n",
    "\n",
    "print(bmatrix(titles_d.round(2).T))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "U, sig, V = la.svd(titles_d.T)\n",
    "fig, ax = plt.subplots()\n",
    "nwords = len(t_v3.get_feature_names())\n",
    "nstrings = len(strings)\n",
    "im = ax.imshow(U, cmap=plt.cm.Oranges)\n",
    "ax.set_yticks(np.arange(nwords))\n",
    "ax.set_yticklabels(t_v3.get_feature_names());\n",
    "plt.savefig(\"./images/U_matrix.png\", bbox_inches='tight');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "im = ax.imshow(V, cmap=plt.cm.Oranges)\n",
    "ax.set_xticks(np.arange(nstrings))\n",
    "ax.set_xticklabels(string_short);\n",
    "plt.savefig(\"./images/V_matrix.png\", bbox_inches='tight');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rank = len(strings)\n",
    "sigma = np.zeros((rank, rank))\n",
    "for i in range(rank):\n",
    "    sigma[i][i] = sig[i]\n",
    "fig, ax = plt.subplots()\n",
    "im = ax.imshow(sigma, cmap=plt.cm.Oranges)\n",
    "\n",
    "plt.savefig(\"./images/sigma_matrix.png\", bbox_inches='tight');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "r = 4\n",
    "sigma_r = np.zeros((r, r))\n",
    "for i in range(r):\n",
    "    sigma_r[i][i] = sig[i]\n",
    "fig, ax = plt.subplots()\n",
    "im = ax.imshow(sigma_r, cmap=plt.cm.Oranges)\n",
    "# We want to show all ticks...\n",
    "ax.set_yticks(np.arange(nstrings))\n",
    "ax.set_xticks(np.arange(nstrings))\n",
    "plt.savefig(\"./images/sigma_r_matrix.png\", bbox_inches='tight');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAR0AAAD4CAYAAADRlDL+AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8rg+JYAAAACXBIWXMAAAsTAAALEwEAmpwYAAAdPElEQVR4nO3debQcZZ3/8feHkJANEjBBE0iICyASQjb4gSAgchgFfqADGgQGIjhBRkHHnzIZcYkwjDLgOALqMQITEQQkOixyNAmQsIQlG9lYHUgcMcg6QAgYlvv9/VFPS9H0ze3bXbe6k3xe59xzq5+q59tP3dz7zVPVVd9SRGBmVpYtWj0AM9u8OOmYWamcdMysVE46ZlYqJx0zK9WWrR5AKw3pv2XsNLh303Gef/EvBYwGBg1ofiwVER2FxOk1cmwhcWzTtHjx4mciYmh3+mzWSWenwb2Zf8q7m45z080PFzAa+Jt9ti8kDkDH+mIS4TY/WlRIHNs0SfpDd/v48MrMSuWkY2alctIxs1I56ZhZqTaapCNprKTDWj0OM2vORpN0gLFAt5KOpM360zmzdlR30pF0oqTlkpZJ+rmknSTdktpukTQybTdD0o8lzZX0mKQDJV0m6UFJM3LxXpL0PUlLUv+hqX2epIlpeYik1ZL6AGcDkyQtlTRJ0oAUd6Gk+yQdlfpMlnStpBuB2cX9qMysCHUlHUm7A2cBB0fEnsAXgYuByyNiDHAlcGGuy7bAwcA/AjcC3wd2B/aQNDZtMwBYEhHjgduAb3X2/hHxKvBN4JqIGBsR16Tx3BoRewEfBs6XNCB12Rc4KSIOrrEvUyQtkrTo6XWv17P7Zlagemc6BwMzI+IZgIh4juwP+xdp/c+B/XPb3xhZoZ4VwJMRsSKyS2TvB0albTqAa9LyFVX963EoMFXSUmAe0BcYmdbNSWN8m4iYHhETI2Li0AE++jIrW71/dQK6qvaVX78+fe/ILVded/aelf6v82Yy7NvFmI6OiLdcDizp/wDruhirmbVIvTOdW4BPSXoHgKTtgLuAY9P644E7G3jvY9Lycbn+q4EJafmY3PZrga1zr2cBp0tSGtO4br6/mbVAXUknIu4HzgVuk7QM+HfgDOAzkpYDf0d2nqc71gG7S1pMdvh2dmq/ADhN0l3AkNz2c4EPVE4kA+cAvYHlklam12bW5tSqGsmSXoqIgS1582TC8H7RXjd8DiskDhR5w+czhcSxTZOkxRExsTt9NqbrdMxsE9CypNPqWY6ZtYZnOmZWqs36QpWIIF5/rek4z65XAaOB/p85r5A4AK/87J8Li2VWJM90zKxUTjpmVionHTMrlZOOmZXKScfMSuWkY2alctIxs1K1fdKRdIKkBelGz59I6rWBqoNnSHogVTO8utVjN7O3a+ukI2k3YBKwX0SMBd4gK6PRWdXBqcC4VM3wc+WP2My60u5XJH+ErLbOwlQ2px/wFG+vOvjrtLwcuFLSdcB1tQJKmgJMARixTbvvvtmmp61nOmTVAX+W6iKPjYhdI2Jaje0q9TkOB35IlqgW13oaRL5c6ZD+vXps4GZWW7snnVuAYyRtD1nFQkk7UaPqoKQtgBERMRc4ExgM+E52szbT1scXEfGApK8Ds1NSeQ34PG+tOvgC2XmfXsAVkgaRzZC+HxHPt2bkZtaZtk46AOlxM9fk2yQREd8AvlG1eXefKGFmJWv3wysz28RslEnHVQfNNl4bZdIxs41X25/T6UlbbP8e+p5xZdNxTtzy+AJGA+su+UohcQBuW/xUIXGOKCSK2Zs80zGzUjnpmFmpnHTMrFROOmZWKicdMyvVJpN0JB0k6TetHoeZbVhbJp1ad4eb2aahJX/ckr5BVozrj8AzwGKyS0LuAvYDbpD0CPB1oA/wLHB8RDwpaRrwXmAHYATwbxHx0xR6oKSZwOgU84SICMysbZSedCRNBI4GxqX3X0KWIAAGR8SBabttgX0iIiR9lqxcxf9L240B9iGrIHifpJtS+zhgd2ANMJ8sgd3Z4ztlZnVrxUxnf+D6iHgFQNKNuXX5u8l3BK6RNIxstrMqt67S/xVJc4G9geeBBRHxeIq7FBhFVdLJVw4cucO7CtspM6tPK87paAPr1uWWLwIujog9gFOBvrl11YdMldfrc21vUCOp5isHDn3HtvWP2swK0YqkcyfwfyX1lTSQrMRoLYOAP6Xlk6rWHZX6vwM4CFjYIyM1s8KVnnQiYiFwA7CMrKD6IrLqf9WmAddKuoPsZHPeAuAm4B7gnIhY02MDNrNCteqj6QsiYpqk/sDtwPdyn0ABEBHXA9d30v+RiJhStf08YF7u9RcKHbGZFaJVSWe6pA+Qnaf5WUQsadE4zKxkLUk6EXFcE32nFTgUMytZW16RbGabrs36doOOpx7jLxd+quk41968quuN6nDC5TMLiQMw8dwTCotlViTPdMysVE46ZlYqJx0zK5WTjpmVyknHzErlpGNmpeqxpCNplKSVPRXfzDZOnumYWal6Oun0kvRTSfdLmi2pn6R5qXogkoZIWp2WJ0u6TtKNklZJ+oKkL0u6T9I9krZL2/29pIWSlkn6VbppFEkzJF0o6S5Jj0k6pof3zcwa0NNJZ2fghxGxO1llv6O72H40cBxZJcBzgZcjYhxwN3Bi2ubXEbFXROwJPAickus/jKwy4RHAd2u9gaQpkhZJWvTMy280tldm1rCeTjqrImJpWl5MVj50Q+ZGxNqIeJqsxk6llOmKXN/Rku6QtIKsuPvuuf7XRURHRDwAvLPWG+QrBw7p36vbO2RmzenppFOrfOjrufftu4HtO3KvO3jzPrEZwBdSGdNvV8XI999QWVQza5FWnEheDUxIy42cd9kaeEJSb7KZjpltRFqRdC4ATpN0FzCkgf7fAO4F5gAPFTkwM+t5PVbaIiJWk50Yrry+ILd6TG7562n9DLJDp8r2o3LLf10XET8Gflzj/SZXvR7Y4NDNrAf5Oh0zK5WTjpmVyknHzEq1WZcrBUDNf7L+WkcB4wB4bH5BgWDrdzVyjt6s53mmY2alctIxs1I56ZhZqZx0zKxUTjpmVqqGkk66haGrbb5UqXXTzdjvl7Q01dF5byPjM7P21VDSiYgP1rHZl4BuJR1JvYCPA9dHxLiIeLT7ozOzdtboTOel9P2gVAlwpqSHJF2pzBnAcGCupLlp20Ml3S1piaRrJQ1M7aslfVPSncAksmT12Vy/6yQtTtUHp+TG8NEUa5mkW1LbAEmXpcqC90k6qvEfjZn1hCIuDhxHVkhrDTAf2C8iLpT0ZeDDEfGMpCFkN3YeEhHrJP0T8GXg7BTjLxGxP4CkXYCXcjeInhwRz0nqByyU9CuyZPlT4ICIWFUpZQqcBdwaESdLGgwskHRzRKyrDDYlrikAI7bxtZFmZSvir25BRDwOIGkpWYW/O6u22Qf4ADBf2RXAfchKkFZcs4H4Z0j6RFoeQVYCdShwe0SsAoiI59L6Q4EjJX0lve4LjCQra0radjowHWD8sL5R706aWTGKSDq1qgNWEzAnIj7dSYx1tRolHQQcAuwbES9LmkeWSATUShgCjo6Ih+sauZmVric/Ml9LVuUP4B5gP0nvA5DUPx1GdWUQ8L8p4byfbMYE2SzpQEnvTvEqh1ezgNOVplOSxhWzK2ZWlJ5MOtOB30qamwqtTwaukrScLAm9v44YvwO2TH3OSf1I8aYAv5a0jDcPz84BegPL04P+zilwf8ysAA0dXlWq8kXEPGBerv0LueWLgItyr28F9qoRa1TV62m55fXAxzoZw2+B31a1vQKcWv+emFnZfEWymZXKScfMSuWkY2al2qyvjtti8PZsdeQZTcc59tULut6oDs/9anohcQAuvuvlQuJMK2bXzP7KMx0zK5WTjpmVyknHzErlpGNmpXLSMbNStTzpSDpS0tRWj8PMytHyj8wj4gbghmbjSOoVEW8UMCQz60E9OtORNCpVFLxE0spUWfAQSfMl/V7S3pImS7o4bT9D0oWS7pL0mKRjUrsknZ9irJA0KbUfJGmupF8AK1LlwJtSNcGVle3MrH2UMdN5H/BJsrvCFwLHAfsDRwJfA66r2n5YWv9+shnQTOBvgbHAnsAQsgqCt6ft9wZGpwqCRwNrIuJwAEmDqgeTrxw48l3bFrWPZlanMs7prIqIFRHRAdwP3BIRAawgqzJY7bqI6IiIB4B3prb9gasi4o2IeBK4jTfvWF9QqSCYYh4i6TxJH4qIF6qDR8T0iJgYEROHDh5Y3F6aWV3KSDr5yoIdudcd1J5p5bdX1fda/lp1MCIeASaQJZ/vSPpmt0drZj2q5Z9e1el2YJKkXpKGAgcAC6o3kjQceDkirgAuAMaXO0wz60rLP72q038B+wLLyGojnxkRf04lTPP2AM6X1AG8BpxW7jDNrCs9mnQiYjUwOvd6cifrZlSvT68rFQoD+Gr6yq+fx1srF84iq5NsZm1qYzm8MrNNhJOOmZXKScfMSrWxnEjuER3PP8X663/QdJynH11TwGjgmbWvFxIH4JtTjyksllmRPNMxs1I56ZhZqZx0zKxUTjpmVionHTMrVVslHUnDJc0sKNY8SROLiGVmxenpIl7d+kg+ItZEhD/rNduEdZl0ctX/fiZpuaSZkvpLmiDpNkmLJc2SNCxtP0/Sv0q6DfiipL1SJcBlkhZI2jrdLX6+pIUp5qm591qZlu+VtHtuHPPSew6QdFnqe5+ko9L6fpKuTvGuAfr1xA/MzJpT70xkV+CUiJgv6TLg88AngKMi4ulUFvRc4OS0/eCIOFBSH+AhYFJELJS0DfAKcArwQkTsJWkrYL6k2WR3kFdcDXwK+FZKaMMjYrGkfwVujYiTJQ0GFki6GTiVrKzFGEljgCW1diRfOXDENpv1tZFmLVHvX90fI2J+Wr6CrMzoaGCOJIBewBO57a9J33cFnoiIhQAR8SKApEOBMZUayMAgYGfgkVyMXwJzgG+RJZ9rU/uhwJGSvpJe9wVGktXYuTC9z3JJy2vtSERMB6YDjB/WN2ptY2Y9p96kU/3HuRa4PyL27WT7SjU/1ehbaT89laJ4s1Ea9dc3jPiTpGfTrGUS2Uym0vfoiHi4qm+tcZpZm6n3RPJISZUE82ngHmBopU1S7/z5l5yHgOGS9krbbZ1OLs8CTpPUO7XvImlAjf5XA2cCgyJiRWqbBZyulGUkjUvttwPHp7bRwJg6983MSlRv0nkQOCkdsmwHXAQcA5wnaRmwFPhgdaeIeJVslnJR2m4O2eHQJcADwJJ04vgn1J51zQSOJTvUqjgH6A0sT33PSe0/BgamMZ5JjXKmZtZ69R5edUTE56ralpKdR3mLiDio6vVCYJ8aMb+WvvJe4K2VBp+sHmNEvMKbh1rV7cd2tgNm1h7a6uJAM9v0dTnTqa5zbGbWDM90zKxUm/XVcZJQ7z5Nx3n02TcKGA2sXlfc/wHj179SWCyzInmmY2alctIxs1I56ZhZqZx0zKxUTjpmVionHTMrVVNJRxknLjOrW7cTRqru96CkH5EVyvpGrgLgt9M2AyTdlKoFrkxFvpC0WtJ5qYLgAknvS+07SbolxbhF0sjUPkPShany4GOV+juShkm6XdLSFP9Dqf1QSXdLWiLpWkkDi/kxmVlRGp2l7ApcDvwTsAOwNzAWmCDpAOCjwJqI2DMiRgO/y/V9MSL2Bi4G/iO1XQxcHhFjgCtJxbiSYcD+wBHAd1PbccCsiBgL7AkslTQE+DpwSESMBxYBX64euKQpkhZJWvT0y8Vc1Gdm9Ws06fwhIu4hq+J3KHAf2azn/WQVAFcAh6RZzYci4oVc36ty3ys1evYFfpGWf06WZCqui4iOiHgAeGdqWwh8RtI0YI+IWEt2J/sHyEqfLgVOAnaqHnhETI+IiRExcWj/Xg3uvpk1qtHbIPKVAb8TET+p3kDSBOAw4DuSZkfE2WlVvrpfZ5X+8u3r82EBIuL2NKM6HPi5pPOB/wXmRMSnu703ZlaaZk8CzwJOrpw7kbSDpO0lDScrkn4FcAEwPtdnUu773Wn5Lt6shXM8cOeG3lTSTsBTEfFT4NIU/x5gv9x5ov6Sdmly/8ysYE3d8BkRsyXtBtydqoe+BJwAvA84X1IH8BpwWq7bVpLuJUt4lVnJGcBlkr4KPA18pou3Pgj4qqTX0nuemJ5KMRm4Kj1hArJzPI/UDmFmraCI8mqZS1oNTIyIZ0p70w2YMLxfzP/se5qOM3/eQwWMBlavUyFxAD4z5WOFxNni1BsLiWObJkmLI6JbT9L1NTZmVqpS6+lExKgy38/M2o9nOmZWqs27cmCfregzYuem44wa9HDXG9Wh1xYdhcQBuOQnvy0kzpS3PXfDrDme6ZhZqZx0zKxUTjpmVionHTMrlZOOmZXKScfMStWWSUfSZv1RvtmmrEeTTq0Kgql64JC0fqKkeWl5mqTpkmYDl0u6V9LuuVjzJE1IMS9L1Qrvk3RUWn+HpLG57edLGtOT+2dm3dfTM50NVRCsZQJwVEQcB1wNfAqy8qTA8IhYDJwF3BoRewEfJrubfQBwCTA5bb8LsFVELK9+g7dUDlz7aiE7aWb16+mks6EKgrXcEBGVh3D/EvhkWv4UcG1aPhSYmqoDzgP6AiPT+iMk9QZOBmbUeoO3VA7cuvnnmJtZ9/TouZOIeKS6giDwOm8mu75VXdbl+v5J0rPpEGkSULkgX8DREfG2ew8kzQGOIktS3brd3szK0dPndGpVEFxNdhgFcHQXIa4GzgQGRcSK1DYLOF2papikcbntLyEr6r4wIp4rZCfMrFA9/SnRHry9gmA/4FJJXwPu7aL/TOAHwDm5tnPIniKxPCWe1WRPiiAiFkt6EfjPAvfBzArU04dXs8hmJtXeVrs4IqbVaHuSqjGmcz41731OM6stgNkNDNfMStCW1+k0QtKJZDOnsyKiuBoRZlaoTeYivIi4nOwBgGbWxjaZmY6ZbRw2mZlOI+LV9bz6x983HWf1C8U8UWP1uuL+D/jsqcU8DcKsaJ7pmFmpnHTMrFROOmZWKicdMyuVk46Zlaptko6kwZL+IS0PlzSz1WMys+K1TdIBBgP/ABARayLimNYOx8x6Qjtdp/Nd4L2pTs7vgd0iYrSkycDHgV7AaOB7QB/g74D1wGER8Zyk9wI/BIYCLwN/HxEPlb0TZrZh7TTTmQo8GhFjga9WrRsNHAfsDZxLVi5jHHA3cGLaZjpwekRMAL4C/KiMQZtZ97TTTGdD5kbEWmCtpBeAG1P7CmCMpIHAB4FrU5kdgK1qBZI0BZgCMGJQ7x4dtJm93caSdNbnljtyrzvI9mEL4Pk0S9qgiJhONitiwvB+xdy/YGZ1a6fDq7XA1o10jIgXgVWSPgmgzJ5FDs7MitE2SScingXmS1oJnN9AiOOBUyQtA+4nq5VsZm2mrQ6v0qNnqttmkHuyQ0SMqrUuIlaRPfLGzNpY28x0zGzz4KRjZqVy0jGzUjnpmFmp2upEctn0rl3pO/XmpuN8eLuCbhMbMLiYOICO/JfCYpkVyTMdMyuVk46ZlcpJx8xK5aRjZqVqadLJVws0s81Dq2c6g0nVAvMk9Sp/KGZWhlYnnb9WC5S0UNJcSb8AVkjqJen81L5c0qmVTpK+mmv/dmobIOkmScskrZQ0qVU7ZWada/V1OlOB0RExVtJBwE3p9apUbOuFiNhL0lZkd6DPBnZOX3sDAm6QdABZmdI1EXE4gKRB5e+OmXWl1Umn2oJ0tzjAoWRVAStX3g0iSzaHpq/7UvvA1H4HcIGk84DfRMQdtd4gXzlw5Igde2QnzKxz7ZZ01uWWRVbzeFZ+A0l/A3wnIn5S3VnSBOAw4DuSZkfE2dXb5CsHThw/1pUDzUrW6nM6G6oWOAs4TVJvAEm7SBqQ2k9OdZGRtIOk7SUNJyvYfgVwATC+54dvZt3V0plORDwrqVIt8BXgydzqS4BRwBJl1dafBj4eEbMl7QbcnYqwvwScALwPOF9SB/AacFp5e2Jm9Wr54VWtaoGpvQP4WvqqXvcD4AdVzY+SzYLMrI21+vDKzDYzTjpmVionHTMrlZOOmZWq5SeSWyn+/DB/+e6BTceZfv3DBYwGPrR9RyFxAPbsVcztazr5V4XEMavwTMfMSuWkY2alctIxs1I56ZhZqZx0zKxUTjpmVqpNOulI2qwvCTBrR231RylpFFkBrtHp9VfIinQ9B3wOeB14ICKOTWUuLgL2INuPaRFxvaTJwOFAX2AAcHDZ+2FmnWurpLMBU4F3R8R6SYNT21nArRFxcmpbIKnyjOB9gTER8Vx1oHzlwBGDevf4wM3srTaWw6vlwJWSTiCb7UBWsnSqpKXAPLKZzci0bk6thANZ5cCImBgRE4f290MnzMrWbknndd46pr7p++HAD4EJwOJ0rkbA0RExNn2NjIgH0/b5sqdm1kbaLek8CWwv6R3pCRBHkI1xRETMBc4ke1bWQLKCXaenqoJIGteaIZtZd7TVOZ2IeE3S2cC9wCrgIaAXcEV6pIyA70fE85LOAf4DWJ4Sz2qyJGVmbaytkg5ARFwIXFjHdq8Ap9ZonwHMKHxgZlaIdju8MrNNnJOOmZXKScfMSqWIzfchl5KeBv7QxWZDgGcKesuiYjmO47RLrF0jorMHZtbUdieSyxQRQ7vaRtKiiJhYxPsVFctxHKddYkla1N0+Prwys1I56ZhZqZx0uja9DWM5juO0S6xux9msTySbWfk80zGzUjnpmFmpnHQ2QNJHJT0s6b8lTW0wxmWSnpK0ssmxjJA0V9KDku6X9MUG4/SVtEDSshTn202Oq5ek+yT9psk4qyWtkLS0kY9hc3EGS5op6aH0s9q3gRi7pnFUvl6U9KUGx/OP6ee8UtJVkvp23atmnC+mGPd3Zyy1fv8kbSdpjqTfp+/bNhjnk2k8HZLq//g9IvxV44vs7vZHgfcAfYBlwAcaiHMAMB5Y2eR4hgHj0/LWwCMNjkfAwLTcm+yO/n2aGNeXgV+QlZltZv9WA0MK+Hf7GfDZtNwHGFzA78GfgZ0a6LsDWbWEfun1L4HJDcQZDawE+pNdW3czsHOjv3/AvwFT0/JU4LwG4+wG7EpWRG9ivfvjmU7n9gb+OyIei4hXgauBo7obJCJuJ6vx3JSIeCIilqTltcCDZL/U3Y0TEfFSetk7fTX0aYKkHckKrF3SSP+iSdqG7I/jUoCIeDUinm8y7EeARyOiqyvXO7Ml0C8VnusPrGkgxm7APRHxckS8DtwGfKKejp38/h1FlpxJ3z/eSJyIeDAiHq5nHHlOOp3bAfhj7vXjNPBH3hNSAftxZLOURvr3SmVenyIr7dpQHLJ6RmcCHQ32zwtgtqTFqY51I94DPA38ZzrkuyQV8G/GscBVjXSMiD8BFwD/AzwBvBARsxsItRI4IBW36w8cBoxoZEzJOyPiiTTGJ4Dtm4jVbU46nVONtpZfXyBpIPAr4EsR8WIjMSLijYgYC+wI7C1pdAPjOAJ4KiIWNzKGGvaLiPHAx4DPSzqggRhbkh0C/DgixpGVrW3oXByApD7AkcC1DfbflmxW8W5gODAg1fnulsjK8J4HzAF+R3ao//oGO7UxJ53OPc5b/zfZkcamxoWR1Jss4VwZEb9uNl469JgHfLSB7vsBR0paTXboebCkK5oYy5r0/Sngv8gOb7vrceDx3MxtJlkSatTHgCUR8WSD/Q8BVkXE0xHxGvBr4IONBIqISyNifEQcQHaY8/sGxwTwpKRhAOn7U03E6jYnnc4tBHaW9O70P96xwA2tGkwqyXop8GBE/HsTcYZWHuMjqR/ZH8ZD3Y0TEf8cETtGxCiyn82tEdHt/8XTOAZI2rqyTPakj25/2hcRfwb+KGnX1PQR4IFGxpR8mgYPrZL/AfaR1D/9+32E7Fxct0naPn0fCfxtk+O6ATgpLZ8EXN9ErO5r5sz+pv5Fduz8CNmnWGc1GOMqsuP518j+Jz6lwTj7kx3eLQeWpq/DGogzBrgvxVkJfLOAn9NBNPHpFdm5mGXp6/5Gf9Yp1lhgUdq/64BtG4zTH3gWGNTkz+bbZEl9JfBzYKsG49xBlkCXAR9p5vcPeAdwC9ls6RZguwbjfCItryd7qMKsesbk2yDMrFQ+vDKzUjnpmFmpnHTMrFROOmZWKicdMyuVk46ZlcpJx8xK9f8BtHpLvc++q48AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "im = ax.imshow(U[:,:r], cmap=plt.cm.Oranges)\n",
    "U_r = U[:,:r]\n",
    "ax.set_yticks(np.arange(nwords))\n",
    "ax.set_xticks(np.arange(nwords))\n",
    "ax.set_yticklabels(t_v3.get_feature_names());\n",
    "plt.savefig(\"./images/U_r_matrix.png\", bbox_inches='tight');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "V_r = V[:r,:]\n",
    "fig, ax = plt.subplots()\n",
    "im = ax.imshow(V[:4,:], cmap=plt.cm.Oranges)\n",
    "ax.set_xticks(np.arange(nstrings))\n",
    "ax.set_yticks(np.arange(nstrings))\n",
    "ax.set_xticklabels(string_short);\n",
    "plt.savefig(\"./images/V_r_matrix.png\", bbox_inches='tight');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What are these concepts?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use the 'V' matrix to show us what words represent which concepts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# need pos U_r\n",
    "posU_r = U_r - np.min(U_r)\n",
    "plt.figure(figsize=(8,5))\n",
    "plt.axis([-1, 10,-1,15])\n",
    "plt.annotate('Topic:', (-1, -1))\n",
    "for i in range(r):\n",
    "    plt.annotate(str(i), (i*3,-1))\n",
    "    for j in range(nwords):\n",
    "#         print(i, j, t_v3.get_feature_names()[j], U_r[j,i])\n",
    "    \n",
    "        plt.annotate(t_v3.get_feature_names()[j], (i*3,2+1.2*j), size=20*posU_r[j,i])\n",
    "plt.axis('off')\n",
    "plt.savefig('concept_words.png')\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Not necessarily very meaningful"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "graph vs tree 0.3504019113046441\n",
      "human vs user 0.11452249197177984\n",
      "graph vs minor 0.9028829871966637\n",
      "human vs interface 0.9521816798157577\n"
     ]
    }
   ],
   "source": [
    "def cos_sim(x,y):\n",
    "    xf = np.ravel(x)\n",
    "    yf = np.ravel(y)\n",
    "    sim = np.dot(xf,yf)/(np.sqrt(sum(xf**2))*np.sqrt(sum(yf**2)))\n",
    "    return sim\n",
    "\n",
    "#['computer', 'eps', 'graph', 'human', 'interface', 'minors', 'perceived', 'response', 'survey', 'time', 'trees', 'user']\n",
    "print(\"graph vs tree\", cos_sim(U_r[2,:], U_r[10,:]))\n",
    "print(\"human vs user\", cos_sim(U_r[3,:], U_r[11,:]))\n",
    "print(\"graph vs minor\", cos_sim(U_r[2,:], U_r[5,:]))\n",
    "print(\"human vs interface\", cos_sim(U_r[3,:], U_r[4,:]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "m1 vs m3 0.9352702052865914\n",
      "g1 vs g2 0.8344678296253983\n",
      "m4 vs g1 0.18185647706860067\n"
     ]
    }
   ],
   "source": [
    "print(\"m1 vs m3\", cos_sim(V_r[:,0], V_r[:,2]))\n",
    "print(\"g1 vs g2\", cos_sim(V_r[:,5], V_r[:,6]))\n",
    "print(\"m4 vs g1\", cos_sim(V_r[:,4], V_r[:,5]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# For visualisation use 2d vectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "r = 2\n",
    "V_r = V[:r,:]\n",
    "U_r = U[:,:r]\n",
    "\n",
    "#in document space\n",
    "plt.plot(V_r[0, :], V_r[1, :], 'b.')\n",
    "for i in range(9):\n",
    "    label = string_short[i]\n",
    "    x = V_r[0, i]\n",
    "    y = V_r[1, i]\n",
    "    plt.annotate(label, xy=(x, y), xytext=(-2, 2),\n",
    "        textcoords='offset points', ha='right', va='bottom');\n",
    "plt.savefig(\"./images/doc_space.eps\", bbox_inches='tight');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#in term space\n",
    "plt.plot(U_r[:, 0], U_r[:, 1], 'b.')\n",
    "for i in range(len(t_v3.get_feature_names())):\n",
    "    label = t_v3.get_feature_names()[i]\n",
    "    x = U_r[i, 0]\n",
    "    y = U_r[i, 1]\n",
    "    plt.annotate(label, xy=(x, y), xytext=(-2, 2),\n",
    "        textcoords='offset points', ha='right', va='bottom');\n",
    "plt.savefig(\"./images/term_space.eps\", bbox_inches='tight');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Machine Translation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [],
   "source": [
    "vocab_size = 2000\n",
    "#data downloaded from https://ddd.uab.cat/record/238990?ln=en\n",
    "file_fr = 'cadlaws_french.txt'\n",
    "file_en = 'cadlaws_english.txt'\n",
    "from nltk.tokenize import sent_tokenize, word_tokenize\n",
    "\n",
    "txt=[]\n",
    "doc_limit = 100\n",
    "with open(file_fr) as f:\n",
    "    i=0\n",
    "    for line in f:\n",
    "        txt.append(line)\n",
    "        i+=1\n",
    "        if i==doc_limit:\n",
    "            break\n",
    "with open(file_en) as f:\n",
    "    i = 0\n",
    "    for line in f:\n",
    "        txt[i] = txt[i] + ' ' + line\n",
    "        i+=1\n",
    "        if i==doc_limit:\n",
    "            break\n",
    "#         print(txt[i])\n",
    "#         break\n",
    "\n",
    "from nltk.corpus import stopwords\n",
    "# need to comment this in below on first run\n",
    "# import nltk\n",
    "# nltk.download('stopwords')\n",
    "final_stopwords_list = stopwords.words('english') + stopwords.words('french')\n",
    "tv5 = TfidfVectorizer(max_features=vocab_size, stop_words=final_stopwords_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<100x357 sparse matrix of type '<class 'numpy.float64'>'\n",
       "\twith 686 stored elements in Compressed Sparse Row format>"
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "laws = tv5.fit_transform(txt)\n",
    "laws"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'règlement': 291, 'établi': 355, 'conformément': 70, 'loi': 176, 'pension': 227, 'retraite': 284, 'gendarmerie': 141, 'royale': 290, 'canada': 51, 'regulations': 268, 'made': 179, 'pursuant': 257, 'royal': 289, 'canadian': 52, 'mounted': 199, 'police': 242, 'superannuation': 315, 'act': 11, 'titre': 327, 'abrégé': 5, 'short': 305, 'title': 326, 'interprétation': 163, 'interpretation': 162, 'membres': 188, 'members': 186, 'force': 132, 'service': 304, 'temps': 322, 'partiel': 220, 'part': 219, 'time': 325, 'nombre': 203, 'heures': 147, 'semaine': 303, 'number': 206, 'hours': 148, 'per': 230, 'week': 345, 'moyenne': 200, 'hebdomadaire': 146, 'travail': 333, 'weekly': 346, 'average': 44, 'work': 348, 'solde': 306, 'membre': 187, 'pay': 221, 'member': 185, 'droit': 96, 'choisir': 63, 'payer': 223, 'égard': 352, 'fraction': 137, 'période': 259, 'right': 288, 'elect': 108, 'period': 231, 'accompagné': 7, 'option': 210, 'costing': 78, 'elective': 111, 'forces': 133, 'canadiennes': 53, 'fonction': 130, 'publique': 256, 'public': 255, 'choix': 64, 'relatif': 269, 'congé': 71, 'non': 204, 'payé': 226, 'election': 109, 'leave': 170, 'absence': 6, 'without': 347, 'après': 38, 'délai': 101, 'imparti': 152, 'prescribed': 246, 'disposition': 94, 'transitoire': 332, 'transitional': 331, 'provision': 250, 'calcul': 49, 'contributeur': 73, 'occupe': 207, 'plus': 241, 'poste': 244, 'determination': 89, 'multiple': 201, 'positions': 243, 'régime': 293, 'pensions': 229, 'plan': 239, 'genres': 142, 'prestations': 247, 'kinds': 169, 'benefits': 47, 'allocations': 23, 'devant': 90, 'être': 356, 'incluses': 155, 'allowances': 25, 'included': 154, 'taux': 321, 'annuel': 30, 'maximal': 181, 'maximum': 182, 'salary': 297, 'alinéa': 21, '6b': 4, 'paragraph': 217, 'modalités': 194, 'paiement': 215, 'défaut': 100, 'terms': 324, 'payment': 224, 'default': 86, 'versements': 339, 'impayés': 153, 'lorsque': 177, 'cesse': 60, 'unpaid': 336, 'instalments': 160, 'contributor': 75, 'ceases': 57, 'embarras': 113, 'pécuniaires': 258, 'financial': 129, 'hardship': 145, 'intérêts': 166, 'exigibles': 128, 'interest': 161, 'payable': 222, 'somme': 307, 'retenue': 282, 'exigible': 127, 'décès': 99, 'amount': 26, 'reservation': 279, 'death': 83, 'divisions': 95, 'ii': 150, 'clause': 67, 'paid': 214, 'globale': 143, 'lump': 178, 'sum': 314, 'annual': 29, 'rate': 262, 'recouvrement': 264, 'montants': 197, 'versés': 340, 'erreur': 120, 'recovery': 265, 'amounts': 27, 'error': 121, 'options': 211, 'elections': 110, 'annulation': 33, 'revocation': 287, 'révocation': 296, 'employé': 115, 'calculation': 50, 'employee': 114, 'paiements': 216, 'enfants': 116, 'payments': 225, 'children': 62, 'fréquentation': 138, 'plein': 240, 'école': 351, 'université': 335, 'peu': 237, 'près': 251, 'sans': 298, 'interruption': 164, 'full': 139, 'attendance': 40, 'school': 301, 'university': 334, 'substantially': 312, 'déclaration': 97, 'attestant': 41, 'inscription': 159, 'cours': 80, 'declaration': 85, 'enrolment': 117, 'restriction': 281, 'applicable': 36, 'limit': 172, 'child': 61, 'entitlement': 118, 'limites': 174, 'applicables': 37, 'survivants': 318, 'survivors': 320, 'équivalent': 354, 'actuariel': 14, 'actuarial': 13, 'equivalent': 119, 'autrement': 43, 'mensuels': 189, 'otherwise': 212, 'monthly': 198, 'preuve': 248, 'requise': 278, 'convaincre': 76, 'ministre': 192, 'selon': 302, '10': 0, 'evidence': 122, 'required': 276, 'satisfy': 299, 'minister': 191, 'personnes': 235, 'déclarées': 98, 'coupables': 79, 'actes': 12, 'criminels': 81, 'persons': 236, 'convicted': 77, 'indictable': 157, 'offences': 208, 'âge': 349, 'retirement': 283, 'age': 18, 'examen': 123, 'médical': 202, 'medical': 184, 'examination': 124, 'invalidité': 167, 'disability': 93, 'rapport': 261, 'report': 275, 'compte': 69, 'account': 9, 'intérêt': 165, 'remboursement': 270, 'contributions': 74, 'toute': 328, 'antérieure': 35, '2001': 3, 'return': 285, 'postérieure': 245, '2000': 2, 'désignation': 103, 'bénéficiaires': 48, 'designation': 88, 'beneficiaries': 46, 'valeur': 337, 'capitalisée': 54, 'capitalized': 55, 'value': 338, 'allocation': 22, 'conjoint': 72, 'survivant': 317, 'respect': 280, 'surviving': 319, 'spouse': 309, 'fournir': 136, 'compliance': 68, 'requirements': 277, 'submit': 310, 'réduction': 292, 'reduction': 266, 'indexation': 156, 'hypothèses': 149, 'actuarielles': 15, 'assumptions': 39, 'révision': 295, 'revision': 286, 'moment': 196, 'effective': 106, 'dates': 82, 'cessation': 59, 'effet': 107, 'effect': 105, 'termination': 323, 'allowance': 24, 'limite': 173, 'annuelle': 31, 'cas': 56, 'mise': 193, 'involuntary': 168, 'périodes': 260, 'âges': 350, 'prévus': 254, 'periods': 232, 'ages': 19, 'prévues': 253, 'transfert': 330, 'transfer': 329, 'admissibilité': 17, 'eligibility': 112, 'délais': 102, 'limits': 175, 'exercice': 125, 'form': 134, 'manner': 180, 'exercise': 126, 'nullité': 205, 'void': 343, 'détermination': 104, 'régimes': 294, 'fonds': 131, 'épargne': 353, 'savings': 300, 'fund': 140, 'rentes': 274, 'viagères': 341, 'différées': 92, 'immediate': 151, 'deferred': 87, 'life': 171, 'annuity': 32, 'adaptation': 16, 'paragraphe': 218, '12': 1, 'subsection': 311, 'deceased': 84, 'accords': 8, 'agreements': 20, 'vue': 344, 'antérieur': 34, 'ouvrant': 213, 'prior': 249, 'pensionable': 228, 'mode': 195, 'attestation': 42, 'certification': 58, 'renoncer': 271, 'rente': 273, 'devenant': 91, 'ancien': 28, 'sous': 308, 'surrender': 316, 'becomes': 45, 'former': 135, 'referred': 267, 'visé': 342, 'rcmp': 263, 'grc': 144, 'personal': 233, 'information': 158, 'renseignements': 272, 'personnels': 234, 'sujet': 313, 'method': 190, 'acknowledgement': 10, 'officielle': 209, 'présent': 252, 'peut': 238, 'cité': 66, 'may': 183, 'cited': 65}\n",
      "['10', '12', '2000', '2001', '6b', 'abrégé', 'absence', 'accompagné', 'accords', 'account', 'acknowledgement', 'act', 'actes', 'actuarial', 'actuariel', 'actuarielles', 'adaptation', 'admissibilité', 'age', 'ages', 'agreements', 'alinéa', 'allocation', 'allocations', 'allowance', 'allowances', 'amount', 'amounts', 'ancien', 'annual', 'annuel', 'annuelle', 'annuity', 'annulation', 'antérieur', 'antérieure', 'applicable', 'applicables', 'après', 'assumptions', 'attendance', 'attestant', 'attestation', 'autrement', 'average', 'becomes', 'beneficiaries', 'benefits', 'bénéficiaires', 'calcul', 'calculation', 'canada', 'canadian', 'canadiennes', 'capitalisée', 'capitalized', 'cas', 'ceases', 'certification', 'cessation', 'cesse', 'child', 'children', 'choisir', 'choix', 'cited', 'cité', 'clause', 'compliance', 'compte', 'conformément', 'congé', 'conjoint', 'contributeur', 'contributions', 'contributor', 'convaincre', 'convicted', 'costing', 'coupables', 'cours', 'criminels', 'dates', 'death', 'deceased', 'declaration', 'default', 'deferred', 'designation', 'determination', 'devant', 'devenant', 'différées', 'disability', 'disposition', 'divisions', 'droit', 'déclaration', 'déclarées', 'décès', 'défaut', 'délai', 'délais', 'désignation', 'détermination', 'effect', 'effective', 'effet', 'elect', 'election', 'elections', 'elective', 'eligibility', 'embarras', 'employee', 'employé', 'enfants', 'enrolment', 'entitlement', 'equivalent', 'erreur', 'error', 'evidence', 'examen', 'examination', 'exercice', 'exercise', 'exigible', 'exigibles', 'financial', 'fonction', 'fonds', 'force', 'forces', 'form', 'former', 'fournir', 'fraction', 'fréquentation', 'full', 'fund', 'gendarmerie', 'genres', 'globale', 'grc', 'hardship', 'hebdomadaire', 'heures', 'hours', 'hypothèses', 'ii', 'immediate', 'imparti', 'impayés', 'included', 'incluses', 'indexation', 'indictable', 'information', 'inscription', 'instalments', 'interest', 'interpretation', 'interprétation', 'interruption', 'intérêt', 'intérêts', 'invalidité', 'involuntary', 'kinds', 'leave', 'life', 'limit', 'limite', 'limites', 'limits', 'loi', 'lorsque', 'lump', 'made', 'manner', 'maximal', 'maximum', 'may', 'medical', 'member', 'members', 'membre', 'membres', 'mensuels', 'method', 'minister', 'ministre', 'mise', 'modalités', 'mode', 'moment', 'montants', 'monthly', 'mounted', 'moyenne', 'multiple', 'médical', 'nombre', 'non', 'nullité', 'number', 'occupe', 'offences', 'officielle', 'option', 'options', 'otherwise', 'ouvrant', 'paid', 'paiement', 'paiements', 'paragraph', 'paragraphe', 'part', 'partiel', 'pay', 'payable', 'payer', 'payment', 'payments', 'payé', 'pension', 'pensionable', 'pensions', 'per', 'period', 'periods', 'personal', 'personnels', 'personnes', 'persons', 'peu', 'peut', 'plan', 'plein', 'plus', 'police', 'positions', 'poste', 'postérieure', 'prescribed', 'prestations', 'preuve', 'prior', 'provision', 'près', 'présent', 'prévues', 'prévus', 'public', 'publique', 'pursuant', 'pécuniaires', 'période', 'périodes', 'rapport', 'rate', 'rcmp', 'recouvrement', 'recovery', 'reduction', 'referred', 'regulations', 'relatif', 'remboursement', 'renoncer', 'renseignements', 'rente', 'rentes', 'report', 'required', 'requirements', 'requise', 'reservation', 'respect', 'restriction', 'retenue', 'retirement', 'retraite', 'return', 'revision', 'revocation', 'right', 'royal', 'royale', 'règlement', 'réduction', 'régime', 'régimes', 'révision', 'révocation', 'salary', 'sans', 'satisfy', 'savings', 'school', 'selon', 'semaine', 'service', 'short', 'solde', 'somme', 'sous', 'spouse', 'submit', 'subsection', 'substantially', 'sujet', 'sum', 'superannuation', 'surrender', 'survivant', 'survivants', 'surviving', 'survivors', 'taux', 'temps', 'termination', 'terms', 'time', 'title', 'titre', 'toute', 'transfer', 'transfert', 'transitional', 'transitoire', 'travail', 'university', 'université', 'unpaid', 'valeur', 'value', 'versements', 'versés', 'viagères', 'visé', 'void', 'vue', 'week', 'weekly', 'without', 'work', 'âge', 'âges', 'école', 'égard', 'épargne', 'équivalent', 'établi', 'être']\n"
     ]
    }
   ],
   "source": [
    "print(tv5.vocabulary_)\n",
    "print(tv5.get_feature_names())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [],
   "source": [
    "Uf, sigf, Vf = la.svd(laws.todense().T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "r = 2\n",
    "V_rf = Vf[:r,:]\n",
    "U_rf = Uf[:,:r]\n",
    "\n",
    "#in document space\n",
    "plt.plot(V_rf[0, :], V_rf[1, :], 'b.')\n",
    "for i in range(4):\n",
    "    label = str(i)\n",
    "    x = V_rf[0, i]\n",
    "    y = V_rf[1, i]\n",
    "    plt.annotate(label, xy=(x, y), xytext=(-2, 2),\n",
    "        textcoords='offset points', ha='right', va='bottom');\n",
    "plt.savefig(\"./images/doc_ef_space.eps\", bbox_inches='tight');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#in term space\n",
    "limit = 100\n",
    "plt.plot(U_rf[:limit, 0], U_rf[:limit, 1], 'b.')\n",
    "for i in range(limit):\n",
    "    label = tv5.get_feature_names()[i]\n",
    "    x = U_rf[i, 0]\n",
    "    y = U_rf[i, 1]\n",
    "    plt.annotate(label, xy=(x, y), xytext=(-2, 2),\n",
    "        textcoords='offset points', ha='right', va='bottom');\n",
    "plt.savefig(\"./images/term_ef_space.eps\", bbox_inches='tight');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# cosine similarities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "children vs enfants -1.3227266504323148e-17\n",
      "with only rank 20 approximation\n",
      "children vs enfants -0.14601982735497263\n"
     ]
    }
   ],
   "source": [
    "n_concepts=20\n",
    "i = 62\n",
    "j=116\n",
    "print(f\"{tv5.get_feature_names()[i]} vs {tv5.get_feature_names()[j]}\", cos_sim(Uf[:,i], Uf[:,j]))\n",
    "print(f'with only rank {n_concepts} approximation')\n",
    "print(f\"{tv5.get_feature_names()[i]} vs {tv5.get_feature_names()[j]}\", cos_sim(Uf[:n_concepts,i], Uf[:n_concepts,j]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 221,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "employee vs employé 1.9854452283640803e-17\n",
      "with only rank 20 approximation\n",
      "employee vs employé 1.0\n"
     ]
    }
   ],
   "source": [
    "i = 114\n",
    "j=115\n",
    "print(f\"{tv5.get_feature_names()[i]} vs {tv5.get_feature_names()[j]}\", cos_sim(Uf[:,i], Uf[:,j]))\n",
    "print(f'with only rank {n_concepts} approximation')\n",
    "print(f\"{tv5.get_feature_names()[i]} vs {tv5.get_feature_names()[j]}\", cos_sim(Uf[:n_concepts,i], Uf[:n_concepts,j]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 222,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "école vs school 8.047342394507888e-19\n",
      "with only rank 20 approximation\n",
      "école vs school 0.9999932249594163\n"
     ]
    }
   ],
   "source": [
    "i = 351\n",
    "j=301\n",
    "print(f\"{tv5.get_feature_names()[i]} vs {tv5.get_feature_names()[j]}\", cos_sim(Uf[:,i], Uf[:,j]))\n",
    "print(f'with only rank {n_concepts} approximation')\n",
    "print(f\"{tv5.get_feature_names()[i]} vs {tv5.get_feature_names()[j]}\", cos_sim(Uf[:n_concepts,i], Uf[:n_concepts,j]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 245,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "hardship vs cited -6.938893903907221e-18\n",
      "with only rank 20 approximation\n",
      "hardship vs cited 0.009388349174985948\n"
     ]
    }
   ],
   "source": [
    "i = 145\n",
    "j=65\n",
    "print(f\"{tv5.get_feature_names()[i]} vs {tv5.get_feature_names()[j]}\", cos_sim(Uf[:,i], Uf[:,j]))\n",
    "print(f'with only rank {n_concepts} approximation')\n",
    "print(f\"{tv5.get_feature_names()[i]} vs {tv5.get_feature_names()[j]}\", cos_sim(Uf[:n_concepts,i], Uf[:n_concepts,j]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 247,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dates vs criminels -2.207435623180486e-16\n",
      "with only rank 20 approximation\n",
      "dates vs criminels 0.6277975676153154\n"
     ]
    }
   ],
   "source": [
    "i = 82\n",
    "j=81\n",
    "print(f\"{tv5.get_feature_names()[i]} vs {tv5.get_feature_names()[j]}\", cos_sim(Uf[:,i], Uf[:,j]))\n",
    "print(f'with only rank {n_concepts} approximation')\n",
    "print(f\"{tv5.get_feature_names()[i]} vs {tv5.get_feature_names()[j]}\", cos_sim(Uf[:n_concepts,i], Uf[:n_concepts,j]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# short example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "command = [\"What is the time\",\n",
    "         \"What is the day\",\n",
    "         \"What time is the meeting\",\n",
    "         \"Cancel the meeting\"]\n",
    "command_names = [\"s1\",\"s2\", \"s3\", \"s4\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'what': 6, 'is': 2, 'the': 4, 'time': 5, 'day': 1, 'meeting': 3, 'cancel': 0}\n",
      "['cancel', 'day', 'is', 'meeting', 'the', 'time', 'what']\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "vocab_size = 7\n",
    "t_v4 = TfidfVectorizer(max_features=vocab_size)\n",
    "\n",
    "coms = t_v4.fit_transform(command)\n",
    "coms_d=coms.todense()\n",
    "plt.imshow(coms_d)\n",
    "plt.colorbar(); plt.savefig(\"./images/coms_matrix.png\");\n",
    "print(t_v4.vocabulary_)\n",
    "print(t_v4.get_feature_names())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Vkn4UEY346cputYEnqP006fFyrfvDiPj7JtT+K+A2SQcBAlaUfhqho8+7KfybW0vJ1/iWkoNvKTn4lpKDbyk5+JaSg28pOfiWkoNvKf0/tvkrpa7v4/gAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "im = ax.imshow(coms_d.T, cmap=plt.cm.Oranges)\n",
    "ax.set_yticks(np.arange(len(t_v4.get_feature_names())))\n",
    "ax.set_xticks(np.arange(len(command)))\n",
    "ax.set_yticklabels(t_v4.get_feature_names());\n",
    "ax.set_xticklabels(command_names); plt.savefig(\"./images/coms_matrix.png\", bbox_inches='tight');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Uc, sigc, Vc = la.svd(coms_d.T)\n",
    "fig, ax = plt.subplots()\n",
    "im = ax.imshow(Uc, cmap=plt.cm.Oranges)\n",
    "\n",
    "ax.set_yticks(np.arange(len(t_v4.get_feature_names())))\n",
    "ax.set_yticklabels(t_v4.get_feature_names());\n",
    "plt.savefig(\"./images/Uc_matrix.png\", bbox_inches='tight');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "im = ax.imshow(Vc, cmap=plt.cm.Oranges)\n",
    "ax.set_xticks(np.arange(len(command_names)))\n",
    "ax.set_xticklabels(command_names);\n",
    "plt.savefig(\"./images/Vn_matrix.png\", bbox_inches='tight');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rank = 4\n",
    "sigmac = np.zeros((rank, rank))\n",
    "for i in range(rank):\n",
    "    sigmac[i][i] = sigc[i]\n",
    "fig, ax = plt.subplots()\n",
    "im = ax.imshow(sigmac, cmap=plt.cm.Oranges)\n",
    "plt.savefig(\"./images/sigmac_matrix.png\", bbox_inches='tight');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "r = 2\n",
    "V_r = Vc[:r,:]\n",
    "U_r = Uc[:,:r]\n",
    "\n",
    "#in document space\n",
    "plt.plot(V_r[0, :], V_r[1, :], 'b.')\n",
    "for i in range(4):\n",
    "    label = command[i]\n",
    "    x = V_r[0, i]\n",
    "    y = V_r[1, i]\n",
    "    plt.annotate(label, xy=(x, y), xytext=(-2, 2),\n",
    "        textcoords='offset points', ha='right', va='bottom');\n",
    "plt.savefig(\"./images/doc_c_space.eps\", bbox_inches='tight');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#in term space\n",
    "plt.plot(U_r[:, 0], U_r[:, 1], 'b.')\n",
    "for i in range(len(t_v4.get_feature_names())):\n",
    "    label = t_v4.get_feature_names()[i]\n",
    "    x = U_r[i, 0]\n",
    "    y = U_r[i, 1]\n",
    "    plt.annotate(label, xy=(x, y), xytext=(-2, 2),\n",
    "        textcoords='offset points', ha='right', va='bottom');\n",
    "plt.savefig(\"./images/term_c_space.eps\", bbox_inches='tight');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "V_r = Vc[:r,:]\n",
    "U_r = Uc[:,:r]\n",
    "c_new = [\"When is the meeting\"]\n",
    "c_pn = t_v4.transform(c_new).todense()\n",
    "V_new = np.dot(c_pn, Uc)[:,:r] #project new data in to semantic space\n",
    "C = np.concatenate([V_r, U_r.T, V_new.T], axis=1)\n",
    "plt.plot(C[0, :], C[1, :], 'b.')\n",
    "labs = command+t_v4.get_feature_names()+[\"When is the meeting\"]\n",
    "for i in range(len(labs)):\n",
    "    label = labs[i]\n",
    "    x =C[0, i]\n",
    "    y =C[1, i]\n",
    "    plt.annotate(label, xy=(x, y), xytext=(-2, 2),\n",
    "        textcoords='offset points', ha='right', va='bottom');\n",
    "plt.savefig(\"./images/both_c_space.eps\", bbox_inches='tight');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# news group example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "n_samples = 1000\n",
    "n_features = 2000\n",
    "n_concepts = 10\n",
    "# n_top_words = 20\n",
    "dataset = fetch_20newsgroups(shuffle=True, random_state=1,\n",
    "                             remove=('headers', 'footers', 'quotes'))\n",
    "data_samples = dataset.data[:n_samples]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<1000x2000 sparse matrix of type '<class 'numpy.float64'>'\n",
       "\twith 34236 stored elements in Compressed Sparse Row format>"
      ]
     },
     "execution_count": 199,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_v1 = TfidfVectorizer(max_features=n_features,\n",
    "                                   stop_words='english')\n",
    "news = t_v1.fit_transform(data_samples)\n",
    "news"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'sure': 1764, 'story': 1733, 'did': 527, 'disagree': 539, 'statement': 1718, 'media': 1108, 'pro': 1386, 'israeli': 929, 'world': 1976, 'having': 821, 'lived': 1037, 'europe': 621, 'realize': 1455, 'described': 509, 'letter': 1012, 'try': 1862, 'ignore': 873, 'degree': 504, 'think': 1812, 'reason': 1458, 'report': 1501, 'clearly': 370, 'daily': 471, 'reports': 1503, 'acts': 102, 'soldiers': 1666, 'received': 1464, 'government': 782, 'makes': 1076, 'away': 212, 'look': 1046, 'jews': 940, 'got': 779, 'power': 1359, 'yeah': 1992, 'expect': 639, 'people': 1299, 'read': 1448, 'faq': 667, 'actually': 104, 'accept': 87, 'hard': 814, 'atheism': 194, 'need': 1196, 'little': 1035, 'faith': 661, 'logic': 1043, 'runs': 1552, 'jim': 942, 'sorry': 1673, 'feelings': 682, 'oh': 1237, 'just': 952, 'end': 603, 'maybe': 1102, 'start': 1710, 'new': 1202, 'newsgroup': 1204, 'alt': 131, 'atheist': 195, 'won': 1966, 'big': 240, 'don': 559, 'forget': 723, 'iii': 875, 'points': 1335, 'like': 1021, 'know': 972, 'ask': 182, 'question': 1430, 'sort': 1674, 'arab': 162, 'countries': 447, 'want': 1930, 'continue': 429, 'tank': 1784, 'israel': 928, 'stop': 1730, 'asking': 184, 'questions': 1431, 'work': 1971, 'treatment': 1850, 'bad': 214, 'begin': 229, 'attack': 198, 'group': 796, 'stupid': 1742, 'center': 327, 'policy': 1337, 'research': 1509, 'legitimate': 1009, 'proposal': 1406, 'change': 335, 'product': 1394, 'area': 166, '1000': 6, 'suspect': 1768, 'clipper': 374, 'phones': 1311, 'came': 297, 'customer': 467, 'key': 958, 'aside': 181, 'yes': 1995, 'technology': 1792, 'eventually': 625, 'drive': 569, 'cost': 442, 'use': 1887, 'present': 1365, 'man': 1079, 'street': 1735, 'going': 772, 'purchase': 1421, 'telephone': 1793, 'especially': 617, 'guy': 802, 'probably': 1387, 'doesn': 554, 'missing': 1142, 'real': 1453, 'gov': 781, 'year': 1993, 'air': 122, 'voice': 1922, 'privacy': 1384, 'phone': 1310, 'line': 1026, 'close': 377, 'pc': 1297, 'unfortunately': 1879, 'time': 1820, 'right': 1533, 'certainly': 332, 'post': 1353, 'rules': 1549, 'does': 553, 'matter': 1099, 'll': 1040, 'enter': 609, 'good': 777, 'let': 1011, 'mail': 1069, 'edu': 590, 'league': 998, 'smith': 1660, 'old': 1242, 'wasn': 1936, 'dead': 484, 'magi': 1068, 'jesus': 938, 'appears': 151, 'day': 481, 'stay': 1722, 'normal': 1213, 'wonder': 1967, 'ok': 1240, 'record': 1469, 'shows': 1635, 'cache': 291, 'small': 1658, 'programs': 1400, '64': 69, 'lot': 1054, '40': 54, 'average': 210, '20': 26, '25': 33, 'difference': 531, 'great': 788, 'simple': 1645, 'card': 305, 'better': 238, 'fpu': 731, 'says': 1570, 'cards': 306, 'offer': 1233, 'bought': 263, 'problems': 1390, 'complete': 402, 'check': 345, 'called': 294, 'performance': 1302, 'numbers': 1222, 'cheers': 346, 'file': 689, 'mr': 1175, 'da': 470, 'cc': 322, 'gl': 763, '33': 46, 'sounds': 1676, 'mean': 1103, 'peace': 1298, 'process': 1391, 'say': 1568, 'test': 1804, 'table': 1776, '18': 17, 'months': 1161, 'prove': 1409, 'fault': 672, 'known': 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'member', 'members', 'memory', 'men', 'mention', 'mentioned', 'menu', 'message', 'method', 'methods', 'mhz', 'mice', 'michael', 'microsoft', 'middle', 'midi', 'mike', 'mil', 'miles', 'military', 'militia', 'miller', 'million', 'mind', 'minutes', 'mirrors', 'misc', 'missing', 'mission', 'missions', 'mistake', 'mit', 'mm', 'mode', 'model', 'modeling', 'models', 'modem', 'modern', 'modes', 'modified', 'module', 'money', 'monitor', 'monitors', 'month', 'months', 'moon', 'moral', 'morality', 'morning', 'mother', 'motherboard', 'motif', 'motion', 'motorcycle', 'mouse', 'moved', 'movie', 'moving', 'mr', 'ms', 'msdos', 'msg', 'multi', 'murder', 'mydisplay', 'myhint', 'named', 'names', 'nasa', 'nation', 'national', 'natural', 'naturally', 'nature', 'navy', 'near', 'nearly', 'necessarily', 'necessary', 'need', 'needed', 'needs', 'neighbors', 'net', 'network', 'new', 'news', 'newsgroup', 'newsletter', 'nff', 'nfotis', 'nhl', 'nice', 'night', 'noise', 'non', 'normal', 'north', 'northern', 'note', 'noted', 'noticed', 'nsa', 'nuclear', 'number', 'numbers', 'ny', 'object', 'objects', 'observations', 'obtain', 'obvious', 'obviously', 'occupied', 'occur', 'occurs', 'offer', 'office', 'officers', 'official', 'oh', 'ohio', 'oil', 'ok', 'okay', 'old', 'older', 'ones', 'online', 'open', 'operation', 'operations', 'opinion', 'opinions', 'opportunity', 'option', 'options', 'orbit', 'orbiter', 'order', 'orders', 'ordnance', 'org', 'organization', 'organizations', 'organized', 'origin', 'original', 'originally', 'os', 'output', 'outside', 'overall', 'owned', 'oz', 'p3d', 'package', 'packages', 'page', 'paid', 'pair', 'panel', 'paper', 'papers', 'parallel', 'parents', 'park', 'particular', 'particularly', 'parts', 'party', 'pass', 'passed', 'past', 'patch', 'patches', 'path', 'patients', 'paul', 'pay', 'pc', 'peace', 'people', 'percent', 'perfect', 'performance', 'period', 'person', 'personal', 'personally', 'persons', 'peter', 'philadelphia', 'phone', 'phones', 'physical', 'physics', 'pick', 'picture', 'piece', 'pin', 'pistol', 'pitt', 'pixel', 'place', 'places', 'plan', 'plane', 'planes', 'planetary', 'planning', 'play', 'played', 'player', 'playing', 'plays', 'plus', 'point', 'points', 'police', 'policy', 'political', 'politics', 'poor', 'pop', 'population', 'port', 'ports', 'position', 'positions', 'positive', 'possessed', 'possession', 'possibility', 'possible', 'possibly', 'post', 'posted', 'posting', 'postings', 'potential', 'pov', 'power', 'practical', 'practice', 'pray', 'pre', 'presence', 'present', 'presented', 'president', 'press', 'pressure', 'presumably', 'pretty', 'prevent', 'previous', 'price', 'prices', 'priesthood', 'primary', 'prime', 'princeton', 'principal', 'print', 'printer', 'prior', 'privacy', 'private', 'pro', 'probably', 'probe', 'problem', 'problems', 'process', 'processing', 'processor', 'product', 'production', 'products', 'professional', 'program', 'programming', 'programs', 'project', 'proof', 'proper', 'properly', 'property', 'proposal', 'proposed', 'protect', 'prove', 'provide', 'provided', 'providence', 'providers', 'provides', 'providing', 'ps', 'pub', 'public', 'puck', 'punishment', 'purchase', 'purchased', 'purpose', 'purposes', 'pursuant', 'push', 'putting', 'quadra', 'quality', 'question', 'questions', 'quick', 'quickly', 'quite', 'quote', 'race', 'radiance', 'radio', 'ram', 'ran', 'random', 'range', 'rare', 'rate', 'rates', 'ray', 'rayshade', 'read', 'reader', 'reading', 'readme', 'ready', 'real', 'reality', 'realize', 'realized', 'really', 'reason', 'reasonable', 'reasons', 'rec', 'recall', 'receive', 'received', 'recent', 'recently', 'recommend', 'recommended', 'record', 'red', 'reduce', 'refer', 'reference', 'references', 'regarding', 'regardless', 'regards', 'register', 'registered', 'regular', 'related', 'relationship', 'release', 'relevant', 'religion', 'religions', 'religious', 'remain', 'remaining', 'remember', 'remote', 'remove', 'renderer', 'rendering', 'renewal', 'repeat', 'replace', 'replaced', 'replies', 'reply', 'report', 'reported', 'reports', 'request', 'requests', 'require', 'required', 'requires', 'research', 'researchers', 'resistance', 'resolution', 'resource', 'resources', 'respect', 'respond', 'response', 'responses', 'responsible', 'rest', 'restrictions', 'result', 'results', 'return', 'revelation', 'revised', 'rich', 'rid', 'ride', 'rider', 'riding', 'rifle', 'right', 'rights', 'risk', 'road', 'robert', 'rochester', 'rocket', 'roger', 'role', 'rom', 'ron', 'room', 'rose', 'round', 'rt', 'rule', 'rules', 'run', 'running', 'runs', 'russian', 'safe', 'safety', 'said', 'sale', 'sales', 'salonica', 'san', 'santa', 'satan', 'satellite', 'saturn', 'save', 'saved', 'saw', 'say', 'saying', 'says', 'sc', 'scale', 'scheme', 'school', 'sci', 'science', 'scientific', 'scientists', 'score', 'scored', 'screen', 'scsi', 'se', 'search', 'season', 'seat', 'second', 'seconds', 'secret', 'secretary', 'section', 'secure', 'security', 'seen', 'sele_pntr', 'select', 'self', 'sell', 'selling', 'semi', 'senate', 'send', 'sense', 'sensing', 'sent', 'separate', 'serial', 'series', 'seriously', 'server', 'servers', 'service', 'services', 'session', 'set', 'sets', 'settings', 'seven', 'sex', 'sexual', 'sf', 'sgi', 'shall', 'shape', 'share', 'shareware', 'sheet', 'ship', 'shipping', 'short', 'shot', 'shouldn', 'showed', 'shown', 'shows', 'shuttle', 'siggraph', 'sign', 'signal', 'significant', 'similar', 'similarly', 'simm', 'simms', 'simple', 'simply', 'sin', 'single', 'sipp', 'site', 'sites', 'situation', 'size', 'skin', 'slave', 'slaves', 'slow', 'small', 'smart', 'smith', 'social', 'society', 'software', 'solar', 'sold', 'soldiers', 'solid', 'solution', 'solve', 'somebody', 'son', 'soon', 'sorry', 'sort', 'sound', 'sounds', 'source', 'sources', 'south', 'soviet', 'sp', 'space', 'spacecraft', 'spd', 'speak', 'speaker', 'special', 'specific', 'specifically', 'speech', 'speed', 'speeds', 'spend', 'spent', 'sphere', 'sports', 'spread', 'springfield', 'square', 'ssf', 'ssrt', 'st', 'stage', 'stand', 'standard', 'standards', 'standing', 'star', 'stars', 'start', 'started', 'starters', 'starting', 'starts', 'startup', 'state', 'stated', 'statement', 'states', 'station', 'status', 'stay', 'steal', 'steering', 'step', 'stephen', 'steve', 'stick', 'stock', 'stop', 'store', 'stories', 'story', 'straight', 'street', 'string', 'strong', 'structure', 'studies', 'study', 'stuff', 'stupid', 'style', 'subject', 'subscribe', 'subscription', 'substance', 'sufficient', 'suggest', 'suggested', 'suggestion', 'suggestions', 'sumgait', 'summary', 'summer', 'sun', 'supply', 'support', 'supported', 'supporting', 'supports', 'suppose', 'supposed', 'sure', 'surface', 'surprised', 'surrender', 'suspect', 'suspension', 'svga', 'svr3', 'svr4', 'sweden', 'switch', 'systems', 'table', 'taken', 'takes', 'taking', 'talent', 'talk', 'talking', 'talks', 'tank', 'tape', 'tar', 'tax', 'team', 'teams', 'tech', 'technical', 'technology', 'telephone', 'telescope', 'tell', 'telling', 'tells', 'temperature', 'tend', 'term', 'terms', 'territory', 'terrorist', 'test', 'testament', 'text', 'thank', 'thanks', 'theory', 'thing', 'things', 'think', 'thinking', 'thomas', 'thought', 'thousands', 'thread', 'threat', 'tie', 'time', 'times', 'titan', 'title', 'today', 'told', 'took', 'tool', 'toolkit', 'tools', 'topic', 'toronto', 'total', 'totally', 'tough', 'town', 'tracer', 'tracers', 'tracing', 'track', 'trade', 'traded', 'tradition', 'traditional', 'traffic', 'transfer', 'transmission', 'travel', 'treat', 'treated', 'treatment', 'trek', 'trial', 'trials', 'tried', 'troops', 'trouble', 'truck', 'true', 'truly', 'trust', 'truth', 'try', 'trying', 'turbo', 'turk', 'turkey', 'turkish', 'turks', 'turn', 'turned', 'tv', 'type', 'types', 'typical', 'uk', 'understand', 'understanding', 'understood', 'unfortunately', 'unit', 'united', 'units', 'university', 'unix', 'unless', 'usa', 'use', 'used', 'useful', 'usenet', 'user', 'users', 'uses', 'using', 'usual', 'usually', 'utah', 'utilities', 'vaccine', 'vaccines', 'valid', 'value', 'values', 'van', 'various', 've', 'vehicle', 'version', 'versions', 'vesa', 'vga', 'video', 'view', 'village', 'villages', 'violates', 'violation', 'virtual', 'virus', 'vision', 'visualization', 'voice', 'vol', 'volume', 'vote', 'vram', 'vs', 'wait', 'walk', 'want', 'wanted', 'wants', 'war', 'warrant', 'washington', 'wasn', 'waste', 'watched', 'water', 'way', 'ways', 'weapon', 'weapons', 'week', 'weeks', 'weight', 'welcome', 'went', 'west', 'western', 'white', 'wide', 'widgets', 'wife', 'willing', 'win', 'window', 'windows', 'wings', 'winning', 'wip', 'wires', 'wish', 'woman', 'women', 'won', 'wonder', 'wondering', 'word', 'words', 'work', 'worked', 'working', 'works', 'workspace', 'world', 'worse', 'worst', 'worth', 'worthy', 'wouldn', 'write', 'writing', 'written', 'wrong', 'wrote', 'x11', 'x11r5', 'x386', 'xfree86', 'xlib', 'yeah', 'year', 'years', 'yes', 'york', 'young', 'zip', 'zone']\n"
     ]
    }
   ],
   "source": [
    "# Use tf-idf features\n",
    "\n",
    "\n",
    "print(t_v1.vocabulary_)\n",
    "print(t_v1.get_feature_names())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "news_d=news.todense()\n",
    "plt.imshow(news_d); plt.savefig(\"./images/news_matrix.png\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Un, sign, Vn = la.svd(news_d.T)\n",
    "fig, ax = plt.subplots()\n",
    "im = ax.imshow(Un, cmap=plt.cm.Oranges)\n",
    "\n",
    "plt.savefig(\"./images/Un_matrix.png\", bbox_inches='tight');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "im = ax.imshow(Vn, cmap=plt.cm.Oranges)\n",
    "\n",
    "plt.savefig(\"./images/Vn_matrix.png\", bbox_inches='tight');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "ename": "IndexError",
     "evalue": "index 1000 is out of bounds for axis 0 with size 1000",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mIndexError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m/var/folders/dl/pczkvbw15215r_302bklrz2m0000gq/T/ipykernel_49145/2729599777.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0msigman\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mzeros\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrank\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrank\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrank\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m     \u001b[0msigman\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msign\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      5\u001b[0m \u001b[0mfig\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0max\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msubplots\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[0mim\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0max\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mimshow\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msigman\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcmap\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mOranges\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mIndexError\u001b[0m: index 1000 is out of bounds for axis 0 with size 1000"
     ]
    }
   ],
   "source": [
    "rank = n_features\n",
    "sigman = np.zeros((rank, rank))\n",
    "for i in range(rank):\n",
    "    sigman[i][i] = sign[i]\n",
    "fig, ax = plt.subplots()\n",
    "im = ax.imshow(sigman, cmap=plt.cm.Oranges)\n",
    "\n",
    "plt.savefig(\"./images/sigman_matrix.png\", bbox_inches='tight');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "r = 100\n",
    "fig, ax = plt.subplots()\n",
    "im = ax.imshow(Un[:,:r], cmap=plt.cm.Oranges)\n",
    "U_nr = Un[:,:r]\n",
    "\n",
    "plt.savefig(\"./images/U_nr_matrix.png\", bbox_inches='tight');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "im = ax.imshow(Vn[:r,:], cmap=plt.cm.Oranges)\n",
    "V_nr = Vn[:,:r]\n",
    "\n",
    "plt.savefig(\"./images/V_nr_matrix.png\", bbox_inches='tight');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPsAAAD7CAYAAACscuKmAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8rg+JYAAAACXBIWXMAAAsTAAALEwEAmpwYAAAb80lEQVR4nO3dW4yc9Znn8e/vraququ7q89lu222DMSaEg+MEcyZxkoVkJmQ1m1FmlRWaicRezO5kRqMdkV1pR3s3F9FocrE7K5QoYjfRRBmIFjZLCIzjhEEExiYmgLHBR3y2u31qu4/V3c9e/MvGgE2fquqtw/ORrOqq6qIe7H76qXrr//+9MjOcc7UvirsA51x5eLM7Vye82Z2rE97sztUJb3bn6oQ3u3N1YknNLulBSe9I2ivpsWIV5ZwrPi32c3ZJCeBd4AvAEWAb8Edm9nbxynPOFUtyCY/9DLDXzPYDSPox8DBwzWZvTMi609C9aiVk25fw1M65qzl46DDDw6d1tfuW0uzLgcNXXD8C3PHhb5L0KPAoQEcK/seGiIe+85/Qjb8PiQaUSC2hBOfclTbe8/lr3reU9+xX++3xkfcEZva4mW00s42rr1vJQ9/5LhzdiT37X7HT7y7h6Z1zC7GUZj8CrLji+gBw7GMfkW0PE31yjPyeHXDxJDY7g6/Pd670lvIyfhuwVtJq4CjwdeDfzvmoRAPc9SekbjkBY2ew156AwTtR9/ollOKcm8uiJ7uZTQP/AfgFsAv4iZntnOtxSqSIej6BBh+A8RFs29Mw/K5Pd+dKbCmTHTN7Fnh2UQ9WBKs2oVwnJNPYgV9iLStQ5/VIvtbHuWKLraskEfXchG78CkRJ2Po92PcrmJ2JqyTnalrsI1QStK6Amz8LLb3Y0C5mzx3CZqfjLs25mhJ7swOocy3a+MfQvhpe/J/wu3+E/ETcZTlXUyqj2RWFxTWZNui9Dpo6sbFhbHQIm8nHXZ5zNWFJB+iKTS3LYNO/x0ZPwfYfYskUuuOb0NgVd2nOVb3KavYoCekcTI9jybCM1qZGIZGGZMaX1jq3BBXV7Jdl2tBn/gTLj8Herdj4OXTr16BledyVOVe1KuI9+4cpkUJN3SjbAePn4MxRbHIEm5nC/KM55xalMif7JckMuuXfYFMX4OwB7NC/wJr7Uftg3JU5V3UqcrJfokQKtQ6gjuvgwhDsfQUunvCltc4tQmVP9kuUgDX3Q886mJ7A9j2PdaxF7avDohzn3JwqerJfoihB1D6IBu6AmUnY9hQMvc1Vts87566hKpr9EknQsRY2fAUactjx15k9954ftHNuHqqq2YHw0v2GL0G6BV7+AezdCrO+ys65uVRfs0thC2xjJwx+Cpq7sJGj2IUTvrTWuY9Rdc1+iVoG0G1fh+718C//C3vzKciPxV2WcxWrOo7GX4WiBEQJSDVhLT3Q0ASTI5jNQkPOl9Y69yFV2+yXNXaiDd8Ijb7rWZjJo1v/EHI9cVfmXEWp+mZXIgWJ1jDRZ/IwcQGbHof8eMiljxJxl+hcRaj6Zr+sIYdu/cPQ6CfewEbPoOs3Q+tA3JU5VxGq9gDdhymRQrke1NQNo2fgxLth84zn0jsH1NJkvySRRtdvxlZ8GsaGsHf3Qd8tqG1V3JU5F6uameyXKEqEzTNd62BiBN7eAucPz/1A52pc7U32SxRB3y3hbLESs4dfgeZl4ReB59K7OlSzP/WSiNpWEa26J+ya++1TcOJ3YLNxl+ZcLGq22T+geRmsuw8yLdiZfdjIMc+ld3WnLppdrQPohocg1wev/RjbtwVmpuIuy7myqo9mV4SiJGpohp410NgeziA7NuwT3tWN2j1AdzW5HnTzH8DYaWzn05BMo0/+QTiI51yNq6tmV5SEKImlxiCZDieUzI9hUQpSmXC/czWqPn+6061houfHsEO/gclRtO5ByPXGXZlzJVOXza5ECrLtYaJPjsLICSw/Hg7aRUn/HN7VpLps9stSGbTuwdDoZ/djx14LoZa+ecbVoLoeYYqSKNcbTig5fhbe24GNn/GNM64m1fdkvyRKooE7sM614X38wV9j7WuI2lbGXZlzRTPnZJe0QtJWSbsk7ZT0rcLtHZJekLSncFm1n19JUVh40/tJmJ6At54LL+t9wrsaMp+X8dPAX5rZemAT8KeSbgIeA7aY2VpgS+F6VZME7Wvg5gchmcFOvomdPxJScJyrcnM2u5kdN7PfFr6+AOwClgMPA08Uvu0J4KslqrGsoraVaPB+SDXCjn/Ejm4DX2XnasCCDtBJGgRuB14Fes3sOIRfCMBVEx4lPSppu6TtQ8Onl1hueUgKp4tetSF8RHfhOHbxlC+tdVVt3s0uKQc8Bfy5mY3M93Fm9riZbTSzjd1dnYupMR4ty9C6L0P7avjdk9ieX0B+Iu6qnFu0eTW7pBSh0X9kZj8t3HxSUn/h/n7gVGlKjIcUoUQDSmahpQfSuRBXPXHOJ7yrSvM5Gi/g+8AuM/vbK+56Bnik8PUjwNPFL68CNHagm/51+Ghu35awgWbiXNxVObdg8/mc/W7g3wFvSnq9cNt/Bv4G+ImkbwKHgK+VpMKYKUpCOofZNMzOhpfy+QksPxbCLT2X3lWJOZvdzF4CdI27Nxe3nArWkEPrvxwafWgnjJ9Hg/dCc3/clTk3L3W9XHYhFCVRYxc0dsD4eTi1D5u66Ln0rmr4ctmFSqTR4L3YstthbBg7ux91f8I3z7iK55N9gRQlUHM/al8DkyOw5yXs4om4y3JuTj7ZF0sR6v4Elu0EjNmj21CuH1qWh2W3zlUYn+yLJAm1DhAt3xhueOMZbHi359K7iuXNXgTK9cMN90NDDju7PyyvnZ2JuyznPsCbvRhalqPVn4XGTnjjp9ihlz2X3lUcb/YikBQO3DXkoOd6yLbBuOfSu8riB+iKqakH3fCl0Oi7fw7pJrTuS5Bpjbsy57zZi0lRAqIslk9DugmiRIi5UsJz6V3s/KevFDJtYaLnx7Cj22FqFF23GZq6467M1TFv9hJQlIRMa5joU6Nw8TRMT2CeS+9i5M1eSqlMmOjTE9i5g3Did6h/A7Qsi7syV4d8xJSQoiRq6g6nlZo4D0fexCbPY2a+ecaVnU/2coiSqH8D1nEdTF3EDr2E2lb75hlXVj7Zy0CKUMsy1LUu5NLv/iU2ctinuysrb/ayUpjoN30RohR26i1s5Kjn0ruy8GYvo0ubZzSwKZwf/s3/i518E3wdvSsDb/YYXM6lX3kbpJvDxpnRIV9a60rKD9DFpbkfNfVgF47Dzmew1j50w0PQ4P8krjT8JysmUgSJKJxTrrWvkEt/AZvNh3BLX1rrisx/ouLW2BEm+uQIduBXAGjtFyHbEW9druZ4s8dMURIakmGiA8zkYXrSc+ld0XmzV4qGXJjo05PYqZ0weQGtvCusvnOuCPxofIVQlAxH6DOtMHkBzhzG8uPY7LR/Du+Kwid7pUmk0cq7sP5xGD2Jnd2Hutb75hm3ZD7ZK4yiBMr1otaBMOH3v4qNDcddlqsBPtkrlSLUvR5r7AKbYfbodtTcD83LPJfeLYpP9goVNs8sJ+q/LSynffs57MxewDfPuMXxZq8Cau6HtfdCqgk7ewC7cMJz6d2CebNXg+ZlaNW9kG2Ht57Gjm4DX0fvFsibvQpICi/rU03QsxYyLTB2Ghs77Ztn3Lx5s1eTpm50/RdRx1rs3eex/VshPx53Va5K+NH4KhJy6RNYMg2ZHCRSIa4aeS69m9O8J7ukhKQdkn5WuN4h6QVJewqX7aUr031ApjVM+IE7sKPbsL2/gIlzcVflKtxCXsZ/C9h1xfXHgC1mthbYUrjuykBREmVaoCEH+QkYOx/W1E9P+lF6d03zanZJA8CXge9dcfPDwBOFr58AvlrUytzcUhm05gG07l+Fj+QObIXRobirchVqvpP974C/Aq7ckdFrZscBCpc9V3ugpEclbZe0fWj49FJqdR+iKIkau6CxC6YuwvG3sakLmM16cq37iDmbXdLvAafM7LXFPIGZPW5mG81sY3dX52L+E24uURL13Qaf+P2QdnPoZbhwLO6qXIWZz2S/G/iKpIPAj4HPSfohcFJSP0Dh8lTJqnQfS1ECNfehjusgPwZ7/xnzZncfMmezm9m3zWzAzAaBrwO/NLNvAM8AjxS+7RHg6ZJV6eZJqH013Ph5iFLMntqJjRzz/fAOWNqimr8BviBpD/CFwnUXI0moZTlatjF8Bv/2s9jwLvBmdyxwUY2Z/Qr4VeHr08Dm4pfklkoSZNqxlRugIYeNHINUFrIdnmlXx3y5bK1q7kOD90OuH3b/HDv8CsxMxl2Vi5Gvr6xRUgSKIJXF2pZBQyNMjGAzU55LX6f8X7zWZTvQdZtDo7/3EkjheqYt7spcmfnL+BqnKIFSjZDKgARmkJ/A8mO+tLbO+GSvFw25MNHzE9jQTpgaQys2QVN33JW5MvHJXifC5pm2EHwxNQbnjsH0hOfS1xGf7PUmkQ4TvX8Cu3gCTu9B3euhuT/uylyJ+WSvM4oSqKk7NPfkBTi8Axs/G3dZrgx8sterS7n0uT6YmSrk0i8L5433XPqa5JO9TkkRau4n6rkpJNXu2Yqdfw/Ppa9d3uwuTPTr7oFk5v1cej9oV3O82V146T5wB6Rb4O3/h538XThPvKsp3uzug7n0fetCtp3n0tccP0Dn3pfrQdkHQqPv2wKZFrRmM6RzcVfmisCb3V0mRZBMY8mGsPgmmS7k0huksr55psr5v577qExbmOj5MezYdpjJo1X3QKNnCFYzb3b3EYqSkM6FiT6Th8mLMDOFTU+GcEsPwKhK3uzu2lLZMNFnprCz++HkGyHFNtcbd2VuEfxovLumkEvfCdmOkEt/ai82Neq59FXKJ7ubWyGX3jrWwuR57PBvUPsa3zxTZXyyuzkpSqBcL2ofDLn0B17BLp6Muyy3QD7Z3QIIta3GbmgERcyeehtl2yHX55tnqoBPdjdvIZd+GVH/7RAl4J3nsdPvei59lfBmd4uibAesuB1STXDhGDY65Jl2Fc6b3S1Org+tvAflerHdP8eOboOZqbirch/Dm90tiqSwuCaZgfYBaGiCyRFs4pxvnqlQfoDOLU22A63+bGj0914KH9OtfgAyrXFX5j7EJ7tbkpBLnw2bZi5tlJn2XPpK5JPdFUdDLkz06Qns1E6YnkDLP+259BXEJ7sripBL3wrp5rDwZuQUTE9iM3mPuKoQPtldcSXSIeJqejLk0p/Zi7puhOa+uCurez7ZXVFdzqXP9YbNM8fewibP+8aZCuCT3ZVGlEBdN2LN/WGL7PEdIdjSN8/Exie7K4mQS9+HOm8IARj7XsTOH/IJHyNvdldSksI0X30nJLPY2f3YxZN+0C4G82p2SW2SnpS0W9IuSXdK6pD0gqQ9hcv2UhfrqlSuDy3/TFhlt/s57NRb4Sw0rqzmO9m/CzxnZjcCtwK7gMeALWa2FthSuO7cR4RceqGGHPTdGHLpR4cLufS+8KZc5mx2SS3AfcD3AcxsyszOAQ8DTxS+7Qngq6Up0dWMpm606l7UsgLbvxU7/BuYnoi7qroxn8m+BhgCfiBph6TvSWoCes3sOEDhsudqD5b0qKTtkrYPDZ8uWuGu+kgRSjSEpbXZ1rCJZmoUm7zgm2fKYD7NngQ2AH9vZrcDoyzgJbuZPW5mG81sY3eX5447Qi796s+i3luw47/FDv46nCveldR8mv0IcMTMXi1cf5LQ/Ccl9QMULk+VpkRXaxQlUEMTpLLhQN3UWFhxNz3p7+FLaM5mN7MTwGFJ6wo3bQbeBp4BHinc9gjwdEkqdLUrlUUr70aD92Fn94UJP+Zv9Uplvivo/iPwI0kNwH7gjwm/KH4i6ZvAIeBrpSnR1SpFSci2Y9MTcHIUTh/EutYVMu3kIZZFNq9mN7PXgY1XuWtzUatx9SlKhVz6rnUwfhYbOeK59CXgK+hc7EIufQ9qGYD8KBx6DRsbjrusmuMbYVzlUITa12DplkIu/U6U7YRcr7+kLwKf7K5iXFpHH/V+MtywZyt2dp/n0heJN7urSMp2Xs6lt5GjnktfBN7srjLletHApnAG2T3/FPbDz+bjrqqqebO7inQpl16p7Pu59BPnPZd+CfwAnats2Q40eF9o9PdegmQarboPMi1xV1Z1fLK7iqYogZIZuLSBRlGIq54a9ffwC+ST3VWHdHOY6NMTIfxiZgot3wiNXXFXVjW82V1VUJSETAs2lQgnkBw9DdNT2Ew+hFvKX6TOxZvdVZdkJkz06SnswjE4/S7qXh+iq93H8l+HrqooSqDGrnBaqamLcPIdbOqip9bOg092V52iBOpej7UsD+/jj++A5mXIzzxzTT7ZXVWSIpTrRR3Xw/QkHHgZu3DMJ/zH8GZ3Ve39XPq7IJn2XPqP4c3uqp6a+1H/7SHA8t1/woZ2gX8G/xHe7K4mXM6l711XyKUf8lz6D/EDdK52NHWjbEdo9AO/hsZ2tOresK7eebO72iFFkIiwZBoa28PL+vxYeP+eyoaFOXWsvv/vXW3KtIWJnh/Djr0GgFZsgkxbvHXFzJvd1RxFCWhoChPdZsMpo6cnQ4ptlAr31yFvdle7Ulm08q7Q6Gf3w9Qo6rs1rL6rQ3403tUsRUmUaYNMK0yNwtkjYbXd7ExdLr7xye5qX5QKE71rHTZ+FkaOoLbVUGdLa32yu5qnKIGauqF5WcilP/I6Nn4m7rLKzie7qx+KUNtqLN0KUHe59D7ZXd0I6+j7iHpuAgz2vYidOxi+rgPe7K4uKdsJA7eHj+jOH6mLXHpvdlefcr1o4DOQboW9v8ROvhHOFV/DvNldXZIU9sSnstCxAlJNMHEOGz9bs7n0foDO1bdsB1p5T2j0Qy8XFuLcDenmuCsrOm92V9cUJSBKYIkGSGXfz6VXFMIta2hprTe7cxBy6VfeXcil3wkzk2j5p8O55mqEN7tzFHLp081hos9Mwvj5msuln9f/gaS/kLRT0luS/kFSRlKHpBck7Slctpe6WOdKLplByz+NBu/FRo5gh1+G0eG4qyqKOZtd0nLgz4CNZnYzkAC+DjwGbDGztcCWwnXnqpqiREi7aewMS2tP7cHyYzWxcWa+r02SQFZSEmgEjgEPA08U7n8C+GrRq3MuLlESda2HtZ+H/Ch2fAd24UTcVS3JnM1uZkeB7wCHgOPAeTN7Hug1s+OF7zkO9Fzt8ZIelbRd0vah4dPFq9y5Egq59D2obVXIpX/vVeziiaqe8PN5Gd9OmOKrgWVAk6RvzPcJzOxxM9toZhu7uzoXX6lzMQjr6ZfB4J2QaMDO7K3aXPr5vIz/PHDAzIbMLA/8FLgLOCmpH6Bweap0ZToXHzX3hf3wiRTs3Yqd3hPirqrMfJr9ELBJUqPCPsDNwC7gGeCRwvc8AjxdmhKdi58klG6BvvUhmvriqarLpZ/zc3Yze1XSk8BvgWlgB/A4kAN+IumbhF8IXytloc7FrqkbNXaGRj/4IjR1hYy7qDHuyuZlXotqzOyvgb/+0M2ThCnvXF2QIlCEJRugsSPk0k+NYjPT0NBU8UtrfQWdcwuVaUer7gmNfuw1kNDAphBsWcGqfw2gc2WmKIFSjZBIg/SBXPpKfg/vk925xWpoDBN9ehI7uw/yY+GofWNX3JVdlU925xYp5NK3QqYF8mMwciI0foXm0vtkd26pohTqvQU612Fjp+H8IdS+BnK9cVf2AT7ZnVui93Pp+8PmmWNvYhPn4y7rI3yyO1csilD7GizbATYTcukbu6CppyJy6X2yO1ckklCul6hrXVhOu/8l7PwhKiWX3pvduRJQthNWbIBU4/u59DGvp/dmd64Ucr1o2aegoRn2bQ25djFHVHuzO1cCH8ylXxU2z4yfLeTSx7PwxpvduVJq7EQr70KtK7FDL2NHt8H0RCyl+NF450pIikLoRaIhTPcoCfmxcMiuzLn03uzOlUO6Ba24C6bHL79/17JPQbZ8ocze7M6VgaIEpHOYBDNTMDUKM1PYzFQItyxDLr03u3PllMyg5RthJo+NHIXh3aj7JmjqLvlT+wE658roci59th2mLsDpg4Vc+tmSb57xye5cHKIk6r4JaxsMIRjHX0cty0u6ecYnu3MxkCLU1I1aV4SP4g5vx0ZLG9Dsk925WAm1LMcGUxAlmT29B6VbQ7hlkTfP+GR3LkaXN8/0fjJ8Br//n0PqjRV/lZ03u3MVQunWkEufupRLP1zUpbXe7M5ViqbucLroxi7s4IvYiTfCZ/JF4s3uXIWQhKIkJBsg1wOpLExdxCZGijLh/QCdc5Um045W3Bka/fhvgUu59C1L+s/6ZHeuwoRc+mzIpUeAwcwklh9f0oT3ye5cpWpoChN9ZhI7sxfy44Vc+sWd+tyb3bkKpSgBmRYsPx5y6S8OFXLpp0GJBX8O783uXKVLNKC+20Kjjw3D+fdQ+3XhIN4C+Ht25yqcokQ4VXSuJ+TSn9iFTS48l94nu3PVQgnUfh3W2AWz0wvOpffJ7lyVCEtre4g614Zc+oO/CXvi55lL783uXBVSYxcMbIBkZt659N7szlWjph7Ufxs05ODAr7Hh3XPm0vt7dueqUHiPLkhlsY7BsHlm/OzHNrw3u3PVrLETDdwRTkBx+BWYHLnmt/rLeOeqmBShRAMogqkxmL32+3aVOuTug4VpCBgFhsv2pEvXRfXUW021QnXVWy21rjKzq0bVlrXZASRtN7ONZX3SJaimequpVqiuequp1mvxl/HO1QlvdufqRBzN/ngMz7kU1VRvNdUK1VVvNdV6VWV/z+6ci4e/jHeuTnizO1cnytbskh6U9I6kvZIeK9fzzpekFZK2StolaaekbxVu75D0gqQ9hcvynVB7DpISknZI+lnheiXX2ibpSUm7C3/Hd1ZqvZL+ovAz8Jakf5CUqdRaF6IszS4pAfx34CHgJuCPJN1UjudegGngL81sPbAJ+NNCjY8BW8xsLbClcL1SfAvYdcX1Sq71u8BzZnYjcCuh7oqrV9Jy4M+AjWZ2M5AAvk4F1rpgZlbyP8CdwC+uuP5t4NvleO4l1Pw08AXgHaC/cFs/8E7ctRVqGSD80H0O+FnhtkqttQU4QOGA8BW3V1y9wHLgMNBB2DvyM+CLlVjrQv+U62X8pb/AS44UbqtIkgaB24FXgV4zOw5QuFxY8Ffp/B3wV8CVi6ErtdY1wBDwg8Lbju9JaqIC6zWzo8B3gEPAceC8mT1PBda6UOVq9qtl5lTkZ36ScsBTwJ+b2bW3EMVI0u8Bp8zstbhrmacksAH4ezO7nbA/oiJfBhfeiz8MrAaWAU2SvhFvVcVRrmY/Aqy44voAcKxMzz1vklKERv+Rmf20cPNJSf2F+/uB0p5Ee37uBr4i6SDwY+Bzkn5IZdYK4d//iJm9Wrj+JKH5K7HezwMHzGzIzPLAT4G7qMxaF6Rczb4NWCtptaQGwgGPZ8r03POikAbwfWCXmf3tFXc9AzxS+PoRwnv5WJnZt81swMwGCX+XvzSzb1CBtQKY2QngsKR1hZs2A29TmfUeAjZJaiz8TGwmHEysxFoXpowHPr4EvAvsA/5L3AcrrlLfPYS3Fm8Arxf+fAnoJBwI21O47Ii71g/V/QDvH6Cr2FqB24Dthb/f/wO0V2q9wH8DdgNvAf8bSFdqrQv548tlnasTvoLOuTrhze5cnfBmd65OeLM7Vye82Z2rE97sztUJb3bn6sT/B3JpOowoThRYAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sigma_nr = np.zeros((r, r))\n",
    "for i in range(r):\n",
    "    sigma_nr[i][i] = sign[i]\n",
    "fig, ax = plt.subplots()\n",
    "im = ax.imshow(sigma_nr, cmap=plt.cm.Oranges)\n",
    "\n",
    "plt.savefig(\"./images/sigma_nr_matrix.png\", bbox_inches='tight');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "r = 2\n",
    "V_r = Vn[:r,:]\n",
    "U_r = Un[:,:r]\n",
    "\n",
    "#in document space\n",
    "plt.plot(V_r[0, :], V_r[1, :], 'b.')\n",
    "\n",
    "plt.savefig(\"./images/doc_n_space.eps\", bbox_inches='tight');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#in term space\n",
    "plt.plot(U_r[:, 0], U_r[:, 1], 'b.')\n",
    "for i in range(len(t_v1.get_feature_names())):\n",
    "    label = t_v1.get_feature_names()[i]\n",
    "    x = U_r[i, 0]\n",
    "    y = U_r[i, 1]\n",
    "    plt.annotate(label, xy=(x, y), xytext=(-2, 2),\n",
    "        textcoords='offset points', ha='right', va='bottom');\n",
    "plt.savefig(\"./images/term_n_space.eps\", bbox_inches='tight');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 242,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "like vs love 0.372261664435121\n"
     ]
    }
   ],
   "source": [
    "i = 1021\n",
    "j = 1056\n",
    "print(f\"{t_v1.get_feature_names()[i]} vs {t_v1.get_feature_names()[j]}\", cos_sim(Un[:n_concepts,i], Un[:n_concepts,j]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}