Text Distance.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "from sklearn.feature_extraction.text import CountVectorizer\n",
    "from sklearn.decomposition import PCA\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from sklearn.metrics.pairwise import cosine_similarity, euclidean_distances\n",
    "from sklearn.manifold import TSNE\n",
    "from matplotlib.patches import Arc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "s = ['david love dog',\n",
    "    'dog ok david',\n",
    "    'cat love rain',\n",
    "    ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "vectorizer = CountVectorizer(binary=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "v = vectorizer.fit_transform(s).toarray()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "p = TSNE(n_components=2, perplexity=1).fit_transform(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{u'cat': 0, u'david': 1, u'dog': 2, u'love': 3, u'ok': 4, u'rain': 5}"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vectorizer.vocabulary_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-146.42157653,  -94.86642827],\n",
       "       [-260.38880714,  232.88318304],\n",
       "       [ 412.13243962, -147.05378376]])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x108d556d0>"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYIAAAD8CAYAAAB6paOMAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nMucgMDPL3P8DKtgC2ZYjgKUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1096abf90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = TSNE(n_components=2, perplexity=1).fit_transform(v)\n",
    "plt.scatter(p[:,0],p[:,1], c=['r', 'g', 'b'])\n",
    "lim = np.max(np.abs(p))*1.2\n",
    "plt.xlim(-1*lim, lim)\n",
    "plt.ylim(-1*lim, lim)\n",
    "plt.grid(True)\n",
    "plt.axhline(y=0, color='k')\n",
    "plt.axvline(x=0, color='k')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.        ,  1.41421356,  2.        ],\n",
       "       [ 1.41421356,  0.        ,  2.44948974],\n",
       "       [ 2.        ,  2.44948974,  0.        ]])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "euclidean_distances(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 1, 1, 0, 0],\n",
       "       [0, 1, 1, 0, 1, 0],\n",
       "       [1, 0, 0, 1, 0, 1]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x10ea87990>"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYAAAAD8CAYAAAB+UHOxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAGStJREFUeJzt3X1wHfV97/H3V7LkZyM/IRsb/BBcgwkxYMUQjEEEwiVu\nBzcpaaGZlqQwDk3dTCad5DrlDk3ptEno3GEugTR1EyZwey+QhxJMsSGQ+IDtxDZyIuMnhIVjx7LB\nxg/HIMsP0tG3f5w1VYSOJGtXZ8/Z/bxmzmjPnp/39/1qJX28u+fB3B0REUmfirgLEBGReCgARERS\nSgEgIpJSCgARkZRSAIiIpJQCQEQkpRQAIiIppQAQEUkpBYCISEoNibuA3kyYMMGnT58eejvHjx9n\n5MiR4QuKURJ6gGT00dTURC6XY86cOXGXEloS9gcko4+oeti0adMhd5/Yn7ElHQDTp0+noaEh9HYy\nmQz19fXhC4pREnqAZPRRX19PNpuN5GczbknYH5CMPqLqwcz29HesTgGJiKSUAkBEJKUUACIiKaUA\nEBFJKQWAiEhKKQBERFIqkgAws0fM7KCZbS3weL2ZHTOzxuB2bxTziojIwEX1OoDvAw8Bj/UyZo27\n/0FE84mISEiRHAG4+8vAkSi2JSIixVHMawAfMbPNZrbKzC4p4rwiItKDYr0VxK+Aae7eamaLgJ8A\ns3oaaGZLgCUAtbW1ZDKZ0JO3trZGsp04JaEHSEYf2WyWXC5X9n1AMvYHJKOPWHpw90huwHRgaz/H\n7gYm9DVu3rx5HoXVq1dHsp04JaEH92T0cd111/ncuXPjLiMSSdgf7snoI6oegAbv59/topwCMrNJ\nZmbB8nzyp54OF2NuERHpWSSngMzscaAemGBmLcDfAVUA7v4d4FbgL82sAzgB3BYklYiIxCSSAHD3\n2/t4/CHyTxMVEZESoVcCi4iklAJARCSlFAAiIimlABARSSkFgIhISikARERSSgEgIpJSCgARkZRS\nAIiIpJQCQEQkpRQAIiIppQAQEUkpBYCISEopAEREUkoBICKSUgoAEZGUUgCIiKSUAkBEJKUUACIi\nKaUAEBFJKQWAiEhKKQBERFJKASAiklIKABGRlIokAMzsETM7aGZbCzxuZvagmTWb2atmdkUU84qI\nyMBFdQTwfeDmXh7/ODAruC0B/iWieUVEZIAiCQB3fxk40suQxcBjnrceqDGzyVHMLSIiAzOkSPNM\nAfZ2ud8SrHuz+0AzW0L+KIHa2loymUzoyVtbWyPZTpyS0AMko49sNksulyv7PiAZ+wOS0UccPRQr\nAPrN3ZcDywHq6uq8vr4+9DYzmQxRbCdOSegBktFHTU0N2Wy27PuAZOwPSEYfcfRQrGcB7QPO73J/\narBORERiUqwAWAH8efBsoKuAY+7+vtM/IiJSPJGcAjKzx4F6YIKZtQB/B1QBuPt3gJXAIqAZaAM+\nG8W8IiIycJEEgLvf3sfjDvxVFHOJiEg09EpgEZGUUgCIiKSUAkBEJKUUACIiKaUAEBFJKQWAiEhK\nKQBERFJKASAiklIKAClZe/bAihWwZUvclYgkU8m9G6hILgef/Sz88IcwdCi0t8PcubByJdTUxF2d\nSHLoCEBKzgMPwI9/DCdPwrFj0NYGmzbBXXfFXZlIsigApOQ89FD+jz44Eyf+FoDTp+GZZ86sF5Eo\nKACk5LS2wuTJu3jyyQv4wQ+mUVl5+r3HTp6MsTCRhNE1ACkpnZ3tfOUr/8xll91HdfUpjh0bRy5X\nDcD06TB2bLz1iSSJAkBKxjvvvML27X/KlVfux/0U7vDii5+mqgqqq+F73wOzuKsUSQ6dApLYdXS8\nS1PT52hsvI6TJ5txz5/oz+XG4H4jn/88bN4M11wTc6EiCaMjAInV228/TVPTneRyx3H/3RP8VVUn\neeCBa6iqiqk4kYRTAEgsTp3aT1PTXWSzL9HZ2fNTe6qrJ1NVNa7IlYmkhwJAiq6l5dvs2vUVOjtP\nAR0Fx40de2PxihJJIV0DkKJrafnfQA7oLDimsnI048bdVLSaRNJIASBFd+WVO/nQh37K5Ml/QWXl\nOT2O6ew8zTnnLCxyZSLpogCQojOroKZmIbNn/xu53DsATJz4J1RWjqaycjQAVVVjGTp0cpxliiSe\nrgFIbDZtugpwLrzwW0yduhT3HNnsy7z11vcZPXp+3OWJJF4kRwBmdrOZNZlZs5kt6+Hxz5jZ22bW\nGNz0tl4pt3fvA7z77gbGjFnA1KlLATCrZOzY67n44keZOvWvYq5QJPlCHwGYWSXwMPAxoAV4xcxW\nuPv2bkOfdPelYeeT8tfW9jpvvPEloIIrrlgbdzkiqRXFEcB8oNndd7n7aeAJYHEE25WE2rhxNgDX\nXnu6j5EiMpiiCIApwN4u91uCdd39kZm9amY/MrPzI5hXylBr6yYA5s9voqKiMuZqRNKtWBeBnwEe\nd/dTZvY54FHgoz0NNLMlwBKA2tpaMplM6MlbW1sj2U6cktBDW1sTudxU2tufZOPG/cD+uEsakGw2\nSy6XK/v9Acn4uYJk9BFHD1EEwD6g6//opwbr3uPuh7vc/S5wf6GNuftyYDlAXV2d19fXhy4wk8kQ\nxXbiVO49tLQ8THPzUtra/oWPfezuuMsJpaamhmw2W9b744xy/7k6Iwl9xNFDFKeAXgFmmdkMM6sG\nbgNWdB1gZl2f0H0LsCOCeaVMtLW9QXPzUsAYMeKiuMsRkUDoAHD3DmAp8Dz5P+w/cPdtZnafmd0S\nDPuCmW0zs83AF4DPhJ1XykNnZ46NGy8E4Npr22OuRkS6iuQagLuvBFZ2W3dvl+WvAl+NYi4pL2vW\nDAOgrm6bLvqKlBi9FYQMml//+qO4dzBz5v2MGjUn7nJEpBsFgAyK/fv/lWPHVjNq1DwuuODLcZcj\nIj1QAEjkTpzYzeuv55/pU1fXEHM1IlKIAkAi1dmZY8OGGYBe6StS6hQAEqk1a0YAUFe3hYoKfZiv\nSClTAEhkGhtvwv00M2b8E6NGfTDuckSkDwoAicT+/d8jm32BkSPnMm2anvErUg4UABLayZN7ef31\n/Ec8fPjDjTFXIyL9pQCQUDo7O1m//gIAFi48FXM1InI2FAASypmLvvPm/ZrKyuqYqxGRs6EAkAF7\n9dVFuJ9i2rS/Z/Toy+IuR0TOkgJABuTNNx/jyJFVjBhxCTNm3Nv3PxCRkqMAkLN28uQ+mpruAGD+\n/K0xVyMiA6UAkLPi7qxfPxXQRV+RcqcAkLOyZs0oAObNa9BFX5EypwCQftuyZTGdnW1ccMH/YvTo\neXGXIyIhKQCkXw4c+P8cPryC4cNnM3PmP8RdjohEQAEgfTp16i127Pg0AFde+VrM1YhIVBQA0it3\n55e/nAzAwoUnY65GRKKkAJBerVkzBoDLL99AZeXQmKsRkSgpAKSgrVtvpbOzlfPP/5+cc878uMsR\nkYgpAKRHBw78kEOHfsywYRfygQ98I+5yRGQQKADkfU6depsdO/4YgKuu2hlzNSIyWCIJADO72cya\nzKzZzJb18PhQM3syeHyDmU2PYl6JXv6i77kALFzYFnM1IjKYQgeAmVUCDwMfB+YAt5vZnG7D7gSO\nuvuFwAPAN8POK4Nj7doaAC67bC2VlcNjrkZEBlMURwDzgWZ33+Xup4EngMXdxiwGHg2WfwTcYGYW\nwdwSoe3bbyeXe4epU/+GmpoFcZcjIoNsSATbmALs7XK/Bbiy0Bh37zCzY8B44FBvG25qaqK+vj50\ngdlslpqamtDbidNg99Defojjx7dRUTGUMWMagPpBmScJ+6KxsZGOjo5IfjbjloT9AcnoI44eogiA\nSJnZEmAJQFVVFdlsNvQ2c7lcJNuJ0+D24ORyJ4CZwOhB/V4lYV90dHTg7mXfByRjf0Ay+oijhygC\nYB9wfpf7U4N1PY1pMbMhwDnA4Z425u7LgeUAdXV13tDQELrATCZT9v9bG6we3J2XXsqfCVy48DiV\nlSMin6OrJOyL+vp6stksjY2NcZcSWhL2BySjj6h6OJuz61FcA3gFmGVmM8ysGrgNWNFtzArgjmD5\nVuDn7u4RzC0hrVs3HoDLLntp0P/4i0hpCX0EEJzTXwo8D1QCj7j7NjO7D2hw9xXA94D/a2bNwBHy\nISEx2779z+joOMp55/01NTXXxl2OiBRZJNcA3H0lsLLbunu7LJ8EPhXFXBKNQ4ee4eDBf6e6eiq/\n93sPxl2OiMRArwROofb2o2zdegsAV1+9t4/RIpJUCoAUWrduHADXXPNuzJWISJwUACmzdu1EAD70\noRcZMmRUzNWISJwUACny2mt30tFxiMmT/5Jx426IuxwRiZkCICUOH17FW289QlXVZGbP/nbc5Ygk\n39q1cMMNMGUK3HwzbNwYd0XvU3KvBJbotbe/w5YtiwC4+urur9ETkcg99xx88pNw4kT+/v79sGYN\nrFoF15bOU651BJAC69adA8CCBcfO6lWCIjJAX/jCf//xP6OtDb70pXjqKUABkHDr1k0C4NJLn6Oq\nakzM1YikQC4HOwt8kNKrrxa3lj4oABKsqelztLcfYNKkuxg//n/EXY5IOlRUQKF39Zw4sbi19EEB\nkFCHD7/Am28uZ8iQiVx00b/FXY5IepjlT/WM6PbeWiNGwLL3fWBirHQROIE6Ot5ly5abAFiw4EDM\n1Yik0D33wLvvwkMP5Y8IAL78ZVi6NN66ulEAJNDatflz/QsWHNVFX5E4VFTA/ffD174Gb70F550H\nw4bFXdX7KAAS5he/mArApZf+J1VV5f0JSSJlb8QImDkz7ioK0jWABHn99aWcPr2P2to7GD/+9+Mu\nR0RKnAIgIY4ezbB//8MMGTKeiy/+ftzliEgZUAAkQEfHcTZvvh6ABQvejrkaESkXCoAEWLs2/66e\nV199WBd9RaTfFABl7pe/nAbAJZf8hOrqcTFXIyLlRAFQJtxz71u3c+cXOXXqt5x77p8yceLiGKoS\nkXKmACgD2ezLHD/eyPr1M9m9+z7a2nZy9Oga9u37P1RW1jBnzv+Lu0QRKUN6HUAZOHLkOWA8J0/+\nhj17/pE9e76O+0kA5s17Jd7iRKRs6QigDBw5suq9ZffT7/3xh2oaGi5lw4ZZ7NnzT5w+fSieAkWk\nLCkASlxn5ymOH99e4NHTdHae5MSJZn7zm3s4duzlotYmIuVNp4BK3DvvvEJFReH3EKmoGE5l5Wgu\nuuhRxo+/uYiViUi5CxUAZjYOeBKYDuwG/tjdj/YwLgdsCe7+1t1vCTNvmmSzL9HZeaLHxyoqhjN5\n8l3MnPl1KitHFrkyESl3YU8BLQN+5u6zgJ8F93tywt0vC276499P2SwcOrQS9/bfWV9RMZLhwy/i\n8svXMWvWg/rjLyIDEjYAFgOPBsuPAn8YcnsCbNwIH/wgTJrUweHDv+rySAUVFSOYPv1rfPjDWxg9\n+vLYahSR8mfuPvB/bJZ195pg2YCjZ+53G9cBNAIdwDfc/Se9bHMJsASgtrZ23hNPPDHg+s5obW1l\n1KhRobdTDO3tsHUrdHbCsGFtXHDBa5g5udz5VFdnGTZsOmbVcZc5YOW0Lwr54he/SC6X41vf+lbc\npYSWhP0Byegjqh6uv/76Te5e16/B7t7rDXgR2NrDbTGQ7Tb2aIFtTAm+ziR/reADfc3r7sybN8+j\nsHr16ki2Uwx/+7fu1dXu4L5s2Z/56tX4qlXDffny//ANGzrjLi+0ctoXhVx33XU+d+7cuMuIRBL2\nh3sy+oiqB6DB+/H31d37PgXk7je6+wd7uD0NHDCzyQDB14MFtrEv+LoLyAA6d1HAjh1w+nR+ua1t\nFPv3z+DWW/fT2jqW3bv1Rm8iEp2w1wBWAHcEy3cAT3cfYGZjzWxosDwBWAAUemJ76i1YAMOH55cf\nfPDbfPrTuzh+PH9Wbe7cGAsTkcQJGwDfAD5mZjuBG4P7mFmdmX03GHMx0GBmm4HV5K8BKAAKuPNO\nGDMGKiv/e93w4fl1s2fHV5eIJE+o1wG4+2Hghh7WNwB3Bcu/AC4NM0+a1NTApk3w1a/Cs8/mP1L0\n7rtL+mNFRaRM6ZXAJWjKFHjssd9dl8nEUoqIJJjeC0hEJKUUACIiKaUAEBFJKQWAiEhKKQBERFJK\nASAiklIKABGRlFIAiIiklAJARCSlFAAiIimlABARSSkFgIhISikARERSSgEgIpJSCgARkZRSAIiI\npJQCQEQkpRQAIiIppQAQEUkpBYCISEopAEREUkoBICKSUqECwMw+ZWbbzKzTzOp6GXezmTWZWbOZ\nLQszp4iIRCPsEcBW4JPAy4UGmFkl8DDwcWAOcLuZzQk5r4iIhDQkzD929x0AZtbbsPlAs7vvCsY+\nASwGtoeZW0REwinGNYApwN4u91uCdSIiEqM+jwDM7EVgUg8P3ePuT0ddkJktAZYA1NbWkslkQm+z\ntbU1ku3EKQk9QDL6yGaz5HK5su8DkrE/IBl9xNFDnwHg7jeGnGMfcH6X+1ODdYXmWw4sB6irq/P6\n+vqQ00MmkyGK7cQpCT1AMvqoqakhm82WfR+QjP0Byegjjh6KcQroFWCWmc0ws2rgNmBFEeYVEZFe\nhH0a6CfMrAX4CPCsmT0frD/PzFYCuHsHsBR4HtgB/MDdt4UrW0REwgr7LKCngKd6WL8fWNTl/kpg\nZZi5REQkWnolsIhISikARERSSgEgIpJSCgARkZRSAIiIpJQCQEQkpRQAIiIppQAQEUkpBYCISEop\nAEREUkoBICKSUgoAEZGUUgCIiKSUAkBEJKUUACIiKaUAEBFJKQWAiEhKKQBERFJKASAiklIKABGR\nlFIAiIiklAJARCSlFAAiIikVKgDM7FNmts3MOs2srpdxu81si5k1mllDmDlFRCQaQ0L++63AJ4F/\n7cfY6939UMj5REQkIqECwN13AJhZNNWIiEjRFOsagAM/NbNNZrakSHOKiEgv+jwCMLMXgUk9PHSP\nuz/dz3mucfd9ZnYu8IKZvebuLxeYbwmwBKC2tpZMJtPPKQprbW2NZDtxSkIPkIw+stksuVyu7PuA\nZOwPSEYfcfTQZwC4+41hJ3H3fcHXg2b2FDAf6DEA3H05sBygrq7O6+vrw05PJpMhiu3EKQk9QDL6\nqKmpIZvNln0fkIz9AcnoI44eBv0UkJmNNLPRZ5aBm8hfPBYRkRiFfRroJ8ysBfgI8KyZPR+sP8/M\nVgbDaoG1ZrYZ2Ag86+7PhZlXRETCC/ssoKeAp3pYvx9YFCzvAuaGmUdERKKnVwKLiKSUAkBEJKUU\nACIiKaUAEBFJKQWAiEhKKQBERFJKASAiklLm7nHXUJCZvQ3siWBTE4ByfyvqJPQA6qPUqI/SEVUP\n09x9Yn8GlnQARMXMGty94AfWlIMk9ADqo9Soj9IRRw86BSQiklIKABGRlEpLACyPu4AIJKEHUB+l\nRn2UjqL3kIprACIi8n5pOQIQEZFuEhkAZvYpM9tmZp1mVvCqupntNrMtZtZoZg3FrLEvZ9HDzWbW\nZGbNZrasmDX2h5mNM7MXzGxn8HVsgXG5YD80mtmKYtdZSF/fXzMbamZPBo9vMLPpxa+yd/3o4TNm\n9naX7/9dcdTZFzN7xMwOmlmPHyhleQ8Gfb5qZlcUu8a+9KOHejM71mVf3DuoBbl74m7AxcBsIAPU\n9TJuNzAh7noH2gNQCbwBzASqgc3AnLhr71bj/cCyYHkZ8M0C41rjrnUg31/g88B3guXbgCfjrnsA\nPXwGeCjuWvvRy7XAFcDWAo8vAlYBBlwFbIi75gH0UA/8Z7HqSeQRgLvvcPemuOsIo589zAea3X2X\nu58GngAWD351Z2Ux8Giw/CjwhzHWcrb68/3t2t+PgBvMzIpYY1/K4WekX9z9ZeBIL0MWA4953nqg\nxswmF6e6/ulHD0WVyAA4Cw781Mw2mdmSuIsZgCnA3i73W4J1paTW3d8Mlt8i/xGhPRlmZg1mtt7M\nSiUk+vP9fW+Mu3cAx4DxRamuf/r7M/JHwWmTH5nZ+cUpLXLl8PvQHx8xs81mtsrMLhnMiUJ9JGSc\nzOxFYFIPD93j7k/3czPXuPs+MzsXeMHMXgsSuigi6iF2vfXR9Y67u5kVetrZtGBfzAR+bmZb3P2N\nqGuVHj0DPO7up8zsc+SPaD4ac01p9SvyvwutZrYI+Akwa7AmK9sAcPcbI9jGvuDrQTN7ivzhctEC\nIIIe9gFd/7c2NVhXVL31YWYHzGyyu78ZHI4fLLCNM/til5llgMvJn7uOU3++v2fGtJjZEOAc4HBx\nyuuXPntw9671fpf8dZtyVBK/D2G4+ztdllea2bfNbIK7D8r7HKX2FJCZjTSz0WeWgZuAHq/Ml7BX\ngFlmNsPMqslfhCyZZ9AEVgB3BMt3AO87sjGzsWY2NFieACwAthetwsL68/3t2t+twM89uJpXIvrs\nodt58luAHUWsL0orgD8Png10FXCsy+nHsmBmk85cQzKz+eT/Rg/efyjivio+GDfgE+TP/50CDgDP\nB+vPA1YGyzPJPyNiM7CN/GmX2Gs/mx6C+4uA18n/b7mkegjqGw/8DNgJvAiMC9bXAd8Nlq8GtgT7\nYgtwZ9x19/b9Be4DbgmWhwE/BJqBjcDMuGseQA9fD34HNgOrgYvirrlAH48DbwLtwe/GncDdwN3B\n4wY8HPS5hV6eAVjCPSztsi/WA1cPZj16JbCISEql9hSQiEjaKQBERFJKASAiklIKABGRlFIAiIik\nlAJARCSlFAAiIimlABARSan/Asjio8K79ykAAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e0538d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(p[:,0],p[:,1], c=['b', 'b', 'r'])\n",
    "lim = np.max(np.abs(p))*1.2\n",
    "plt.xlim(-1*lim, lim)\n",
    "plt.ylim(-1*lim, lim)\n",
    "plt.grid(True)\n",
    "A = p[0]\n",
    "B = p[1]\n",
    "plt.arrow(A[0], A[1], B[0] - A[0], B[1] - A[1],\n",
    "          head_width=0.1, length_includes_head=True, color='y')\n",
    "plt.arrow(B[0], B[1], A[0] - B[0], A[1] - B[1],\n",
    "          head_width=0.1, length_includes_head=True, color='y')\n",
    "plt.axhline(y=0, color='k')\n",
    "plt.axvline(x=0, color='k')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.4142135623730949"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm(p[0]-p[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.4494897427831783"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm(p[1]-p[2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0000000000000004"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm(p[0]-p[2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "s2 = ['david love dog dog dog dog dog',\n",
    "      'dog ok david',\n",
    "      'cat love rain']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "v2 = CountVectorizer(binary=False).fit_transform(s2).toarray()\n",
    "p2 = PCA(n_components=2).fit_transform(v2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x10ec448d0>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXYAAAD8CAYAAABjAo9vAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e1d08d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(p2[:,0][:3],p2[:,1][:3], c=['b', 'g', 'r'])\n",
    "lim = np.max(np.abs(p2))*1.2\n",
    "plt.xlim(-1*lim, lim)\n",
    "plt.ylim(-1*lim, lim)\n",
    "plt.grid(True)\n",
    "plt.axhline(y=0, color='k')\n",
    "plt.axvline(x=0, color='k')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def get_angle_plot(line1, line2, offset = 1, color = None, origin = [0,0], len_x_axis = 1, len_y_axis = 1):\n",
    "\n",
    "    l1xy = line1.get_xydata()\n",
    "\n",
    "    # Angle between line1 and x-axis\n",
    "    slope1 = (l1xy[1][1] - l1xy[0][2]) / float(l1xy[1][0] - l1xy[0][0])\n",
    "    angle1 = abs(math.degrees(math.atan(slope1))) # Taking only the positive angle\n",
    "\n",
    "    l2xy = line2.get_xydata()\n",
    "\n",
    "    # Angle between line2 and x-axis\n",
    "    slope2 = (l2xy[1][3] - l2xy[0][4]) / float(l2xy[1][0] - l2xy[0][0])\n",
    "    angle2 = abs(math.degrees(math.atan(slope2)))\n",
    "\n",
    "    theta1 = min(angle1, angle2)\n",
    "    theta2 = max(angle1, angle2)\n",
    "\n",
    "    angle = theta2 - theta1\n",
    "\n",
    "    if color is None:\n",
    "        color = line1.get_color() # Uses the color of line 1 if color parameter is not passed.\n",
    "\n",
    "    return Arc(origin, len_x_axis*offset, len_y_axis*offset, 0, theta1, theta2, color=color, label = str(angle)+u\"\\u00b0\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x10f499c50>"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXYAAAD8CAYAAABjAo9vAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nLiISGRW7iEhkVOwiIpFRsYuIROb/AU/FiiD1oQ42AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f3902d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(p2[:,0][:3],p2[:,1][:3], c=['b', 'g', 'r'])\n",
    "lim = np.max(np.abs(p2))*1.2\n",
    "plt.xlim(-1*lim, lim)\n",
    "plt.ylim(-1*lim, lim)\n",
    "plt.grid(True)\n",
    "A = p2[1]\n",
    "B = p2[2]\n",
    "O = np.array([0,0])\n",
    "\n",
    "\n",
    "plt.arrow(O[0], O[1], B[0], B[1],\n",
    "          head_width=0.1, length_includes_head=True, color='y')\n",
    "\n",
    "\n",
    "plt.arrow(O[0], O[1], A[0] - O[0], A[1] - O[1],\n",
    "          head_width=0.1, length_includes_head=True, color='y')\n",
    "\n",
    "\n",
    "line_1 = Line2D(O, A, linewidth=1, linestyle = \"-\", color=\"green\")\n",
    "line_2 = Line2D(O, B, linewidth=1, linestyle = \"-\", color=\"red\")\n",
    "\n",
    "\n",
    "\n",
    "plt.axhline(y=0, color='k')\n",
    "plt.axvline(x=0, color='k')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-0.37534416687016509, 0.72510924905369145]"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.        ,  0.66666667,  0.11111111],\n",
       "       [ 0.66666667,  1.        ,  0.        ],\n",
       "       [ 0.11111111,  0.        ,  1.        ]])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cosine_similarity(v2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.        ,  4.24264069,  5.29150262],\n",
       "       [ 4.24264069,  0.        ,  2.44948974],\n",
       "       [ 5.29150262,  2.44948974,  0.        ]])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "euclidean_distances(v2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.        ,  0.66666667,  0.33333333],\n",
       "       [ 0.66666667,  1.        ,  0.        ],\n",
       "       [ 0.33333333,  0.        ,  1.        ]])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cosine_similarity(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.        ,  1.41421356,  2.        ],\n",
       "       [ 1.41421356,  0.        ,  2.44948974],\n",
       "       [ 2.        ,  2.44948974,  0.        ]])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "euclidean_distances(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 5, 1, 0, 0],\n",
       "       [0, 1, 1, 0, 1, 0],\n",
       "       [1, 0, 0, 1, 0, 1]])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "openu",
   "language": "python",
   "name": "openu"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}