Nick Wilson 03-31-14 In-Class Activity (Netflixish).ipynb

{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import matplotlib.pyplot as plt\n",
      "import numpy as np\n",
      "import sklearn.cluster"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 134
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Load the data."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = np.loadtxt('/tmp/Netflixishdata.txt', dtype=int)\n",
      "print zip(data.shape, ('customers', 'movies'))\n",
      "print np.prod(data.size), 'ratings'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[(200, 'customers'), (100, 'movies')]\n",
        "20000 ratings\n"
       ]
      }
     ],
     "prompt_number": 131
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Plotting a histogram of all 20,000 ratings shows that there are about 4,000 instances of each rating. That's odd."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.hist(data.flatten(), bins=np.linspace(0.5, 5.5, 6))\n",
      "plt.title(\"Histogram of all ratings\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 125,
       "text": [
        "<matplotlib.text.Text at 0xd30508c>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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m1hw4cCDknMYY7d+/3z3OqcrLy92f8/LylJeX155LAQAAAM6qurpa1dXVHd6v\nXaH6VC0tLWptbdXAgQPl8/lUVVWl7OxsSdKxY8dUU1Ojxx57TJKUnZ2tqKgoVVVVaeLEiZKkvXv3\navv27crNzZUk5eTkqLGxUX6/311X7ff7dfToUbfmVCeHagAAAKAznHqzdt68ee3ar81Q/b3vfU9F\nRUVKT0/X3//+d1VUVGjjxo1at26dpI8fl7dgwQINGTJEGRkZmj9/vhISEjRp0iRJUmJiombMmKG5\nc+fK6/Wqb9++mjNnjrKyspSfny9JyszM1MiRI1VaWqply5bJGKPS0lKNGjVKGRkZHX0tAAAAgE9V\nm6E6GAxq8uTJCgQCSkxMVFZWltatW6eCggJJ0ty5c9XU1KRZs2apvr5e1157raqqqhQXF+ceY/Hi\nxYqMjNSECRPU1NSk/Px8rVq1KmTddUVFhcrKynTjjTdKkkaPHq0lS5Z09vUCAAAAnc4xYfiJQcdx\nLtgPOo4fP00vvpgnaVo3jwQdd1zSRZIuzPfmZ4Mj5i+cMX/hi7kLbxduLpPanzs79JxqAAAAAKcj\nVAMAAACWCNUAAACAJUI1AAAAYIlQDQAAAFgiVAMAAACWCNUAAACAJUI1AAAAYIlQDQAAAFgiVAMA\nAACWCNUAAACAJUI1AAAAYIlQDQAAAFgiVAMAAACWCNUAAACAJUI1AAAAYIlQDQAAAFgiVAMAAACW\nCNUAAACAJUI1AAAAYIlQDQAAAFgiVAMAAACWCNUAAACAJUI1AAAAYIlQDQAAAFgiVAMAAACWCNUA\nAACAJUI1AAAAYIlQDQAAAFgiVAMAAACWCNUAAACAJUI1AAAAYIlQDQAAAFgiVAMAAACWCNUAAACA\nJUI1AAAAYIlQDQAAAFgiVAMAAACWCNUAAACAJUI1AAAAYIlQDQAAAFgiVAMAAACWCNUAAACAJUI1\nAAAAYIlQDQAAAFgiVAMAAACWCNUAAACApTZD9SOPPKKrr75aiYmJ8nq9Ki4u1jvvvBNSM23aNHk8\nnpCWm5sbUtPc3KyysjKlpKQoPj5eo0eP1r59+0Jq6uvrVVJSoqSkJCUlJWnKlClqaGjohMsEAAAA\nuk6boXrjxo361re+Jb/fr9///veKjIxUfn6+6uvr3RrHcVRQUKBAIOC21157LeQ4s2fP1tq1a7V6\n9Wpt2rRJR44cUVFRkVpbW92aSZMmacuWLaqsrNS6dev05ptvqqSkpBMvFwAAAOh8kW0VrFu3LuT3\n5557ToncafSZAAAfY0lEQVSJiaqtrdVXv/pVSZIxRtHR0fJ6vWc8RkNDg5599lmtWLFCN9xwg3uc\n/v37a/369SosLNS7776ryspKbd68Wddcc40kaenSpbr++uu1c+dOXXbZZVYXCgAAAHSVDq+pPnLk\niFpbW9WnTx+3z3Ec1dTUKDU1VYMHD9bMmTN14MABd3tdXZ1OnDihwsJCty89PV2ZmZny+/2SJL/f\nr/j4eOXk5Lg1ubm5iouLc2sAAACAnqjNO9Wnuvvuu3XllVeGhN+RI0dq3LhxGjhwoHbv3q37779f\nI0aMUF1dnaKjoxUIBBQREaHk5OSQY6WmpioQCEiSAoGAUlJSQrY7jiOv1+vWAAAAAD1Rh0L1nDlz\nVFtbq5qaGjmO4/ZPmDDB/fnyyy9Xdna2+vfvr1dffVVjx4496/GMMecxZAAAAKBnaXeovueee7Rm\nzRpt2LBBAwYMOGdtWlqa0tPTtWvXLkmSz+dTS0uLDh06FHK3OhgMatiwYW7NyUtGpI9D9/79++Xz\n+U47R3l5uftzXl6e8vLy2nspAAAAwBlVV1erurq64zuadrjrrrtMWlqa2b59e3vKzf79+010dLR5\n7rnnjDHGHD582ERHR5uKigq3Zs+ePcbj8ZiqqipjjDHbtm0zjuOY2tpat2bz5s3GcRyzc+fOkOO3\nc9hhady4qUZabiRDC7vWbCT1gHHQzr8xf+HdmL/wbcxdeDd1d3zqUu29vjbvVM+aNUurVq3Sb37z\nGyUmJrrrmxMSEhQXF6ejR4/qwQcf1Pjx4+Xz+fT+++/r3nvvVWpqqrv0IzExUTNmzNDcuXPl9XrV\nt29fzZkzR1lZWcrPz5ckZWZmauTIkSotLdWyZctkjFFpaalGjRqljIyMjv+1AAAAAHxa2krdjuMY\nj8djHMcJafPmzTPGGNPU1GRuvPFG4/V6TXR0tOnfv7+ZPn262bt3b8hxmpubTVlZmUlOTjaxsbGm\nuLj4tJr6+nozefJk07t3b9O7d29TUlJiGhoazvsvhnDEnepwbtypDv/G/IV3Y/7CtzF34d3U3fGp\nS7X3+pz/Kw4rjuMoDIfdLuPHT9OLL+ZJmtbNI0HHHZd0kaQL87352eCI+QtnzF/4Yu7C24Wby6T2\n584OP6caAAAAQChCNQAAAGCJUA0AAABYIlQDAAAAlgjVAAAAgCVCNQAAAGCJUA0AAABYIlQDAAAA\nlgjVAAAAgCVCNQAAAGCJUA0AAABYIlQDAAAAlgjVAAAAgCVCNQAAAGCJUA0AAABYIlQDAAAAlgjV\nAAAAgCVCNQAAAGCJUA0AAABYIlQDAAAAlgjVAAAAgCVCNQAAAGCJUA0AAABYIlQDAAAAlgjVAAAA\ngCVCNQAAAGCJUA0AAABYIlQDAAAAlgjVAAAAgCVCNQAAAGCJUA0AAABYIlQDAAAAlgjVAAAAgCVC\nNQAAAGCJUA0AAABYIlQDAAAAlgjVAAAAgCVCNQAAAGCJUA0AAABYIlQDAAAAlgjVAAAAgCVCNQAA\nAGCJUA0AAABYIlQDAAAAlgjVAAAAgCVCNQAAAGCJUA0AAABYajNUP/LII7r66quVmJgor9er4uJi\nvfPOO6fVlZeX65JLLlFsbKyGDx+ubdu2hWxvbm5WWVmZUlJSFB8fr9GjR2vfvn0hNfX19SopKVFS\nUpKSkpI0ZcoUNTQ0WF4iAAAA0LXaDNUbN27Ut771Lfn9fv3+979XZGSk8vPzVV9f79YsXLhQixYt\n0pIlS/TGG2/I6/WqoKBAjY2Nbs3s2bO1du1arV69Wps2bdKRI0dUVFSk1tZWt2bSpEnasmWLKisr\ntW7dOr355psqKSnp5EsGAAAAOpnpoMbGRhMREWFeeeUVY4wxra2txufzmQULFrg1TU1NJiEhwSxd\nutQYY8zhw4dNdHS0qaiocGv27NljPB6PqaysNMYYs23bNuM4jqmtrXVrampqjOM4ZseOHSFjOI9h\nh41x46YaabmRDC3sWrOR1APGQTv/xvyFd2P+wrcxd+Hd1N3xqUu19/o6vKb6yJEjam1tVZ8+fSRJ\nu3fvVjAYVGFhoVvTq1cvDR06VLW1tZKkuro6nThxIqQmPT1dmZmZ8vv9kiS/36/4+Hjl5OS4Nbm5\nuYqLi3NrAAAAgJ6ow6H67rvv1pVXXumG30AgIElKTU0NqfN6ve62QCCgiIgIJScnh9SkpqaG1KSk\npIRsdxwn5DgAAABATxTZkeI5c+aotrZWNTU1chynzfq2aj6+o35+ysvL3Z/z8vKUl5d33scCAAAA\nJKm6ulrV1dUd3q/dofqee+7RmjVrtGHDBg0YMMDt9/l8kqRgMKj09HS3PxgMutt8Pp9aWlp06NCh\nkLvVwWBQw4YNc2sOHDgQck5jjPbv3+8e52Qnh2oAAACgM5x6s3bevHnt2q9dyz/uvvtu/fKXv9Tv\nf/97XXbZZSHbBg4cKJ/Pp6qqKrfv2LFjqqmpUW5uriQpOztbUVFRITV79+7V9u3b3ZqcnBw1NjaG\nrJ/2+/06evSoWwMAAAD0RG3eqZ41a5ZWrVql3/zmN0pMTHTXNyckJCguLk6O42j27NlasGCBhgwZ\nooyMDM2fP18JCQmaNGmSJCkxMVEzZszQ3Llz5fV61bdvX82ZM0dZWVnKz8+XJGVmZmrkyJEqLS3V\nsmXLZIxRaWmpRo0apYyMjC58CQAAAABLbT0exHEc4/F4jOM4IW3evHkhdeXl5SYtLc306tXL5OXl\nmXfeeSdke3NzsykrKzPJyckmNjbWFBcXm71794bU1NfXm8mTJ5vevXub3r17m5KSEtPQ0HDejzYJ\nRzxSL5wbj9QL/8b8hXdj/sK3MXfh3dTd8alLtff6nP8rDiuO4ygMh90u48dP04sv5kma1s0jQccd\nl3SRpAvzvfnZ4Ij5C2fMX/hi7sLbhZvLpPbnzg4/Ug8AAABAKEI1AAAAYIlQDQAAAFgiVAMAAACW\nCNUAAACAJUI1AAAAYIlQDQAAAFgiVAMAAACWCNUAAACAJUI1AAAAYIlQDQAAAFgiVAMAAACWCNUA\nAACAJUI1AAAAYIlQDQAAAFgiVAMAAACWCNUAAACAJUI1AAAAYIlQDQAAAFgiVAMAAACWCNUAAACA\nJUI1AAAAYIlQDQAAAFgiVAMAAACWCNUAAACAJUI1AAAAYIlQDQAAAFgiVAMAAACWCNUAAACAJUI1\nAAAAYIlQDQAAAFgiVAMAAACWCNUAAACAJUI1AAAAYIlQDQAAAFgiVAMAAACWCNUAAACAJUI1AAAA\nYIlQDQAAAFgiVAMAAACWCNUAAACAJUI1AAAAYIlQDQAAAFgiVAMAAACWCNUAAACAJUI1AAAAYKnN\nUP2HP/xBxcXFSk9Pl8fj0cqVK0O2T5s2TR6PJ6Tl5uaG1DQ3N6usrEwpKSmKj4/X6NGjtW/fvpCa\n+vp6lZSUKCkpSUlJSZoyZYoaGho64RIBAACArtVmqD569KiuuOIKPf7444qJiZHjOCHbHcdRQUGB\nAoGA21577bWQmtmzZ2vt2rVavXq1Nm3apCNHjqioqEitra1uzaRJk7RlyxZVVlZq3bp1evPNN1VS\nUtJJlwkAAAB0nci2Cm666SbddNNNkj6+K30qY4yio6Pl9XrPuH9DQ4OeffZZrVixQjfccIMk6bnn\nnlP//v21fv16FRYW6t1331VlZaU2b96sa665RpK0dOlSXX/99dq5c6cuu+yy870+AAAAoMtZr6l2\nHEc1NTVKTU3V4MGDNXPmTB04cMDdXldXpxMnTqiwsNDtS09PV2Zmpvx+vyTJ7/crPj5eOTk5bk1u\nbq7i4uLcGgAAAKCnavNOdVtGjhypcePGaeDAgdq9e7fuv/9+jRgxQnV1dYqOjlYgEFBERISSk5ND\n9ktNTVUgEJAkBQIBpaSkhGx3HEder9etAQAAAHoq61A9YcIE9+fLL79c2dnZ6t+/v1599VWNHTv2\nrPsZY2xPDQAAAPQI1qH6VGlpaUpPT9euXbskST6fTy0tLTp06FDI3epgMKhhw4a5NScvGZE+Dt37\n9++Xz+c743nKy8vdn/Py8pSXl9e5FwIAAIDPnOrqalVXV3d4v04P1QcOHNC+ffuUlpYmScrOzlZU\nVJSqqqo0ceJESdLevXu1fft299F7OTk5amxslN/vd9dV+/1+HT169LTH833i5FANAAAAdIZTb9bO\nmzevXfu1GaqPHj2qv/zlL5Kk1tZWffDBB9qyZYuSk5PVt29fPfjggxo/frx8Pp/ef/993XvvvUpN\nTXWXfiQmJmrGjBmaO3euvF6v+vbtqzlz5igrK0v5+fmSpMzMTI0cOVKlpaVatmyZjDEqLS3VqFGj\nlJGR0dHXAgAAAPh0mTZs2LDBOI5jHMcxHo/H/Xn69OmmqanJ3Hjjjcbr9Zro6GjTv39/M336dLN3\n796QYzQ3N5uysjKTnJxsYmNjTXFx8Wk19fX1ZvLkyaZ3796md+/epqSkxDQ0NJxxTO0YdtgaN26q\nkZYbydDCrjUbST1gHLTzb8xfeDfmL3wbcxfeTd0dn7pUe6/P+b/isOI4jsJw2O0yfvw0vfhinqRp\n3TwSdNxxSRdJujDfm58Njpi/cMb8hS/mLrxduLlMan/utH5ONQAAAPBZR6gGAAAALBGqAQAAAEuE\nagAAAMASoRoAAACwRKgGAAAALBGqAQAAAEuEagAAAMASoRoAAACwRKgGAAAALBGqAQAAAEuEagAA\nAMASoRoAAACwRKgGAAAALBGqAQAAAEuEagAAAMASoRoAAACwRKgGAAAALBGqAQAAAEuEagAAAMAS\noRoAAACwRKgGAAAALBGqAQAAAEuEagAAAMASoRoAAACwRKgGAAAALBGqAQAAAEuEagAAAMASoRoA\nAACwRKgGAAAALBGqAQAAAEuEagAAAMASoRoAAACwRKgGAAAALBGqAQAAAEuEagAAAMASoRoAAACw\nRKgGAAAALBGqAQAAAEuEagAAAMASoRoAAACwRKgGAAAALBGqAQAAAEuEagAAAMASoRoAAACwRKgG\nAAAALBGqAQAAAEtthuo//OEPKi4uVnp6ujwej1auXHlaTXl5uS655BLFxsZq+PDh2rZtW8j25uZm\nlZWVKSUlRfHx8Ro9erT27dsXUlNfX6+SkhIlJSUpKSlJU6ZMUUNDg+XlAQAAAF2vzVB99OhRXXHF\nFXr88ccVExMjx3FCti9cuFCLFi3SkiVL9MYbb8jr9aqgoECNjY1uzezZs7V27VqtXr1amzZt0pEj\nR1RUVKTW1la3ZtKkSdqyZYsqKyu1bt06vfnmmyopKenESwUAAAC6iOmA+Ph4s3LlSvf31tZW4/P5\nzIIFC9y+pqYmk5CQYJYuXWqMMebw4cMmOjraVFRUuDV79uwxHo/HVFZWGmOM2bZtm3Ecx9TW1ro1\nNTU1xnEcs2PHjtPG0cFhh5Vx46YaabmRDC3sWrOR1APGQTv/xvyFd2P+wrcxd+Hd1N3xqUu19/qs\n1lTv3r1bwWBQhYWFbl+vXr00dOhQ1dbWSpLq6up04sSJkJr09HRlZmbK7/dLkvx+v+Lj45WTk+PW\n5ObmKi4uzq0BAAAAeiqrUB0IBCRJqampIf1er9fdFggEFBERoeTk5JCa1NTUkJqUlJSQ7Y7jhBwH\nAAAA6Km67Okfp669PtXHd9MBAACA8Bdps7PP55MkBYNBpaenu/3BYNDd5vP51NLSokOHDoXcrQ4G\ngxo2bJhbc+DAgZBjG2O0f/9+9zinKi8vd3/Oy8tTXl6ezaUAAAAAqq6uVnV1dYf3swrVAwcOlM/n\nU1VVlbKzsyVJx44dU01NjR577DFJUnZ2tqKiolRVVaWJEydKkvbu3avt27crNzdXkpSTk6PGxkb5\n/X53XbXf79fRo0fdmlOdHKoBAACAznDqzdp58+a1a782Q/XRo0f1l7/8RZLU2tqqDz74QFu2bFFy\ncrL69eun2bNna8GCBRoyZIgyMjI0f/58JSQkaNKkSZKkxMREzZgxQ3PnzpXX61Xfvn01Z84cZWVl\nKT8/X5KUmZmpkSNHqrS0VMuWLZMxRqWlpRo1apQyMjI6+loAAAAAn662Hg+yYcMG4ziOcRzHeDwe\n9+fp06e7NeXl5SYtLc306tXL5OXlmXfeeSfkGM3NzaasrMwkJyeb2NhYU1xcbPbu3RtSU19fbyZP\nnmx69+5tevfubUpKSkxDQ4PVo03CEY/UC+fGI/XCvzF/4d2Yv/BtzF14N3V3fOpS7b0+5/+Kw4rj\nOArDYbfL+PHT9OKLeZKmdfNI0HHHJV0k6cJ8b342OGL+whnzF76Yu/B24eYyqf25s8ue/gEAAAB8\nVhCqAQAAAEuEagAAAMASoRoAAACwRKgGAAAALBGqAQAAAEuEagAAAMASoRoAAACwRKgGAAAALBGq\nAQAAAEuEagAAAMASoRoAAACwRKgGAAAALBGqAQAAAEuEagAAAMASoRoAAACwRKgGAAAALBGqAQAA\nAEuEagAAAMASoRoAAACwRKgGAAAALBGqAQAAAEuEagAAAMASoRoAAACwRKgGAAAALBGqAQAAAEuE\nagAAAMASoRoAAACwRKgGAAAALBGqAQAAAEuEagAAAMASoRoAAACwRKgGAAAALBGqAQAAAEuEagAA\nAMASoRoAAACwRKgGAAAALBGqAQAAAEuEagAAAMASoRoAAACwRKgGAAAALBGqAQAAAEuEagAAAMAS\noRoAAACwRKgGAAAALBGqAQAAAEudEqrLy8vl8XhC2sUXX3xazSWXXKLY2FgNHz5c27ZtC9ne3Nys\nsrIypaSkKD4+XqNHj9a+ffs6Y3gAAABAl+q0O9VDhgxRIBBw25///Gd328KFC7Vo0SItWbJEb7zx\nhrxerwoKCtTY2OjWzJ49W2vXrtXq1au1adMmHTlyREVFRWptbe2sIQIAAABdIrKzDhQRESGv13ta\nvzFGixcv1r333quxY8dKklauXCmv16uKigrNnDlTDQ0NevbZZ7VixQrdcMMNkqTnnntO/fv31/r1\n61VYWNhZwwQAAAA6XafdqX7vvfd0ySWX6NJLL9XEiRO1e/duSdLu3bsVDAZDgnGvXr00dOhQ1dbW\nSpLq6up04sSJkJr09HRlZma6NQAAAEBP1Smh+tprr9XKlStVWVmpp556SoFAQLm5ufroo48UCAQk\nSampqSH7eL1ed1sgEFBERISSk5NDalJTUxUMBjtjiAAAAECX6ZTlHyNHjnR//td//Vfl5ORo4MCB\nWrlypa655pqz7uc4TmecHgAAAOhWnbam+mSxsbG6/PLLtWvXLo0ZM0aSFAwGlZ6e7tYEg0H5fD5J\nks/nU0tLiw4dOhRytzoQCGjo0KFnPEd5ebn7c15envLy8jr/QgAAAPCZUl1drerq6g7v1yWh+tix\nY3r33Xc1YsQIDRw4UD6fT1VVVcrOzna319TU6LHHHpMkZWdnKyoqSlVVVZo4caIkae/evdq+fbty\nc3PPeI6TQzUAAADQGU69WTtv3rx27dcpofrb3/62iouL1a9fP+3fv18/+MEP1NTUpKlTp0r6+HF5\nCxYs0JAhQ5SRkaH58+crISFBkyZNkiQlJiZqxowZmjt3rrxer/r27as5c+YoKytL+fn5nTFEAAAA\noMt0Sqjet2+fJk6cqIMHDyolJUU5OTn64x//qH79+kmS5s6dq6amJs2aNUv19fW69tprVVVVpbi4\nOPcYixcvVmRkpCZMmKCmpibl5+dr1apVrLsGAABAj+cYY0x3D6KjHMdRGA67XcaPn6YXX8yTNK2b\nR4KOOy7pIkkX5nvzs8ER8xfOmL/wxdyFtws3l0ntz52d9pxqAAAA4LOKUA0AAABYIlQDAAAAlgjV\nAAAAgCVCNQAAAGCJUA0AAABYIlQDAAAAlgjVAAAAgCVCNQAAAGCJUA0AAABYIlQDAAAAlgjVAAAA\ngCVCNQAAAGCJUA0AAABYIlQDAAAAlgjVAAAAgCVCNQAAAGCJUA0AAABYIlQDAAAAlgjVAAAAgCVC\nNQAAAGCJUA0AAABYIlQDAAAAlgjVAAAAgCVCNQAAAGCJUA0AAABYIlQDAAAAlgjVAAAAgCVCNQAA\nAGCJUA0AAABYIlQDAAAAlgjVAAAAgCVCNQAAAGCJUA0AAABYIlQDAAAAlgjVAAAAgCVCNQAAAGCJ\nUA0AAABYIlQDAAAAlgjVAAAAgCVCNQAAAGCJUA0AAABYIlQDAAAAlgjVAAAAgCVCNQAAAGCJUA0A\nAABYIlQDAAAAlnpcqP7pT3+qgQMHKiYmRldddZVqamq6e0gAAADAOfWoUP3LX/5Ss2fP1v33368t\nW7YoNzdXN910k/bs2dPdQwMAAADOqkeF6kWLFmn69OmaMWOGBg8erJ/85CdKS0vTz372s+4eGjpV\ndXcPAOetursHACvV3T0AnLfq7h4ArFR39wDwKegxofr48eN68803VVhYGNJfWFio2trabhoVukZ1\ndw8A5626uwcAK9XdPQCct+ruHgCsVHf3APAp6DGh+uDBg2ppaVFqampIv9frVSAQ6KZRAQAAAG2L\n7O4BIFRkpEcxMYsVFfVidw+lyxw7tkO9etV19zC6QKuOHOnuMQAAgO7QY0L15z73OUVERCgYDIb0\nB4NBpaWlhfQNGjRIjuN8msP71DU1be3uIXSp48f/0t1D6EIX9ntTmtfdA+hizF94u5Dnj7kLbxf2\n/F3IuWzQoEHtqusxoTo6OlrZ2dmqqqrSuHHj3P7XX39dX//610Nqd+3a9WkPDwCA/9fe/YU01cdx\nHP9sZf4pOYiwYDoyCR0tXaO18ggVURAUo8BML8q6SAKTMelC6maRueiu7EgyIgYRZQR20SgDh04y\niHBmoSUs6sYR/bMYebOd5+IhqedBd3QP/HZ8Pi84MA784A2Cfvl5dn5ERPPKmqEaANra2nD06FG4\nXC7Isozr168jHo/j1KlTotOIiIiIiOaVVUN1fX09Pn/+jI6ODkxPT6OqqgqhUAgWi0V0GhERERHR\nvAyqqqqiI4iIiIiI9CxrXqmnFY8x16ehoSG43W6UlpbCaDQiGAyKTiKN/H4/tm7dCkmSYDKZ4Ha7\n8fr1a9FZpJGiKLDb7ZAkCZIkQZZlhEIh0Vm0BH6/H0ajEa2traJTSAOfzwej0fjHZTabRWeRRtPT\n02hqaoLJZEJ+fj5sNhuGhoYWXKOroZrHmOtXIpFAdXU1rly5gvz8/GX9LeHlZnBwEKdPn8bIyAgG\nBgawcuVK7NmzB1+/fhWdRhpYLBZcvnwZo6OjePHiBXbv3o2DBw9ibGx5v2FouXn27BkCgQCqq6v5\n+1NHrFYr4vH43DU+Pi46iTT49u0bamtrYTAYEAqFMDk5iWvXrsFkMi24TlePf2zbtg2bN29GT0/P\n3L2KigrU1dWhs7NTYBktRmFhIRRFwbFjx0Sn0BIkEglIkoQHDx5g//79onNoCYqLi3Hp0iWcPHlS\ndAppMDMzgy1btuDGjRvw+XyoqqrC1atXRWdRGj6fD/fv3+cgrUNnz55FJBJBJBJZ1Drd7FTzGHOi\n7PD9+3ekUikUFRWJTqFFSiaTuHPnDmZnZ7Fjxw7ROaRRc3MzDh8+jJ07d0JH+2AEIBaLoaSkBOXl\n5WhsbMS7d+9EJ5EGfX19cLlcOHLkCNauXQuHwwFFUdKu081QzWPMibKDx+OBw+FATU2N6BTSaHx8\nHGvWrEFeXh6am5vR29uLyspK0VmkQSAQQCwWQ0dHB4DlfcDGcrN9+3YEg0E8fvwYgUAA8Xgcsizj\ny5cvotMojVgshu7ubmzYsAH9/f3weDxob29PO1hn1Sv1iCi7tbW14enTpxgeHuYfdx2xWq14+fIl\nZmZmcO/ePTQ0NCAcDsPpdIpOowW8efMG586dw/DwMFasWAEAUFWVu9U6sW/fvrnPmzZtQk1NDdav\nX49gMAiv1yuwjNJJpVJwuVy4ePEiAMBut2NqagqKoqClpWXedboZqhdzjDkR/fe8Xi96e3sRDodR\nVlYmOocWIScnB+Xl5QAAh8OB58+fQ1EU3Lx5U3AZLWRkZASfPn2CzWabu5dMJhGJRNDT04NEIoGc\nnByBhbQYBQUFsNlsPBVaB8xmMzZu3PjHPavVig8fPiy4TjePf/x+jPnvnjx5AlmWBVUR/T94PB7c\nvXsXAwMDqKioEJ1DGUomk0ilUqIzKI1Dhw7h1atXGBsbw9jYGKLRKJxOJxobGxGNRjlQ68zs7Cwm\nJia4EagDtbW1mJyc/OPe27dv024o6WanGuAx5nqWSCQwNTUF4O9/q7x//x7RaBTFxcU8MTPLtbS0\n4NatW+jr64MkSXPfYSgsLMTq1asF11E67e3tOHDgAEpLS/Hjxw/cvn0bg4ODePTokeg0SuPXu8V/\nV1BQgKKion/tolH2OXPmDNxuNywWCz5+/IgLFy7g58+faGpqEp1GaXi9XsiyjM7OTtTX12N0dBRd\nXV3w+/0LL1R1pru7Wy0rK1Nzc3NVp9OpRiIR0UmkQTgcVg0Gg2owGFSj0Tj3+cSJE6LTKI1//sx+\nXefPnxedRhocP35cXbdunZqbm6uaTCZ17969an9/v+gsWqJdu3apra2tojNIg4aGBtVsNqurVq1S\nS0pK1Lq6OnViYkJ0Fmn08OFD1W63q3l5eWplZaXa1dWVdo2u3lNNRERERJSNdPNMNRERERFRtuJQ\nTURERESUIQ7VREREREQZ4lBNRERERJQhDtVERERERBniUE1ERERElCEO1UREREREGeJQTURERESU\nIQ7VREREREQZ+gvBjBASxJaEfAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xd28972c>"
       ]
      }
     ],
     "prompt_number": 125
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Looking even closer shows that there's actually one rating of 0!"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i in xrange(6):\n",
      "    print sum(sum(data == i)), \"movies have a rating of\", i"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1 movies have a rating of 0\n",
        "4000 movies have a rating of 1\n",
        "4000 movies have a rating of 2\n",
        "4000 movies have a rating of 3\n",
        "4000 movies have a rating of 4\n",
        "3999 movies have a rating of 5\n"
       ]
      }
     ],
     "prompt_number": 132
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now I average over columns (movies) and rows (customers) to show the distributions of average movie ratings and customer ratings."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, (ax1, ax2) = plt.subplots(1, 2)\n",
      "ax1.hist(np.mean(data, axis=0), bins=25)\n",
      "ax1.set_title(\"Average Movie Ratings\")\n",
      "ax2.hist(np.mean(data, axis=1), bins=25)\n",
      "ax2.set_title(\"Average Customer Ratings\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 133,
       "text": [
        "<matplotlib.text.Text at 0xd44808c>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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lS5cWeO3Yn3/+WcaYUvPIvZB8aXiUplpLW72lqdbSVm9pqtUYU+rDYnh4uFq0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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xd3a0eac>"
       ]
      }
     ],
     "prompt_number": 133
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Finally, I use K-means to cluster the movies into a varying number of clusters. Inertia, an overall measure of how close the data points are to their centroids (lower is a better fit), is reported. The inertia can always be decreased by using more clusters (e.g., setting k equal to the number of data points can provide a perfect fit), but the plot below shows that the inertia begins to level off above 4 clusters which suggests there are 4 main types of movies."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "k_range = range(1, 15)\n",
      "inertias = [sklearn.cluster.KMeans(k=k).fit(data.T).inertia_ for k in k_range]\n",
      "plt.plot(k_range, inertias)\n",
      "plt.xlabel('Number of Clusters (k)')\n",
      "plt.ylabel('Inertia')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 139,
       "text": [
        "<matplotlib.text.Text at 0xd95c18c>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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WkpNNVwMAAAIR4zdAA7VoIf3+99Kzz5quBAAA4OzRqfcAnfrAUFAgJSVJ27dL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\n4W+z2XxPx9XX1/Pdd98RGRmJl5cXrq6uNvudOnW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       "text": [
        "<matplotlib.figure.Figure at 0xd7567ac>"
       ]
      }
     ],
     "prompt_number": 139
    }
   ],
   "metadata": {}
  }
 ]
}