nearest-neighbor-search/1_nearest-neighbors-locality-sensitive-hashing-implementation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Locality Sensitive Hashing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Locality Sensitive Hashing (LSH) provides for a fast, efficient approximate nearest neighbor search. The algorithm scales well with respect to the number of data points as well as dimensions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import necessary packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import graphlab\n",
    "from scipy.sparse import csr_matrix\n",
    "from sklearn.metrics.pairwise import pairwise_distances\n",
    "import time\n",
    "from copy import copy\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "'''Check GraphLab Create version'''\n",
    "from distutils.version import StrictVersion\n",
    "assert (StrictVersion(graphlab.version) >= StrictVersion('1.8.5')), 'GraphLab Create must be version 1.8.5 or later.'\n",
    "\n",
    "'''compute norm of a sparse vector'''\n",
    "def norm(x):\n",
    "    sum_sq=x.dot(x.T)\n",
    "    norm=np.sqrt(sum_sq)\n",
    "    return(norm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "## Load in the Wikipedia dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "This non-commercial license of GraphLab Create for academic use is assigned to agrawal.pr@husky.neu.edu and will expire on March 12, 2018.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[INFO] graphlab.cython.cy_server: GraphLab Create v2.1 started. Logging: C:\\Users\\agraw\\AppData\\Local\\Temp\\graphlab_server_1513699195.log.0\n"
     ]
    }
   ],
   "source": [
    "wiki = graphlab.SFrame('people_wiki.gl/')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us assign a unique ID to each document."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\"><table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">id</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">URI</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">name</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">text</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Digby_Morrell&gt; ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Digby Morrell</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">digby morrell born 10<br>october 1979 is a former ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Alfred_J._Lewy&gt; ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Alfred J. Lewy</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">alfred j lewy aka sandy<br>lewy graduated from ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Harpdog_Brown&gt; ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Harpdog Brown</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">harpdog brown is a singer<br>and harmonica player who ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Franz_Rottensteiner&gt; ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Franz Rottensteiner</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">franz rottensteiner born<br>in waidmannsfeld lower ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/G-Enka&gt; ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">G-Enka</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">henry krvits born 30<br>december 1974 in tallinn ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Sam_Henderson&gt; ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Sam Henderson</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">sam henderson born<br>october 18 1969 is an ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">6</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Aaron_LaCrate&gt; ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Aaron LaCrate</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">aaron lacrate is an<br>american music producer ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">7</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Trevor_Ferguson&gt; ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Trevor Ferguson</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">trevor ferguson aka john<br>farrow born 11 november ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">8</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Grant_Nelson&gt; ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Grant Nelson</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">grant nelson born 27<br>april 1971 in london  ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">9</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Cathy_Caruth&gt; ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Cathy Caruth</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">cathy caruth born 1955 is<br>frank h t rhodes ...</td>\n",
       "    </tr>\n",
       "</table>\n",
       "[59071 rows x 4 columns]<br/>Note: Only the head of the SFrame is printed.<br/>You can use print_rows(num_rows=m, num_columns=n) to print more rows and columns.\n",
       "</div>"
      ],
      "text/plain": [
       "Columns:\n",
       "\tid\tint\n",
       "\tURI\tstr\n",
       "\tname\tstr\n",
       "\ttext\tstr\n",
       "\n",
       "Rows: 59071\n",
       "\n",
       "Data:\n",
       "+----+-------------------------------+---------------------+\n",
       "| id |              URI              |         name        |\n",
       "+----+-------------------------------+---------------------+\n",
       "| 0  | <http://dbpedia.org/resour... |    Digby Morrell    |\n",
       "| 1  | <http://dbpedia.org/resour... |    Alfred J. Lewy   |\n",
       "| 2  | <http://dbpedia.org/resour... |    Harpdog Brown    |\n",
       "| 3  | <http://dbpedia.org/resour... | Franz Rottensteiner |\n",
       "| 4  | <http://dbpedia.org/resour... |        G-Enka       |\n",
       "| 5  | <http://dbpedia.org/resour... |    Sam Henderson    |\n",
       "| 6  | <http://dbpedia.org/resour... |    Aaron LaCrate    |\n",
       "| 7  | <http://dbpedia.org/resour... |   Trevor Ferguson   |\n",
       "| 8  | <http://dbpedia.org/resour... |     Grant Nelson    |\n",
       "| 9  | <http://dbpedia.org/resour... |     Cathy Caruth    |\n",
       "+----+-------------------------------+---------------------+\n",
       "+-------------------------------+\n",
       "|              text             |\n",
       "+-------------------------------+\n",
       "| digby morrell born 10 octo... |\n",
       "| alfred j lewy aka sandy le... |\n",
       "| harpdog brown is a singer ... |\n",
       "| franz rottensteiner born i... |\n",
       "| henry krvits born 30 decem... |\n",
       "| sam henderson born october... |\n",
       "| aaron lacrate is an americ... |\n",
       "| trevor ferguson aka john f... |\n",
       "| grant nelson born 27 april... |\n",
       "| cathy caruth born 1955 is ... |\n",
       "+-------------------------------+\n",
       "[59071 rows x 4 columns]\n",
       "Note: Only the head of the SFrame is printed.\n",
       "You can use print_rows(num_rows=m, num_columns=n) to print more rows and columns."
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wiki = wiki.add_row_number()\n",
    "wiki"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Extract TF-IDF matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We first use GraphLab Create to compute a TF-IDF representation for each document."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\"><table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">id</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">URI</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">name</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">text</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">tf_idf</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Digby_Morrell&gt; ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Digby Morrell</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">digby morrell born 10<br>october 1979 is a former ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">{'since':<br>1.455376717308041, ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Alfred_J._Lewy&gt; ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Alfred J. Lewy</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">alfred j lewy aka sandy<br>lewy graduated from ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">{'precise':<br>6.44320060695519, ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Harpdog_Brown&gt; ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Harpdog Brown</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">harpdog brown is a singer<br>and harmonica player who ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">{'just':<br>2.7007299687108643, ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Franz_Rottensteiner&gt; ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Franz Rottensteiner</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">franz rottensteiner born<br>in waidmannsfeld lower ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">{'all':<br>1.6431112434912472, ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/G-Enka&gt; ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">G-Enka</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">henry krvits born 30<br>december 1974 in tallinn ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">{'legendary':<br>4.280856294365192, ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Sam_Henderson&gt; ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Sam Henderson</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">sam henderson born<br>october 18 1969 is an ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">{'now': 1.96695239252401,<br>'currently': ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">6</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Aaron_LaCrate&gt; ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Aaron LaCrate</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">aaron lacrate is an<br>american music producer ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">{'exclusive':<br>10.455187230695827, ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">7</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Trevor_Ferguson&gt; ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Trevor Ferguson</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">trevor ferguson aka john<br>farrow born 11 november ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">{'taxi':<br>6.0520214560945025, ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">8</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Grant_Nelson&gt; ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Grant Nelson</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">grant nelson born 27<br>april 1971 in london  ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">{'houston':<br>3.935505942157149, ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">9</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Cathy_Caruth&gt; ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Cathy Caruth</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">cathy caruth born 1955 is<br>frank h t rhodes ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">{'phenomenon':<br>5.750053426395245, ...</td>\n",
       "    </tr>\n",
       "</table>\n",
       "[59071 rows x 5 columns]<br/>Note: Only the head of the SFrame is printed.<br/>You can use print_rows(num_rows=m, num_columns=n) to print more rows and columns.\n",
       "</div>"
      ],
      "text/plain": [
       "Columns:\n",
       "\tid\tint\n",
       "\tURI\tstr\n",
       "\tname\tstr\n",
       "\ttext\tstr\n",
       "\ttf_idf\tdict\n",
       "\n",
       "Rows: 59071\n",
       "\n",
       "Data:\n",
       "+----+-------------------------------+---------------------+\n",
       "| id |              URI              |         name        |\n",
       "+----+-------------------------------+---------------------+\n",
       "| 0  | <http://dbpedia.org/resour... |    Digby Morrell    |\n",
       "| 1  | <http://dbpedia.org/resour... |    Alfred J. Lewy   |\n",
       "| 2  | <http://dbpedia.org/resour... |    Harpdog Brown    |\n",
       "| 3  | <http://dbpedia.org/resour... | Franz Rottensteiner |\n",
       "| 4  | <http://dbpedia.org/resour... |        G-Enka       |\n",
       "| 5  | <http://dbpedia.org/resour... |    Sam Henderson    |\n",
       "| 6  | <http://dbpedia.org/resour... |    Aaron LaCrate    |\n",
       "| 7  | <http://dbpedia.org/resour... |   Trevor Ferguson   |\n",
       "| 8  | <http://dbpedia.org/resour... |     Grant Nelson    |\n",
       "| 9  | <http://dbpedia.org/resour... |     Cathy Caruth    |\n",
       "+----+-------------------------------+---------------------+\n",
       "+-------------------------------+-------------------------------+\n",
       "|              text             |             tf_idf            |\n",
       "+-------------------------------+-------------------------------+\n",
       "| digby morrell born 10 octo... | {'since': 1.45537671730804... |\n",
       "| alfred j lewy aka sandy le... | {'precise': 6.443200606955... |\n",
       "| harpdog brown is a singer ... | {'just': 2.700729968710864... |\n",
       "| franz rottensteiner born i... | {'all': 1.6431112434912472... |\n",
       "| henry krvits born 30 decem... | {'legendary': 4.2808562943... |\n",
       "| sam henderson born october... | {'now': 1.96695239252401, ... |\n",
       "| aaron lacrate is an americ... | {'exclusive': 10.455187230... |\n",
       "| trevor ferguson aka john f... | {'taxi': 6.052021456094502... |\n",
       "| grant nelson born 27 april... | {'houston': 3.935505942157... |\n",
       "| cathy caruth born 1955 is ... | {'phenomenon': 5.750053426... |\n",
       "+-------------------------------+-------------------------------+\n",
       "[59071 rows x 5 columns]\n",
       "Note: Only the head of the SFrame is printed.\n",
       "You can use print_rows(num_rows=m, num_columns=n) to print more rows and columns."
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wiki['tf_idf'] = graphlab.text_analytics.tf_idf(wiki['text'])\n",
    "wiki"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "We will be using sparse [matrices](https://en.wikipedia.org/wiki/Matrix_(mathematics%29 ) that have a small number of nonzero entries. A good data structure for sparse matrices would only store the nonzero entries to save space and speed up computation. SciPy provides a highly-optimized library for sparse matrices. Many matrix operations available for NumPy arrays are also available for SciPy sparse matrices.\n",
    "\n",
    "We first convert the TF-IDF column (in dictionary format) into the SciPy sparse matrix format."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def sframe_to_scipy(column):\n",
    "    \"\"\" \n",
    "    Convert a dict-typed SArray into a SciPy sparse matrix.\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "        mat : a SciPy sparse matrix where mat[i, j] is the value of word j for document i.\n",
    "        mapping : a dictionary where mapping[j] is the word whose values are in column j.\n",
    "    \"\"\"\n",
    "    # Create triples of (row_id, feature_id, count).\n",
    "    x = graphlab.SFrame({'X1':column})\n",
    "    \n",
    "    # 1. Add a row number.\n",
    "    x = x.add_row_number()\n",
    "    # 2. Stack will transform x to have a row for each unique (row, key) pair.\n",
    "    x = x.stack('X1', ['feature', 'value'])\n",
    "\n",
    "    # Map words into integers using a OneHotEncoder feature transformation.\n",
    "    f = graphlab.feature_engineering.OneHotEncoder(features=['feature'])\n",
    "\n",
    "    # We first fit the transformer using the above data.\n",
    "    f.fit(x)\n",
    "\n",
    "    # The transform method will add a new column that is the transformed version\n",
    "    # of the 'word' column.\n",
    "    x = f.transform(x)\n",
    "\n",
    "    # Get the feature mapping.\n",
    "    mapping = f['feature_encoding']\n",
    "\n",
    "    # Get the actual word id.\n",
    "    x['feature_id'] = x['encoded_features'].dict_keys().apply(lambda x: x[0])\n",
    "\n",
    "    # Create numpy arrays that contain the data for the sparse matrix.\n",
    "    i = np.array(x['id'])\n",
    "    j = np.array(x['feature_id'])\n",
    "    v = np.array(x['value'])\n",
    "    width = x['id'].max() + 1\n",
    "    height = x['feature_id'].max() + 1\n",
    "\n",
    "    # Create a sparse matrix.\n",
    "    mat = csr_matrix((v, (i, j)), shape=(width, height))\n",
    "\n",
    "    return mat, mapping"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The conversion should take a few minutes to complete."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "108.414000034\n"
     ]
    }
   ],
   "source": [
    "start=time.time()\n",
    "corpus, mapping = sframe_to_scipy(wiki['tf_idf'])\n",
    "end=time.time()\n",
    "print end-start"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Checkpoint**: The following code block should return 'Check passed correctly', indicating that your matrix contains TF-IDF values for 59071 documents and 547979 unique words.  Otherwise, it will return Error."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Check passed correctly!\n"
     ]
    }
   ],
   "source": [
    "assert corpus.shape == (59071, 547979)\n",
    "print 'Check passed correctly!'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Train an LSH model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "LSH performs an efficient neighbor search by randomly partitioning all reference data points into different bins. Today we will build a popular variant of LSH known as random binary projection, which approximates cosine distance. There are other variants we could use for other choices of distance metrics.\n",
    "\n",
    "The first step is to generate a collection of random vectors from the standard Gaussian distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def generate_random_vectors(num_vector, dim):\n",
    "    return np.random.randn(dim, num_vector)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To visualize these Gaussian random vectors, let's look at an example in low-dimensions.  Below, we generate 3 random vectors each of dimension 5."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.76405235,  0.40015721,  0.97873798],\n",
       "       [ 2.2408932 ,  1.86755799, -0.97727788],\n",
       "       [ 0.95008842, -0.15135721, -0.10321885],\n",
       "       [ 0.4105985 ,  0.14404357,  1.45427351],\n",
       "       [ 0.76103773,  0.12167502,  0.44386323]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Generate 3 random vectors of dimension 5, arranged into a single 5 x 3 matrix.\n",
    "np.random.seed(0) # set seed=0 for consistent results\n",
    "generate_random_vectors(num_vector=3, dim=5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now generate random vectors of the same dimensionality as our vocubulary size (547979).  Each vector can be used to compute one bit in the bin encoding.  We generate 16 vectors, leading to a 16-bit encoding of the bin index for each document."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(547979L, 16L)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Generate 16 random vectors of dimension 547979\n",
    "np.random.seed(0)\n",
    "random_vectors = generate_random_vectors(num_vector=16, dim=547979)\n",
    "random_vectors.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we partition data points into bins. Instead of using explicit loops, we'd like to utilize matrix operations for greater efficiency. Let's walk through the construction step by step.\n",
    "\n",
    "We'd like to decide which bin document 0 should go. Since 16 random vectors were generated in the previous cell, we have 16 bits to represent the bin index. The first bit is given by the sign of the dot product between the first random vector and the document's TF-IDF vector."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True], dtype=bool)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "doc = corpus[0, :] # vector of tf-idf values for document 0\n",
    "doc.dot(random_vectors[:, 0]) >= 0 # True if positive sign; False if negative sign"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similarly, the second bit is computed as the sign of the dot product between the second random vector and the document vector."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True], dtype=bool)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "doc.dot(random_vectors[:, 1]) >= 0 # True if positive sign; False if negative sign"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can compute all of the bin index bits at once as follows. Note the absence of the explicit `for` loop over the 16 vectors. Matrix operations let us batch dot-product computation in a highly efficent manner, unlike the `for` loop construction. Given the relative inefficiency of loops in Python, the advantage of matrix operations is even greater."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ True,  True, False, False, False,  True,  True, False,  True,\n",
       "         True,  True, False, False,  True, False,  True]], dtype=bool)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "doc.dot(random_vectors) >= 0 # should return an array of 16 True/False bits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array(doc.dot(random_vectors) >= 0, dtype=int) # display index bits in 0/1's"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All documents that obtain exactly this vector will be assigned to the same bin. We'd like to repeat the identical operation on all documents in the Wikipedia dataset and compute the corresponding bin indices. Again, we use matrix operations  so that no explicit loop is needed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ True,  True, False, False, False,  True,  True, False,  True,\n",
       "         True,  True, False, False,  True, False,  True],\n",
       "       [ True, False, False, False,  True,  True, False,  True,  True,\n",
       "        False,  True, False,  True, False, False,  True]], dtype=bool)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "corpus[0:2].dot(random_vectors) >= 0 # compute bit indices of first two documents"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ True,  True, False, ...,  True, False,  True],\n",
       "       [ True, False, False, ..., False, False,  True],\n",
       "       [False,  True, False, ...,  True, False,  True],\n",
       "       ..., \n",
       "       [ True,  True, False, ...,  True,  True,  True],\n",
       "       [False,  True,  True, ...,  True, False,  True],\n",
       "       [ True, False,  True, ..., False, False,  True]], dtype=bool)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "corpus.dot(random_vectors) >= 0 # compute bit indices of ALL documents"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We're almost done! To make it convenient to refer to individual bins, we convert each binary bin index into a single integer: \n",
    "```\n",
    "Bin index                      integer\n",
    "[0,0,0,0,0,0,0,0,0,0,0,0]   => 0\n",
    "[0,0,0,0,0,0,0,0,0,0,0,1]   => 1\n",
    "[0,0,0,0,0,0,0,0,0,0,1,0]   => 2\n",
    "[0,0,0,0,0,0,0,0,0,0,1,1]   => 3\n",
    "...\n",
    "[1,1,1,1,1,1,1,1,1,1,0,0]   => 65532\n",
    "[1,1,1,1,1,1,1,1,1,1,0,1]   => 65533\n",
    "[1,1,1,1,1,1,1,1,1,1,1,0]   => 65534\n",
    "[1,1,1,1,1,1,1,1,1,1,1,1]   => 65535 (= 2^16-1)\n",
    "```\n",
    "By the [rules of binary number representation](https://en.wikipedia.org/wiki/Binary_number#Decimal), we just need to compute the dot product between the document vector and the vector consisting of powers of 2:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ True  True False False False  True  True False  True  True  True False\n",
      "  False  True False  True]]\n",
      "[32768 16384  8192  4096  2048  1024   512   256   128    64    32    16\n",
      "     8     4     2     1]\n",
      "[50917]\n"
     ]
    }
   ],
   "source": [
    "doc = corpus[0, :]  # first document\n",
    "index_bits = (doc.dot(random_vectors) >= 0)\n",
    "powers_of_two = (1 << np.arange(15, -1, -1))\n",
    "print index_bits\n",
    "print powers_of_two\n",
    "print index_bits.dot(powers_of_two)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since it's the dot product again, we batch it with a matrix operation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([50917, 36265, 19365, ..., 52983, 27589, 41449])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "index_bits = corpus.dot(random_vectors) >= 0\n",
    "index_bits.dot(powers_of_two)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This array gives us the integer index of the bins for all documents.\n",
    "\n",
    "Now we are ready to complete the following function. Given the integer bin indices for the documents, you should compile a list of document IDs that belong to each bin. Since a list is to be maintained for each unique bin index, a dictionary of lists is used.\n",
    "\n",
    "1. Compute the integer bin indices. This step is already completed.\n",
    "2. For each document in the dataset, do the following:\n",
    "   * Get the integer bin index for the document.\n",
    "   * Fetch the list of document ids associated with the bin; if no list yet exists for this bin, assign the bin an empty list.\n",
    "   * Add the document id to the end of the list.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def train_lsh(data, num_vector=16, seed=None):\n",
    "    \n",
    "    dim = data.shape[1]\n",
    "    if seed is not None:\n",
    "        np.random.seed(seed)\n",
    "    random_vectors = generate_random_vectors(num_vector, dim)\n",
    "  \n",
    "    powers_of_two = 1 << np.arange(num_vector-1, -1, -1)\n",
    "  \n",
    "    table = {}\n",
    "    \n",
    "    # Partition data points into bins\n",
    "    bin_index_bits = (data.dot(random_vectors) >= 0)\n",
    "  \n",
    "    # Encode bin index bits into integers\n",
    "    bin_indices = bin_index_bits.dot(powers_of_two)\n",
    "    \n",
    "    # Update `table` so that `table[i]` is the list of document ids with bin index equal to i.\n",
    "    for data_index, bin_index in enumerate(bin_indices):\n",
    "        if bin_index not in table:\n",
    "            # If no list yet exists for this bin, assign the bin an empty list.\n",
    "            table[bin_index] = []\n",
    "        # Fetch the list of document ids associated with the bin and add the document id to the end.\n",
    "        table[bin_index].append(data_index)\n",
    "\n",
    "    model = {'data': data,\n",
    "             'bin_index_bits': bin_index_bits,\n",
    "             'bin_indices': bin_indices,\n",
    "             'table': table,\n",
    "             'random_vectors': random_vectors,\n",
    "             'num_vector': num_vector}\n",
    "    \n",
    "    return model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Checkpoint**. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Passed!\n"
     ]
    }
   ],
   "source": [
    "model = train_lsh(corpus, num_vector=16, seed=143)\n",
    "table = model['table']\n",
    "if   0 in table and table[0]   == [39583] and \\\n",
    "   143 in table and table[143] == [19693, 28277, 29776, 30399]:\n",
    "    print 'Passed!'\n",
    "else:\n",
    "    print 'Check your code.'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note.** We will be using the model trained here in the following sections, unless otherwise indicated."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Inspect bins"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us look at some documents and see which bins they fall into."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\"><table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">id</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">URI</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">name</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">text</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">tf_idf</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">35817</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Barack_Obama&gt; ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Barack Obama</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">barack hussein obama ii<br>brk husen bm born august ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">{'operations':<br>3.811771079388818, ...</td>\n",
       "    </tr>\n",
       "</table>\n",
       "[? rows x 5 columns]<br/>Note: Only the head of the SFrame is printed. This SFrame is lazily evaluated.<br/>You can use sf.materialize() to force materialization.\n",
       "</div>"
      ],
      "text/plain": [
       "Columns:\n",
       "\tid\tint\n",
       "\tURI\tstr\n",
       "\tname\tstr\n",
       "\ttext\tstr\n",
       "\ttf_idf\tdict\n",
       "\n",
       "Rows: Unknown\n",
       "\n",
       "Data:\n",
       "+-------+-------------------------------+--------------+\n",
       "|   id  |              URI              |     name     |\n",
       "+-------+-------------------------------+--------------+\n",
       "| 35817 | <http://dbpedia.org/resour... | Barack Obama |\n",
       "+-------+-------------------------------+--------------+\n",
       "+-------------------------------+-------------------------------+\n",
       "|              text             |             tf_idf            |\n",
       "+-------------------------------+-------------------------------+\n",
       "| barack hussein obama ii br... | {'operations': 3.811771079... |\n",
       "+-------------------------------+-------------------------------+\n",
       "[? rows x 5 columns]\n",
       "Note: Only the head of the SFrame is printed. This SFrame is lazily evaluated.\n",
       "You can use sf.materialize() to force materialization."
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wiki[wiki['name'] == 'Barack Obama']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Document `id` of Barack Obama's article*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "35817L"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wiki[wiki['name'] == 'Barack Obama']['id'][0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "*Bin that contains Barack Obama's article*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "50194"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model['bin_indices'][35817]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recall from the nearest neighbors search notebook that Joe Biden was a close neighbor of Barack Obama."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\"><table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">id</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">URI</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">name</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">text</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">tf_idf</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">24478</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Joe_Biden&gt; ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Joe Biden</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">joseph robinette joe<br>biden jr dosf rbnt badn ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">{'delaware':<br>11.396456717061318, ...</td>\n",
       "    </tr>\n",
       "</table>\n",
       "[? rows x 5 columns]<br/>Note: Only the head of the SFrame is printed. This SFrame is lazily evaluated.<br/>You can use sf.materialize() to force materialization.\n",
       "</div>"
      ],
      "text/plain": [
       "Columns:\n",
       "\tid\tint\n",
       "\tURI\tstr\n",
       "\tname\tstr\n",
       "\ttext\tstr\n",
       "\ttf_idf\tdict\n",
       "\n",
       "Rows: Unknown\n",
       "\n",
       "Data:\n",
       "+-------+-------------------------------+-----------+\n",
       "|   id  |              URI              |    name   |\n",
       "+-------+-------------------------------+-----------+\n",
       "| 24478 | <http://dbpedia.org/resour... | Joe Biden |\n",
       "+-------+-------------------------------+-----------+\n",
       "+-------------------------------+-------------------------------+\n",
       "|              text             |             tf_idf            |\n",
       "+-------------------------------+-------------------------------+\n",
       "| joseph robinette joe biden... | {'delaware': 11.3964567170... |\n",
       "+-------------------------------+-------------------------------+\n",
       "[? rows x 5 columns]\n",
       "Note: Only the head of the SFrame is printed. This SFrame is lazily evaluated.\n",
       "You can use sf.materialize() to force materialization."
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wiki[wiki['name'] == 'Joe Biden']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Lets examine bit representations of the bins containing Barack Obama and Joe Biden and see how many bits are same*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(model['bin_index_bits'][35817] == model['bin_index_bits'][24478])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compare the result with a former British diplomat, whose bin representation agrees with Obama's in only 8 out of 16 places."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\"><table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">id</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">URI</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">name</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">text</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">tf_idf</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">22745</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Wynn_Normington_H ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Wynn Normington Hugh-<br>Jones ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">sir wynn normington<br>hughjones kb sometimes ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">{'forced':<br>3.919175540571719, ...</td>\n",
       "    </tr>\n",
       "</table>\n",
       "[? rows x 5 columns]<br/>Note: Only the head of the SFrame is printed. This SFrame is lazily evaluated.<br/>You can use sf.materialize() to force materialization.\n",
       "</div>"
      ],
      "text/plain": [
       "Columns:\n",
       "\tid\tint\n",
       "\tURI\tstr\n",
       "\tname\tstr\n",
       "\ttext\tstr\n",
       "\ttf_idf\tdict\n",
       "\n",
       "Rows: Unknown\n",
       "\n",
       "Data:\n",
       "+-------+-------------------------------+----------------------------+\n",
       "|   id  |              URI              |            name            |\n",
       "+-------+-------------------------------+----------------------------+\n",
       "| 22745 | <http://dbpedia.org/resour... | Wynn Normington Hugh-Jones |\n",
       "+-------+-------------------------------+----------------------------+\n",
       "+-------------------------------+-------------------------------+\n",
       "|              text             |             tf_idf            |\n",
       "+-------------------------------+-------------------------------+\n",
       "| sir wynn normington hughjo... | {'forced': 3.9191755405717... |\n",
       "+-------------------------------+-------------------------------+\n",
       "[? rows x 5 columns]\n",
       "Note: Only the head of the SFrame is printed. This SFrame is lazily evaluated.\n",
       "You can use sf.materialize() to force materialization."
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wiki[wiki['name']=='Wynn Normington Hugh-Jones']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0]\n",
      "4660\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([False, False,  True, False,  True, False, False,  True,  True,\n",
       "        True, False,  True,  True, False, False,  True], dtype=bool)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print np.array(model['bin_index_bits'][22745], dtype=int) # list of 0/1's\n",
    "print model['bin_indices'][22745] # integer format\n",
    "model['bin_index_bits'][35817] == model['bin_index_bits'][22745]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How about the documents in the same bin as Barack Obama? Are they necessarily more similar to Obama than Biden?  Let's look at which documents are in the same bin as the Barack Obama article."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[21426, 35817, 39426, 50261, 53937]"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model['table'][model['bin_indices'][35817]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are four other documents that belong to the same bin. Which documents are they?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\"><table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">id</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">URI</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">name</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">text</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">tf_idf</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">21426</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Mark_Boulware&gt; ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Mark Boulware</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">mark boulware born 1948<br>is an american diplomat ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">{'ambassador':<br>15.90834582606623, ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">39426</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/John_Wells_(polit ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">John Wells (politician)</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">sir john julius wells<br>born 30 march 1925 is a ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">{'when':<br>1.3806055739282235, ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">50261</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Francis_Longstaff&gt; ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Francis Longstaff</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">francis a longstaff born<br>august 3 1956 is an ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">{'all':<br>1.6431112434912472, ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">53937</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Madurai_T._Sriniv ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Madurai T. Srinivasan</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">maduraitsrinivasan is a<br>wellknown figure in the ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">{'alarmelu':<br>21.972990778450388, ...</td>\n",
       "    </tr>\n",
       "</table>\n",
       "[4 rows x 5 columns]<br/>\n",
       "</div>"
      ],
      "text/plain": [
       "Columns:\n",
       "\tid\tint\n",
       "\tURI\tstr\n",
       "\tname\tstr\n",
       "\ttext\tstr\n",
       "\ttf_idf\tdict\n",
       "\n",
       "Rows: 4\n",
       "\n",
       "Data:\n",
       "+-------+-------------------------------+-------------------------+\n",
       "|   id  |              URI              |           name          |\n",
       "+-------+-------------------------------+-------------------------+\n",
       "| 21426 | <http://dbpedia.org/resour... |      Mark Boulware      |\n",
       "| 39426 | <http://dbpedia.org/resour... | John Wells (politician) |\n",
       "| 50261 | <http://dbpedia.org/resour... |    Francis Longstaff    |\n",
       "| 53937 | <http://dbpedia.org/resour... |  Madurai T. Srinivasan  |\n",
       "+-------+-------------------------------+-------------------------+\n",
       "+-------------------------------+-------------------------------+\n",
       "|              text             |             tf_idf            |\n",
       "+-------------------------------+-------------------------------+\n",
       "| mark boulware born 1948 is... | {'ambassador': 15.90834582... |\n",
       "| sir john julius wells born... | {'when': 1.380605573928223... |\n",
       "| francis a longstaff born a... | {'all': 1.6431112434912472... |\n",
       "| maduraitsrinivasan is a we... | {'alarmelu': 21.9729907784... |\n",
       "+-------------------------------+-------------------------------+\n",
       "[4 rows x 5 columns]"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "doc_ids = list(model['table'][model['bin_indices'][35817]])\n",
    "doc_ids.remove(35817) # display documents other than Obama\n",
    "\n",
    "docs = wiki.filter_by(values=doc_ids, column_name='id') # filter by id column\n",
    "docs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It turns out that Joe Biden is much closer to Barack Obama than any of the four documents, even though Biden's bin representation differs from Obama's by 2 bits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "================= Cosine distance from Barack Obama\n",
      "Barack Obama - Joe Biden               : 0.703139\n",
      "Barack Obama - Mark Boulware           : 0.950867\n",
      "Barack Obama - John Wells (politician) : 0.975966\n",
      "Barack Obama - Francis Longstaff       : 0.978256\n",
      "Barack Obama - Madurai T. Srinivasan   : 0.993092\n"
     ]
    }
   ],
   "source": [
    "def cosine_distance(x, y):\n",
    "    xy = x.dot(y.T)\n",
    "    dist = xy/(norm(x)*norm(y))\n",
    "    return 1-dist[0,0]\n",
    "\n",
    "obama_tf_idf = corpus[35817,:]\n",
    "biden_tf_idf = corpus[24478,:]\n",
    "\n",
    "print '================= Cosine distance from Barack Obama'\n",
    "print 'Barack Obama - {0:24s}: {1:f}'.format('Joe Biden',\n",
    "                                             cosine_distance(obama_tf_idf, biden_tf_idf))\n",
    "for doc_id in doc_ids:\n",
    "    doc_tf_idf = corpus[doc_id,:]\n",
    "    print 'Barack Obama - {0:24s}: {1:f}'.format(wiki[doc_id]['name'],\n",
    "                                                 cosine_distance(obama_tf_idf, doc_tf_idf))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Moral of the story**. Similar data points will in general _tend to_ fall into _nearby_ bins, but that's all we can say about LSH. In a high-dimensional space such as text features, we often get unlucky with our selection of only a few random vectors such that dissimilar data points go into the same bin while similar data points fall into different bins. **Given a query document, we must consider all documents in the nearby bins and sort them according to their actual distances from the query.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Query the LSH model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us first implement the logic for searching nearby neighbors, which goes like this:\n",
    "```\n",
    "1. Let L be the bit representation of the bin that contains the query documents.\n",
    "2. Consider all documents in bin L.\n",
    "3. Consider documents in the bins whose bit representation differs from L by 1 bit.\n",
    "4. Consider documents in the bins whose bit representation differs from L by 2 bits.\n",
    "...\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To obtain candidate bins that differ from the query bin by some number of bits, we use `itertools.combinations`, which produces all possible subsets of a given list. See [this documentation](https://docs.python.org/3/library/itertools.html#itertools.combinations) for details.\n",
    "```\n",
    "1. Decide on the search radius r. This will determine the number of different bits between the two vectors.\n",
    "2. For each subset (n_1, n_2, ..., n_r) of the list [0, 1, 2, ..., num_vector-1], do the following:\n",
    "   * Flip the bits (n_1, n_2, ..., n_r) of the query bin to produce a new bit vector.\n",
    "   * Fetch the list of documents belonging to the bin indexed by the new bit vector.\n",
    "   * Add those documents to the candidate set.\n",
    "```\n",
    "\n",
    "Each line of output from the following cell is a 3-tuple indicating where the candidate bin would differ from the query bin. For instance,\n",
    "```\n",
    "(0, 1, 3)\n",
    "```\n",
    "indicates that the candiate bin differs from the query bin in first, second, and fourth bits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from itertools import combinations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0, 1, 2)\n",
      "(0, 1, 3)\n",
      "(0, 1, 4)\n",
      "(0, 1, 5)\n",
      "(0, 1, 6)\n",
      "(0, 1, 7)\n",
      "(0, 1, 8)\n",
      "(0, 1, 9)\n",
      "(0, 1, 10)\n",
      "(0, 1, 11)\n",
      "(0, 1, 12)\n",
      "(0, 1, 13)\n",
      "(0, 1, 14)\n",
      "(0, 1, 15)\n",
      "(0, 2, 3)\n",
      "(0, 2, 4)\n",
      "(0, 2, 5)\n",
      "(0, 2, 6)\n",
      "(0, 2, 7)\n",
      "(0, 2, 8)\n",
      "(0, 2, 9)\n",
      "(0, 2, 10)\n",
      "(0, 2, 11)\n",
      "(0, 2, 12)\n",
      "(0, 2, 13)\n",
      "(0, 2, 14)\n",
      "(0, 2, 15)\n",
      "(0, 3, 4)\n",
      "(0, 3, 5)\n",
      "(0, 3, 6)\n",
      "(0, 3, 7)\n",
      "(0, 3, 8)\n",
      "(0, 3, 9)\n",
      "(0, 3, 10)\n",
      "(0, 3, 11)\n",
      "(0, 3, 12)\n",
      "(0, 3, 13)\n",
      "(0, 3, 14)\n",
      "(0, 3, 15)\n",
      "(0, 4, 5)\n",
      "(0, 4, 6)\n",
      "(0, 4, 7)\n",
      "(0, 4, 8)\n",
      "(0, 4, 9)\n",
      "(0, 4, 10)\n",
      "(0, 4, 11)\n",
      "(0, 4, 12)\n",
      "(0, 4, 13)\n",
      "(0, 4, 14)\n",
      "(0, 4, 15)\n",
      "(0, 5, 6)\n",
      "(0, 5, 7)\n",
      "(0, 5, 8)\n",
      "(0, 5, 9)\n",
      "(0, 5, 10)\n",
      "(0, 5, 11)\n",
      "(0, 5, 12)\n",
      "(0, 5, 13)\n",
      "(0, 5, 14)\n",
      "(0, 5, 15)\n",
      "(0, 6, 7)\n",
      "(0, 6, 8)\n",
      "(0, 6, 9)\n",
      "(0, 6, 10)\n",
      "(0, 6, 11)\n",
      "(0, 6, 12)\n",
      "(0, 6, 13)\n",
      "(0, 6, 14)\n",
      "(0, 6, 15)\n",
      "(0, 7, 8)\n",
      "(0, 7, 9)\n",
      "(0, 7, 10)\n",
      "(0, 7, 11)\n",
      "(0, 7, 12)\n",
      "(0, 7, 13)\n",
      "(0, 7, 14)\n",
      "(0, 7, 15)\n",
      "(0, 8, 9)\n",
      "(0, 8, 10)\n",
      "(0, 8, 11)\n",
      "(0, 8, 12)\n",
      "(0, 8, 13)\n",
      "(0, 8, 14)\n",
      "(0, 8, 15)\n",
      "(0, 9, 10)\n",
      "(0, 9, 11)\n",
      "(0, 9, 12)\n",
      "(0, 9, 13)\n",
      "(0, 9, 14)\n",
      "(0, 9, 15)\n",
      "(0, 10, 11)\n",
      "(0, 10, 12)\n",
      "(0, 10, 13)\n",
      "(0, 10, 14)\n",
      "(0, 10, 15)\n",
      "(0, 11, 12)\n",
      "(0, 11, 13)\n",
      "(0, 11, 14)\n",
      "(0, 11, 15)\n",
      "(0, 12, 13)\n",
      "(0, 12, 14)\n",
      "(0, 12, 15)\n",
      "(0, 13, 14)\n",
      "(0, 13, 15)\n",
      "(0, 14, 15)\n",
      "(1, 2, 3)\n",
      "(1, 2, 4)\n",
      "(1, 2, 5)\n",
      "(1, 2, 6)\n",
      "(1, 2, 7)\n",
      "(1, 2, 8)\n",
      "(1, 2, 9)\n",
      "(1, 2, 10)\n",
      "(1, 2, 11)\n",
      "(1, 2, 12)\n",
      "(1, 2, 13)\n",
      "(1, 2, 14)\n",
      "(1, 2, 15)\n",
      "(1, 3, 4)\n",
      "(1, 3, 5)\n",
      "(1, 3, 6)\n",
      "(1, 3, 7)\n",
      "(1, 3, 8)\n",
      "(1, 3, 9)\n",
      "(1, 3, 10)\n",
      "(1, 3, 11)\n",
      "(1, 3, 12)\n",
      "(1, 3, 13)\n",
      "(1, 3, 14)\n",
      "(1, 3, 15)\n",
      "(1, 4, 5)\n",
      "(1, 4, 6)\n",
      "(1, 4, 7)\n",
      "(1, 4, 8)\n",
      "(1, 4, 9)\n",
      "(1, 4, 10)\n",
      "(1, 4, 11)\n",
      "(1, 4, 12)\n",
      "(1, 4, 13)\n",
      "(1, 4, 14)\n",
      "(1, 4, 15)\n",
      "(1, 5, 6)\n",
      "(1, 5, 7)\n",
      "(1, 5, 8)\n",
      "(1, 5, 9)\n",
      "(1, 5, 10)\n",
      "(1, 5, 11)\n",
      "(1, 5, 12)\n",
      "(1, 5, 13)\n",
      "(1, 5, 14)\n",
      "(1, 5, 15)\n",
      "(1, 6, 7)\n",
      "(1, 6, 8)\n",
      "(1, 6, 9)\n",
      "(1, 6, 10)\n",
      "(1, 6, 11)\n",
      "(1, 6, 12)\n",
      "(1, 6, 13)\n",
      "(1, 6, 14)\n",
      "(1, 6, 15)\n",
      "(1, 7, 8)\n",
      "(1, 7, 9)\n",
      "(1, 7, 10)\n",
      "(1, 7, 11)\n",
      "(1, 7, 12)\n",
      "(1, 7, 13)\n",
      "(1, 7, 14)\n",
      "(1, 7, 15)\n",
      "(1, 8, 9)\n",
      "(1, 8, 10)\n",
      "(1, 8, 11)\n",
      "(1, 8, 12)\n",
      "(1, 8, 13)\n",
      "(1, 8, 14)\n",
      "(1, 8, 15)\n",
      "(1, 9, 10)\n",
      "(1, 9, 11)\n",
      "(1, 9, 12)\n",
      "(1, 9, 13)\n",
      "(1, 9, 14)\n",
      "(1, 9, 15)\n",
      "(1, 10, 11)\n",
      "(1, 10, 12)\n",
      "(1, 10, 13)\n",
      "(1, 10, 14)\n",
      "(1, 10, 15)\n",
      "(1, 11, 12)\n",
      "(1, 11, 13)\n",
      "(1, 11, 14)\n",
      "(1, 11, 15)\n",
      "(1, 12, 13)\n",
      "(1, 12, 14)\n",
      "(1, 12, 15)\n",
      "(1, 13, 14)\n",
      "(1, 13, 15)\n",
      "(1, 14, 15)\n",
      "(2, 3, 4)\n",
      "(2, 3, 5)\n",
      "(2, 3, 6)\n",
      "(2, 3, 7)\n",
      "(2, 3, 8)\n",
      "(2, 3, 9)\n",
      "(2, 3, 10)\n",
      "(2, 3, 11)\n",
      "(2, 3, 12)\n",
      "(2, 3, 13)\n",
      "(2, 3, 14)\n",
      "(2, 3, 15)\n",
      "(2, 4, 5)\n",
      "(2, 4, 6)\n",
      "(2, 4, 7)\n",
      "(2, 4, 8)\n",
      "(2, 4, 9)\n",
      "(2, 4, 10)\n",
      "(2, 4, 11)\n",
      "(2, 4, 12)\n",
      "(2, 4, 13)\n",
      "(2, 4, 14)\n",
      "(2, 4, 15)\n",
      "(2, 5, 6)\n",
      "(2, 5, 7)\n",
      "(2, 5, 8)\n",
      "(2, 5, 9)\n",
      "(2, 5, 10)\n",
      "(2, 5, 11)\n",
      "(2, 5, 12)\n",
      "(2, 5, 13)\n",
      "(2, 5, 14)\n",
      "(2, 5, 15)\n",
      "(2, 6, 7)\n",
      "(2, 6, 8)\n",
      "(2, 6, 9)\n",
      "(2, 6, 10)\n",
      "(2, 6, 11)\n",
      "(2, 6, 12)\n",
      "(2, 6, 13)\n",
      "(2, 6, 14)\n",
      "(2, 6, 15)\n",
      "(2, 7, 8)\n",
      "(2, 7, 9)\n",
      "(2, 7, 10)\n",
      "(2, 7, 11)\n",
      "(2, 7, 12)\n",
      "(2, 7, 13)\n",
      "(2, 7, 14)\n",
      "(2, 7, 15)\n",
      "(2, 8, 9)\n",
      "(2, 8, 10)\n",
      "(2, 8, 11)\n",
      "(2, 8, 12)\n",
      "(2, 8, 13)\n",
      "(2, 8, 14)\n",
      "(2, 8, 15)\n",
      "(2, 9, 10)\n",
      "(2, 9, 11)\n",
      "(2, 9, 12)\n",
      "(2, 9, 13)\n",
      "(2, 9, 14)\n",
      "(2, 9, 15)\n",
      "(2, 10, 11)\n",
      "(2, 10, 12)\n",
      "(2, 10, 13)\n",
      "(2, 10, 14)\n",
      "(2, 10, 15)\n",
      "(2, 11, 12)\n",
      "(2, 11, 13)\n",
      "(2, 11, 14)\n",
      "(2, 11, 15)\n",
      "(2, 12, 13)\n",
      "(2, 12, 14)\n",
      "(2, 12, 15)\n",
      "(2, 13, 14)\n",
      "(2, 13, 15)\n",
      "(2, 14, 15)\n",
      "(3, 4, 5)\n",
      "(3, 4, 6)\n",
      "(3, 4, 7)\n",
      "(3, 4, 8)\n",
      "(3, 4, 9)\n",
      "(3, 4, 10)\n",
      "(3, 4, 11)\n",
      "(3, 4, 12)\n",
      "(3, 4, 13)\n",
      "(3, 4, 14)\n",
      "(3, 4, 15)\n",
      "(3, 5, 6)\n",
      "(3, 5, 7)\n",
      "(3, 5, 8)\n",
      "(3, 5, 9)\n",
      "(3, 5, 10)\n",
      "(3, 5, 11)\n",
      "(3, 5, 12)\n",
      "(3, 5, 13)\n",
      "(3, 5, 14)\n",
      "(3, 5, 15)\n",
      "(3, 6, 7)\n",
      "(3, 6, 8)\n",
      "(3, 6, 9)\n",
      "(3, 6, 10)\n",
      "(3, 6, 11)\n",
      "(3, 6, 12)\n",
      "(3, 6, 13)\n",
      "(3, 6, 14)\n",
      "(3, 6, 15)\n",
      "(3, 7, 8)\n",
      "(3, 7, 9)\n",
      "(3, 7, 10)\n",
      "(3, 7, 11)\n",
      "(3, 7, 12)\n",
      "(3, 7, 13)\n",
      "(3, 7, 14)\n",
      "(3, 7, 15)\n",
      "(3, 8, 9)\n",
      "(3, 8, 10)\n",
      "(3, 8, 11)\n",
      "(3, 8, 12)\n",
      "(3, 8, 13)\n",
      "(3, 8, 14)\n",
      "(3, 8, 15)\n",
      "(3, 9, 10)\n",
      "(3, 9, 11)\n",
      "(3, 9, 12)\n",
      "(3, 9, 13)\n",
      "(3, 9, 14)\n",
      "(3, 9, 15)\n",
      "(3, 10, 11)\n",
      "(3, 10, 12)\n",
      "(3, 10, 13)\n",
      "(3, 10, 14)\n",
      "(3, 10, 15)\n",
      "(3, 11, 12)\n",
      "(3, 11, 13)\n",
      "(3, 11, 14)\n",
      "(3, 11, 15)\n",
      "(3, 12, 13)\n",
      "(3, 12, 14)\n",
      "(3, 12, 15)\n",
      "(3, 13, 14)\n",
      "(3, 13, 15)\n",
      "(3, 14, 15)\n",
      "(4, 5, 6)\n",
      "(4, 5, 7)\n",
      "(4, 5, 8)\n",
      "(4, 5, 9)\n",
      "(4, 5, 10)\n",
      "(4, 5, 11)\n",
      "(4, 5, 12)\n",
      "(4, 5, 13)\n",
      "(4, 5, 14)\n",
      "(4, 5, 15)\n",
      "(4, 6, 7)\n",
      "(4, 6, 8)\n",
      "(4, 6, 9)\n",
      "(4, 6, 10)\n",
      "(4, 6, 11)\n",
      "(4, 6, 12)\n",
      "(4, 6, 13)\n",
      "(4, 6, 14)\n",
      "(4, 6, 15)\n",
      "(4, 7, 8)\n",
      "(4, 7, 9)\n",
      "(4, 7, 10)\n",
      "(4, 7, 11)\n",
      "(4, 7, 12)\n",
      "(4, 7, 13)\n",
      "(4, 7, 14)\n",
      "(4, 7, 15)\n",
      "(4, 8, 9)\n",
      "(4, 8, 10)\n",
      "(4, 8, 11)\n",
      "(4, 8, 12)\n",
      "(4, 8, 13)\n",
      "(4, 8, 14)\n",
      "(4, 8, 15)\n",
      "(4, 9, 10)\n",
      "(4, 9, 11)\n",
      "(4, 9, 12)\n",
      "(4, 9, 13)\n",
      "(4, 9, 14)\n",
      "(4, 9, 15)\n",
      "(4, 10, 11)\n",
      "(4, 10, 12)\n",
      "(4, 10, 13)\n",
      "(4, 10, 14)\n",
      "(4, 10, 15)\n",
      "(4, 11, 12)\n",
      "(4, 11, 13)\n",
      "(4, 11, 14)\n",
      "(4, 11, 15)\n",
      "(4, 12, 13)\n",
      "(4, 12, 14)\n",
      "(4, 12, 15)\n",
      "(4, 13, 14)\n",
      "(4, 13, 15)\n",
      "(4, 14, 15)\n",
      "(5, 6, 7)\n",
      "(5, 6, 8)\n",
      "(5, 6, 9)\n",
      "(5, 6, 10)\n",
      "(5, 6, 11)\n",
      "(5, 6, 12)\n",
      "(5, 6, 13)\n",
      "(5, 6, 14)\n",
      "(5, 6, 15)\n",
      "(5, 7, 8)\n",
      "(5, 7, 9)\n",
      "(5, 7, 10)\n",
      "(5, 7, 11)\n",
      "(5, 7, 12)\n",
      "(5, 7, 13)\n",
      "(5, 7, 14)\n",
      "(5, 7, 15)\n",
      "(5, 8, 9)\n",
      "(5, 8, 10)\n",
      "(5, 8, 11)\n",
      "(5, 8, 12)\n",
      "(5, 8, 13)\n",
      "(5, 8, 14)\n",
      "(5, 8, 15)\n",
      "(5, 9, 10)\n",
      "(5, 9, 11)\n",
      "(5, 9, 12)\n",
      "(5, 9, 13)\n",
      "(5, 9, 14)\n",
      "(5, 9, 15)\n",
      "(5, 10, 11)\n",
      "(5, 10, 12)\n",
      "(5, 10, 13)\n",
      "(5, 10, 14)\n",
      "(5, 10, 15)\n",
      "(5, 11, 12)\n",
      "(5, 11, 13)\n",
      "(5, 11, 14)\n",
      "(5, 11, 15)\n",
      "(5, 12, 13)\n",
      "(5, 12, 14)\n",
      "(5, 12, 15)\n",
      "(5, 13, 14)\n",
      "(5, 13, 15)\n",
      "(5, 14, 15)\n",
      "(6, 7, 8)\n",
      "(6, 7, 9)\n",
      "(6, 7, 10)\n",
      "(6, 7, 11)\n",
      "(6, 7, 12)\n",
      "(6, 7, 13)\n",
      "(6, 7, 14)\n",
      "(6, 7, 15)\n",
      "(6, 8, 9)\n",
      "(6, 8, 10)\n",
      "(6, 8, 11)\n",
      "(6, 8, 12)\n",
      "(6, 8, 13)\n",
      "(6, 8, 14)\n",
      "(6, 8, 15)\n",
      "(6, 9, 10)\n",
      "(6, 9, 11)\n",
      "(6, 9, 12)\n",
      "(6, 9, 13)\n",
      "(6, 9, 14)\n",
      "(6, 9, 15)\n",
      "(6, 10, 11)\n",
      "(6, 10, 12)\n",
      "(6, 10, 13)\n",
      "(6, 10, 14)\n",
      "(6, 10, 15)\n",
      "(6, 11, 12)\n",
      "(6, 11, 13)\n",
      "(6, 11, 14)\n",
      "(6, 11, 15)\n",
      "(6, 12, 13)\n",
      "(6, 12, 14)\n",
      "(6, 12, 15)\n",
      "(6, 13, 14)\n",
      "(6, 13, 15)\n",
      "(6, 14, 15)\n",
      "(7, 8, 9)\n",
      "(7, 8, 10)\n",
      "(7, 8, 11)\n",
      "(7, 8, 12)\n",
      "(7, 8, 13)\n",
      "(7, 8, 14)\n",
      "(7, 8, 15)\n",
      "(7, 9, 10)\n",
      "(7, 9, 11)\n",
      "(7, 9, 12)\n",
      "(7, 9, 13)\n",
      "(7, 9, 14)\n",
      "(7, 9, 15)\n",
      "(7, 10, 11)\n",
      "(7, 10, 12)\n",
      "(7, 10, 13)\n",
      "(7, 10, 14)\n",
      "(7, 10, 15)\n",
      "(7, 11, 12)\n",
      "(7, 11, 13)\n",
      "(7, 11, 14)\n",
      "(7, 11, 15)\n",
      "(7, 12, 13)\n",
      "(7, 12, 14)\n",
      "(7, 12, 15)\n",
      "(7, 13, 14)\n",
      "(7, 13, 15)\n",
      "(7, 14, 15)\n",
      "(8, 9, 10)\n",
      "(8, 9, 11)\n",
      "(8, 9, 12)\n",
      "(8, 9, 13)\n",
      "(8, 9, 14)\n",
      "(8, 9, 15)\n",
      "(8, 10, 11)\n",
      "(8, 10, 12)\n",
      "(8, 10, 13)\n",
      "(8, 10, 14)\n",
      "(8, 10, 15)\n",
      "(8, 11, 12)\n",
      "(8, 11, 13)\n",
      "(8, 11, 14)\n",
      "(8, 11, 15)\n",
      "(8, 12, 13)\n",
      "(8, 12, 14)\n",
      "(8, 12, 15)\n",
      "(8, 13, 14)\n",
      "(8, 13, 15)\n",
      "(8, 14, 15)\n",
      "(9, 10, 11)\n",
      "(9, 10, 12)\n",
      "(9, 10, 13)\n",
      "(9, 10, 14)\n",
      "(9, 10, 15)\n",
      "(9, 11, 12)\n",
      "(9, 11, 13)\n",
      "(9, 11, 14)\n",
      "(9, 11, 15)\n",
      "(9, 12, 13)\n",
      "(9, 12, 14)\n",
      "(9, 12, 15)\n",
      "(9, 13, 14)\n",
      "(9, 13, 15)\n",
      "(9, 14, 15)\n",
      "(10, 11, 12)\n",
      "(10, 11, 13)\n",
      "(10, 11, 14)\n",
      "(10, 11, 15)\n",
      "(10, 12, 13)\n",
      "(10, 12, 14)\n",
      "(10, 12, 15)\n",
      "(10, 13, 14)\n",
      "(10, 13, 15)\n",
      "(10, 14, 15)\n",
      "(11, 12, 13)\n",
      "(11, 12, 14)\n",
      "(11, 12, 15)\n",
      "(11, 13, 14)\n",
      "(11, 13, 15)\n",
      "(11, 14, 15)\n",
      "(12, 13, 14)\n",
      "(12, 13, 15)\n",
      "(12, 14, 15)\n",
      "(13, 14, 15)\n"
     ]
    }
   ],
   "source": [
    "num_vector = 16\n",
    "search_radius = 3\n",
    "\n",
    "for diff in combinations(range(num_vector), search_radius):\n",
    "    print diff"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With this output in mind, implement the logic for nearby bin search:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def search_nearby_bins(query_bin_bits, table, search_radius=2, initial_candidates=set()):\n",
    "    \"\"\"\n",
    "    For a given query vector and trained LSH model, return all candidate neighbors for\n",
    "    the query among all bins within the given search radius.\n",
    "    \n",
    "    Example usage\n",
    "    -------------\n",
    "    >>> model = train_lsh(corpus, num_vector=16, seed=143)\n",
    "    >>> q = model['bin_index_bits'][0]  # vector for the first document\n",
    "  \n",
    "    >>> candidates = search_nearby_bins(q, model['table'])\n",
    "    \"\"\"\n",
    "    num_vector = len(query_bin_bits)\n",
    "    powers_of_two = 1 << np.arange(num_vector-1, -1, -1)\n",
    "    \n",
    "    # Allow the user to provide an initial set of candidates.\n",
    "    candidate_set = copy(initial_candidates)\n",
    "    \n",
    "    for different_bits in combinations(range(num_vector), search_radius):       \n",
    "        # Flip the bits (n_1,n_2,...,n_r) of the query bin to produce a new bit vector.\n",
    "        ## Hint: you can iterate over a tuple like a list\n",
    "        alternate_bits = copy(query_bin_bits)\n",
    "        for i in different_bits:\n",
    "            alternate_bits[i] = ~alternate_bits[i]\n",
    "        \n",
    "        # Convert the new bit vector to an integer index\n",
    "        nearby_bin = alternate_bits.dot(powers_of_two)\n",
    "        \n",
    "        # Fetch the list of documents belonging to the bin indexed by the new bit vector.\n",
    "        # Then add those documents to candidate_set\n",
    "        # Make sure that the bin exists in the table!\n",
    "        # Hint: update() method for sets lets you add an entire list to the set\n",
    "        if nearby_bin in table:\n",
    "            more_docs = table[nearby_bin] # Get all document_ids of the bin\n",
    "            candidate_set.update(more_docs)\n",
    "            \n",
    "    return candidate_set"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Checkpoint**. Running the function with `search_radius=0` should yield the list of documents belonging to the same bin as the query."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Passed test\n",
      "List of documents in the same bin as Obama: 35817, 21426, 53937, 39426, 50261\n"
     ]
    }
   ],
   "source": [
    "obama_bin_index = model['bin_index_bits'][35817] # bin index of Barack Obama\n",
    "candidate_set = search_nearby_bins(obama_bin_index, model['table'], search_radius=0)\n",
    "if candidate_set == set([35817, 21426, 53937, 39426, 50261]):\n",
    "    print 'Passed test'\n",
    "else:\n",
    "    print 'Check your code'\n",
    "print 'List of documents in the same bin as Obama: 35817, 21426, 53937, 39426, 50261'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Checkpoint**. Running the function with `search_radius=1` adds more documents to the fore."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Passed test\n"
     ]
    }
   ],
   "source": [
    "candidate_set = search_nearby_bins(obama_bin_index, model['table'], search_radius=1, initial_candidates=candidate_set)\n",
    "if candidate_set == set([39426, 38155, 38412, 28444, 9757, 41631, 39207, 59050, 47773, 53937, 21426, 34547,\n",
    "                         23229, 55615, 39877, 27404, 33996, 21715, 50261, 21975, 33243, 58723, 35817, 45676,\n",
    "                         19699, 2804, 20347]):\n",
    "    print 'Passed test'\n",
    "else:\n",
    "    print 'Check your code'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**. Don't be surprised if few of the candidates look similar to Obama. This is why we add as many candidates as our computational budget allows and sort them by their distance to the query."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we have a function that can return all the candidates from neighboring bins. Next we write a function to collect all candidates and compute their true distance to the query."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "def query(vec, model, k, max_search_radius):\n",
    "  \n",
    "    data = model['data']\n",
    "    table = model['table']\n",
    "    random_vectors = model['random_vectors']\n",
    "    num_vector = random_vectors.shape[1]\n",
    "    \n",
    "    \n",
    "    # Compute bin index for the query vector, in bit representation.\n",
    "    bin_index_bits = (vec.dot(random_vectors) >= 0).flatten()\n",
    "    \n",
    "    # Search nearby bins and collect candidates\n",
    "    candidate_set = set()\n",
    "    for search_radius in xrange(max_search_radius+1):\n",
    "        candidate_set = search_nearby_bins(bin_index_bits, table, search_radius, initial_candidates=candidate_set)\n",
    "    \n",
    "    # Sort candidates by their true distances from the query\n",
    "    nearest_neighbors = graphlab.SFrame({'id':candidate_set})\n",
    "    candidates = data[np.array(list(candidate_set)),:]\n",
    "    nearest_neighbors['distance'] = pairwise_distances(candidates, vec, metric='cosine').flatten()\n",
    "    \n",
    "    return nearest_neighbors.topk('distance', k, reverse=True), len(candidate_set)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try it out with Obama:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Columns:\n",
       " \tid\tint\n",
       " \tdistance\tfloat\n",
       " \n",
       " Rows: 10\n",
       " \n",
       " Data:\n",
       " +-------+--------------------+\n",
       " |   id  |      distance      |\n",
       " +-------+--------------------+\n",
       " | 35817 | -6.66133814775e-16 |\n",
       " | 24478 |   0.703138676734   |\n",
       " | 56008 |   0.856848127628   |\n",
       " | 37199 |   0.874668698194   |\n",
       " | 40353 |   0.890034225981   |\n",
       " |  9267 |   0.898377208819   |\n",
       " | 55909 |   0.899340396322   |\n",
       " |  9165 |   0.900921029925   |\n",
       " | 57958 |   0.903003263483   |\n",
       " | 49872 |   0.909532800353   |\n",
       " +-------+--------------------+\n",
       " [10 rows x 2 columns], 727)"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "query(corpus[35817,:], model, k=10, max_search_radius=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To identify the documents, it's helpful to join this table with the Wikipedia table:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\"><table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">id</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">distance</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">name</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">35817</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-6.66133814775e-16</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Barack Obama</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">24478</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.703138676734</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Joe Biden</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">56008</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.856848127628</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Nathan Cullen</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">37199</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.874668698194</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Barry Sullivan (lawyer)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">40353</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.890034225981</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Neil MacBride</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">9267</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.898377208819</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Vikramaditya Khanna</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">55909</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.899340396322</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Herman Cain</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">9165</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.900921029925</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Raymond F. Clevenger</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">57958</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.903003263483</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Michael J. Malbin</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">49872</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.909532800353</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Lowell Barron</td>\n",
       "    </tr>\n",
       "</table>\n",
       "[10 rows x 3 columns]<br/>\n",
       "</div>"
      ],
      "text/plain": [
       "Columns:\n",
       "\tid\tint\n",
       "\tdistance\tfloat\n",
       "\tname\tstr\n",
       "\n",
       "Rows: 10\n",
       "\n",
       "Data:\n",
       "+-------+--------------------+-------------------------+\n",
       "|   id  |      distance      |           name          |\n",
       "+-------+--------------------+-------------------------+\n",
       "| 35817 | -6.66133814775e-16 |       Barack Obama      |\n",
       "| 24478 |   0.703138676734   |        Joe Biden        |\n",
       "| 56008 |   0.856848127628   |      Nathan Cullen      |\n",
       "| 37199 |   0.874668698194   | Barry Sullivan (lawyer) |\n",
       "| 40353 |   0.890034225981   |      Neil MacBride      |\n",
       "|  9267 |   0.898377208819   |   Vikramaditya Khanna   |\n",
       "| 55909 |   0.899340396322   |       Herman Cain       |\n",
       "|  9165 |   0.900921029925   |   Raymond F. Clevenger  |\n",
       "| 57958 |   0.903003263483   |    Michael J. Malbin    |\n",
       "| 49872 |   0.909532800353   |      Lowell Barron      |\n",
       "+-------+--------------------+-------------------------+\n",
       "[10 rows x 3 columns]"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "query(corpus[35817,:], model, k=10, max_search_radius=3)[0].join(wiki[['id', 'name']], on='id').sort('distance')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have shown that we have a working LSH implementation!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Experimenting with your LSH implementation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the following sections we have implemented a few experiments so that you can gain intuition for how your LSH implementation behaves in different situations. This will help you understand the effect of searching nearby bins and the performance of LSH versus computing nearest neighbors using a brute force search."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Effect of nearby bin search"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How does nearby bin search affect the outcome of LSH? There are three variables that are affected by the search radius:\n",
    "* Number of candidate documents considered\n",
    "* Query time\n",
    "* Distance of approximate neighbors from the query"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us run LSH multiple times, each with different radii for nearby bin search. We will measure the three variables as discussed above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\"><table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">id</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">URI</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">name</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">text</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">tf_idf</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">35817</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">&lt;http://dbpedia.org/resou<br>rce/Barack_Obama&gt; ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">Barack Obama</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">barack hussein obama ii<br>brk husen bm born august ...</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">{'operations':<br>3.811771079388818, ...</td>\n",
       "    </tr>\n",
       "</table>\n",
       "[? rows x 5 columns]<br/>Note: Only the head of the SFrame is printed. This SFrame is lazily evaluated.<br/>You can use sf.materialize() to force materialization.\n",
       "</div>"
      ],
      "text/plain": [
       "Columns:\n",
       "\tid\tint\n",
       "\tURI\tstr\n",
       "\tname\tstr\n",
       "\ttext\tstr\n",
       "\ttf_idf\tdict\n",
       "\n",
       "Rows: Unknown\n",
       "\n",
       "Data:\n",
       "+-------+-------------------------------+--------------+\n",
       "|   id  |              URI              |     name     |\n",
       "+-------+-------------------------------+--------------+\n",
       "| 35817 | <http://dbpedia.org/resour... | Barack Obama |\n",
       "+-------+-------------------------------+--------------+\n",
       "+-------------------------------+-------------------------------+\n",
       "|              text             |             tf_idf            |\n",
       "+-------------------------------+-------------------------------+\n",
       "| barack hussein obama ii br... | {'operations': 3.811771079... |\n",
       "+-------------------------------+-------------------------------+\n",
       "[? rows x 5 columns]\n",
       "Note: Only the head of the SFrame is printed. This SFrame is lazily evaluated.\n",
       "You can use sf.materialize() to force materialization."
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wiki[wiki['name']=='Barack Obama']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Radius: 0\n",
      "+-------+--------------------+-------------------------+\n",
      "|   id  |      distance      |           name          |\n",
      "+-------+--------------------+-------------------------+\n",
      "| 35817 | -6.66133814775e-16 |       Barack Obama      |\n",
      "| 21426 |   0.950866757525   |      Mark Boulware      |\n",
      "| 39426 |   0.97596600411    | John Wells (politician) |\n",
      "| 50261 |   0.978256163041   |    Francis Longstaff    |\n",
      "| 53937 |   0.993092148424   |  Madurai T. Srinivasan  |\n",
      "+-------+--------------------+-------------------------+\n",
      "[5 rows x 3 columns]\n",
      "\n",
      "Radius: 1\n",
      "+-------+--------------------+-------------------------------+\n",
      "|   id  |      distance      |              name             |\n",
      "+-------+--------------------+-------------------------------+\n",
      "| 35817 | -6.66133814775e-16 |          Barack Obama         |\n",
      "| 41631 |   0.947459482005   |          Binayak Sen          |\n",
      "| 21426 |   0.950866757525   |         Mark Boulware         |\n",
      "| 33243 |   0.951765770113   |        Janice Lachance        |\n",
      "| 33996 |   0.960859054157   |          Rufus Black          |\n",
      "| 28444 |   0.961080585824   |        John Paul Phelan       |\n",
      "| 20347 |   0.974129605472   |        Gianni De Fraja        |\n",
      "| 39426 |   0.97596600411    |    John Wells (politician)    |\n",
      "| 34547 |   0.978214931987   | Nathan Murphy (Australian ... |\n",
      "| 50261 |   0.978256163041   |       Francis Longstaff       |\n",
      "+-------+--------------------+-------------------------------+\n",
      "[10 rows x 3 columns]\n",
      "\n",
      "Radius: 2\n",
      "+-------+--------------------+---------------------+\n",
      "|   id  |      distance      |         name        |\n",
      "+-------+--------------------+---------------------+\n",
      "| 35817 | -6.66133814775e-16 |     Barack Obama    |\n",
      "| 24478 |   0.703138676734   |      Joe Biden      |\n",
      "|  9267 |   0.898377208819   | Vikramaditya Khanna |\n",
      "| 55909 |   0.899340396322   |     Herman Cain     |\n",
      "|  6949 |   0.925713001103   |  Harrison J. Goldin |\n",
      "| 23524 |   0.926397988994   |    Paul Bennecke    |\n",
      "|  5823 |   0.928498260316   |    Adeleke Mamora   |\n",
      "| 37262 |   0.93445433211    |      Becky Cain     |\n",
      "| 10121 |   0.936896394645   |     Bill Bradley    |\n",
      "| 54782 |   0.937809202206   |  Thomas F. Hartnett |\n",
      "+-------+--------------------+---------------------+\n",
      "[10 rows x 3 columns]\n",
      "\n",
      "Radius: 3\n",
      "+-------+--------------------+-------------------------+\n",
      "|   id  |      distance      |           name          |\n",
      "+-------+--------------------+-------------------------+\n",
      "| 35817 | -6.66133814775e-16 |       Barack Obama      |\n",
      "| 24478 |   0.703138676734   |        Joe Biden        |\n",
      "| 56008 |   0.856848127628   |      Nathan Cullen      |\n",
      "| 37199 |   0.874668698194   | Barry Sullivan (lawyer) |\n",
      "| 40353 |   0.890034225981   |      Neil MacBride      |\n",
      "|  9267 |   0.898377208819   |   Vikramaditya Khanna   |\n",
      "| 55909 |   0.899340396322   |       Herman Cain       |\n",
      "|  9165 |   0.900921029925   |   Raymond F. Clevenger  |\n",
      "| 57958 |   0.903003263483   |    Michael J. Malbin    |\n",
      "| 49872 |   0.909532800353   |      Lowell Barron      |\n",
      "+-------+--------------------+-------------------------+\n",
      "[10 rows x 3 columns]\n",
      "\n",
      "Radius: 4\n",
      "+-------+--------------------+--------------------+\n",
      "|   id  |      distance      |        name        |\n",
      "+-------+--------------------+--------------------+\n",
      "| 35817 | -6.66133814775e-16 |    Barack Obama    |\n",
      "| 24478 |   0.703138676734   |     Joe Biden      |\n",
      "| 36452 |   0.833985493688   |    Bill Clinton    |\n",
      "| 24848 |   0.839406735668   |  John C. Eastman   |\n",
      "| 43155 |   0.840839007484   |    Goodwin Liu     |\n",
      "| 42965 |   0.849077676943   |  John O. Brennan   |\n",
      "| 56008 |   0.856848127628   |   Nathan Cullen    |\n",
      "| 38495 |   0.857573828556   |    Barney Frank    |\n",
      "| 18752 |   0.858899032522   |   Dan W. Reicher   |\n",
      "|  2092 |   0.874643264756   | Richard Blumenthal |\n",
      "+-------+--------------------+--------------------+\n",
      "[10 rows x 3 columns]\n",
      "\n",
      "Radius: 5\n",
      "+-------+--------------------+-------------------------+\n",
      "|   id  |      distance      |           name          |\n",
      "+-------+--------------------+-------------------------+\n",
      "| 35817 | -6.66133814775e-16 |       Barack Obama      |\n",
      "| 24478 |   0.703138676734   |        Joe Biden        |\n",
      "| 38714 |   0.770561227601   | Eric Stern (politician) |\n",
      "| 46811 |   0.800197384104   |      Jeff Sessions      |\n",
      "| 14754 |   0.826854025897   |       Mitt Romney       |\n",
      "| 36452 |   0.833985493688   |       Bill Clinton      |\n",
      "| 40943 |   0.834534928232   |      Jonathan Alter     |\n",
      "| 55044 |   0.837013236281   |       Wesley Clark      |\n",
      "| 24848 |   0.839406735668   |     John C. Eastman     |\n",
      "| 43155 |   0.840839007484   |       Goodwin Liu       |\n",
      "+-------+--------------------+-------------------------+\n",
      "[10 rows x 3 columns]\n",
      "\n",
      "Radius: 6\n",
      "+-------+--------------------+-------------------------+\n",
      "|   id  |      distance      |           name          |\n",
      "+-------+--------------------+-------------------------+\n",
      "| 35817 | -6.66133814775e-16 |       Barack Obama      |\n",
      "| 24478 |   0.703138676734   |        Joe Biden        |\n",
      "| 38714 |   0.770561227601   | Eric Stern (politician) |\n",
      "| 44681 |   0.790926415366   |  Jesse Lee (politician) |\n",
      "| 46811 |   0.800197384104   |      Jeff Sessions      |\n",
      "| 48693 |   0.809192212293   |       Artur Davis       |\n",
      "| 23737 |   0.810164633465   |    John D. McCormick    |\n",
      "|  4032 |   0.814554748671   |   Kenneth D. Thompson   |\n",
      "| 28447 |   0.823228984384   |      George W. Bush     |\n",
      "| 14754 |   0.826854025897   |       Mitt Romney       |\n",
      "+-------+--------------------+-------------------------+\n",
      "[10 rows x 3 columns]\n",
      "\n",
      "Radius: 7\n",
      "+-------+--------------------+-------------------------+\n",
      "|   id  |      distance      |           name          |\n",
      "+-------+--------------------+-------------------------+\n",
      "| 35817 | -6.66133814775e-16 |       Barack Obama      |\n",
      "| 24478 |   0.703138676734   |        Joe Biden        |\n",
      "| 38376 |   0.742981902328   |      Samantha Power     |\n",
      "| 57108 |   0.758358397887   |  Hillary Rodham Clinton |\n",
      "| 38714 |   0.770561227601   | Eric Stern (politician) |\n",
      "| 44681 |   0.790926415366   |  Jesse Lee (politician) |\n",
      "| 18827 |   0.798322602893   |       Henry Waxman      |\n",
      "| 46811 |   0.800197384104   |      Jeff Sessions      |\n",
      "| 48693 |   0.809192212293   |       Artur Davis       |\n",
      "| 23737 |   0.810164633465   |    John D. McCormick    |\n",
      "+-------+--------------------+-------------------------+\n",
      "[10 rows x 3 columns]\n",
      "\n",
      "Radius: 8\n",
      "+-------+--------------------+-------------------------+\n",
      "|   id  |      distance      |           name          |\n",
      "+-------+--------------------+-------------------------+\n",
      "| 35817 | -6.66133814775e-16 |       Barack Obama      |\n",
      "| 24478 |   0.703138676734   |        Joe Biden        |\n",
      "| 38376 |   0.742981902328   |      Samantha Power     |\n",
      "| 57108 |   0.758358397887   |  Hillary Rodham Clinton |\n",
      "| 38714 |   0.770561227601   | Eric Stern (politician) |\n",
      "| 44681 |   0.790926415366   |  Jesse Lee (politician) |\n",
      "| 18827 |   0.798322602893   |       Henry Waxman      |\n",
      "| 46811 |   0.800197384104   |      Jeff Sessions      |\n",
      "| 48693 |   0.809192212293   |       Artur Davis       |\n",
      "| 23737 |   0.810164633465   |    John D. McCormick    |\n",
      "+-------+--------------------+-------------------------+\n",
      "[10 rows x 3 columns]\n",
      "\n",
      "Radius: 9\n",
      "+-------+--------------------+-------------------------+\n",
      "|   id  |      distance      |           name          |\n",
      "+-------+--------------------+-------------------------+\n",
      "| 35817 | -6.66133814775e-16 |       Barack Obama      |\n",
      "| 24478 |   0.703138676734   |        Joe Biden        |\n",
      "| 38376 |   0.742981902328   |      Samantha Power     |\n",
      "| 57108 |   0.758358397887   |  Hillary Rodham Clinton |\n",
      "| 38714 |   0.770561227601   | Eric Stern (politician) |\n",
      "| 46140 |   0.784677504751   |       Robert Gibbs      |\n",
      "| 44681 |   0.790926415366   |  Jesse Lee (politician) |\n",
      "| 18827 |   0.798322602893   |       Henry Waxman      |\n",
      "| 46811 |   0.800197384104   |      Jeff Sessions      |\n",
      "| 39357 |   0.809050776238   |       John McCain       |\n",
      "+-------+--------------------+-------------------------+\n",
      "[10 rows x 3 columns]\n",
      "\n",
      "Radius: 10\n",
      "+-------+--------------------+-------------------------+\n",
      "|   id  |      distance      |           name          |\n",
      "+-------+--------------------+-------------------------+\n",
      "| 35817 | -6.66133814775e-16 |       Barack Obama      |\n",
      "| 24478 |   0.703138676734   |        Joe Biden        |\n",
      "| 38376 |   0.742981902328   |      Samantha Power     |\n",
      "| 57108 |   0.758358397887   |  Hillary Rodham Clinton |\n",
      "| 38714 |   0.770561227601   | Eric Stern (politician) |\n",
      "| 46140 |   0.784677504751   |       Robert Gibbs      |\n",
      "| 44681 |   0.790926415366   |  Jesse Lee (politician) |\n",
      "| 18827 |   0.798322602893   |       Henry Waxman      |\n",
      "|  2412 |   0.799466360042   |     Joe the Plumber     |\n",
      "| 46811 |   0.800197384104   |      Jeff Sessions      |\n",
      "+-------+--------------------+-------------------------+\n",
      "[10 rows x 3 columns]\n",
      "\n",
      "Radius: 11\n",
      "+-------+--------------------+-------------------------+\n",
      "|   id  |      distance      |           name          |\n",
      "+-------+--------------------+-------------------------+\n",
      "| 35817 | -6.66133814775e-16 |       Barack Obama      |\n",
      "| 24478 |   0.703138676734   |        Joe Biden        |\n",
      "| 38376 |   0.742981902328   |      Samantha Power     |\n",
      "| 57108 |   0.758358397887   |  Hillary Rodham Clinton |\n",
      "| 38714 |   0.770561227601   | Eric Stern (politician) |\n",
      "| 46140 |   0.784677504751   |       Robert Gibbs      |\n",
      "| 44681 |   0.790926415366   |  Jesse Lee (politician) |\n",
      "| 18827 |   0.798322602893   |       Henry Waxman      |\n",
      "|  2412 |   0.799466360042   |     Joe the Plumber     |\n",
      "| 46811 |   0.800197384104   |      Jeff Sessions      |\n",
      "+-------+--------------------+-------------------------+\n",
      "[10 rows x 3 columns]\n",
      "\n",
      "Radius: 12\n",
      "+-------+--------------------+-------------------------+\n",
      "|   id  |      distance      |           name          |\n",
      "+-------+--------------------+-------------------------+\n",
      "| 35817 | -6.66133814775e-16 |       Barack Obama      |\n",
      "| 24478 |   0.703138676734   |        Joe Biden        |\n",
      "| 38376 |   0.742981902328   |      Samantha Power     |\n",
      "| 57108 |   0.758358397887   |  Hillary Rodham Clinton |\n",
      "| 38714 |   0.770561227601   | Eric Stern (politician) |\n",
      "| 46140 |   0.784677504751   |       Robert Gibbs      |\n",
      "|  6796 |   0.788039072943   |       Eric Holder       |\n",
      "| 44681 |   0.790926415366   |  Jesse Lee (politician) |\n",
      "| 18827 |   0.798322602893   |       Henry Waxman      |\n",
      "|  2412 |   0.799466360042   |     Joe the Plumber     |\n",
      "+-------+--------------------+-------------------------+\n",
      "[10 rows x 3 columns]\n",
      "\n",
      "Radius: 13\n",
      "+-------+--------------------+-------------------------+\n",
      "|   id  |      distance      |           name          |\n",
      "+-------+--------------------+-------------------------+\n",
      "| 35817 | -6.66133814775e-16 |       Barack Obama      |\n",
      "| 24478 |   0.703138676734   |        Joe Biden        |\n",
      "| 38376 |   0.742981902328   |      Samantha Power     |\n",
      "| 57108 |   0.758358397887   |  Hillary Rodham Clinton |\n",
      "| 38714 |   0.770561227601   | Eric Stern (politician) |\n",
      "| 46140 |   0.784677504751   |       Robert Gibbs      |\n",
      "|  6796 |   0.788039072943   |       Eric Holder       |\n",
      "| 44681 |   0.790926415366   |  Jesse Lee (politician) |\n",
      "| 18827 |   0.798322602893   |       Henry Waxman      |\n",
      "|  2412 |   0.799466360042   |     Joe the Plumber     |\n",
      "+-------+--------------------+-------------------------+\n",
      "[10 rows x 3 columns]\n",
      "\n",
      "Radius: 14\n",
      "+-------+--------------------+-------------------------+\n",
      "|   id  |      distance      |           name          |\n",
      "+-------+--------------------+-------------------------+\n",
      "| 35817 | -6.66133814775e-16 |       Barack Obama      |\n",
      "| 24478 |   0.703138676734   |        Joe Biden        |\n",
      "| 38376 |   0.742981902328   |      Samantha Power     |\n",
      "| 57108 |   0.758358397887   |  Hillary Rodham Clinton |\n",
      "| 38714 |   0.770561227601   | Eric Stern (politician) |\n",
      "| 46140 |   0.784677504751   |       Robert Gibbs      |\n",
      "|  6796 |   0.788039072943   |       Eric Holder       |\n",
      "| 44681 |   0.790926415366   |  Jesse Lee (politician) |\n",
      "| 18827 |   0.798322602893   |       Henry Waxman      |\n",
      "|  2412 |   0.799466360042   |     Joe the Plumber     |\n",
      "+-------+--------------------+-------------------------+\n",
      "[10 rows x 3 columns]\n",
      "\n",
      "Radius: 15\n",
      "+-------+--------------------+-------------------------+\n",
      "|   id  |      distance      |           name          |\n",
      "+-------+--------------------+-------------------------+\n",
      "| 35817 | -6.66133814775e-16 |       Barack Obama      |\n",
      "| 24478 |   0.703138676734   |        Joe Biden        |\n",
      "| 38376 |   0.742981902328   |      Samantha Power     |\n",
      "| 57108 |   0.758358397887   |  Hillary Rodham Clinton |\n",
      "| 38714 |   0.770561227601   | Eric Stern (politician) |\n",
      "| 46140 |   0.784677504751   |       Robert Gibbs      |\n",
      "|  6796 |   0.788039072943   |       Eric Holder       |\n",
      "| 44681 |   0.790926415366   |  Jesse Lee (politician) |\n",
      "| 18827 |   0.798322602893   |       Henry Waxman      |\n",
      "|  2412 |   0.799466360042   |     Joe the Plumber     |\n",
      "+-------+--------------------+-------------------------+\n",
      "[10 rows x 3 columns]\n",
      "\n",
      "Radius: 16\n",
      "+-------+--------------------+-------------------------+\n",
      "|   id  |      distance      |           name          |\n",
      "+-------+--------------------+-------------------------+\n",
      "| 35817 | -6.66133814775e-16 |       Barack Obama      |\n",
      "| 24478 |   0.703138676734   |        Joe Biden        |\n",
      "| 38376 |   0.742981902328   |      Samantha Power     |\n",
      "| 57108 |   0.758358397887   |  Hillary Rodham Clinton |\n",
      "| 38714 |   0.770561227601   | Eric Stern (politician) |\n",
      "| 46140 |   0.784677504751   |       Robert Gibbs      |\n",
      "|  6796 |   0.788039072943   |       Eric Holder       |\n",
      "| 44681 |   0.790926415366   |  Jesse Lee (politician) |\n",
      "| 18827 |   0.798322602893   |       Henry Waxman      |\n",
      "|  2412 |   0.799466360042   |     Joe the Plumber     |\n",
      "+-------+--------------------+-------------------------+\n",
      "[10 rows x 3 columns]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "num_candidates_history = []\n",
    "query_time_history = []\n",
    "max_distance_from_query_history = []\n",
    "min_distance_from_query_history = []\n",
    "average_distance_from_query_history = []\n",
    "\n",
    "for max_search_radius in xrange(17):\n",
    "    start=time.time()\n",
    "    result, num_candidates = query(corpus[35817,:], model, k=10,\n",
    "                                   max_search_radius=max_search_radius)\n",
    "    end=time.time()\n",
    "    query_time = end-start\n",
    "    \n",
    "    print 'Radius:', max_search_radius\n",
    "    print result.join(wiki[['id', 'name']], on='id').sort('distance')\n",
    "    \n",
    "    average_distance_from_query = result['distance'][1:].mean()\n",
    "    max_distance_from_query = result['distance'][1:].max()\n",
    "    min_distance_from_query = result['distance'][1:].min()\n",
    "    \n",
    "    num_candidates_history.append(num_candidates)\n",
    "    query_time_history.append(query_time)\n",
    "    average_distance_from_query_history.append(average_distance_from_query)\n",
    "    max_distance_from_query_history.append(max_distance_from_query)\n",
    "    min_distance_from_query_history.append(min_distance_from_query)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that the top 10 query results become more relevant as the search radius grows. Let's plot the three variables:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6oi1xCXwFLG3KieoxN/q+LPp+EDA7U4QBzGwB8BTQL/a8g6K8HozFVREun/eW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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x5e30af60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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G8Prr0L59cnGJVIpS1ohvAA4mzKJ1P2HscKOZWXfgKmB7wixdLwInu/ukmMf3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\nibVlffvCm29C67JdtkREylW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      "text/plain": [
       "<matplotlib.figure.Figure at 0x5d5382b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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UKZK2ofbzg9KlUUrx9tvw8suPmy1aBBMnQqlS5l1+3Oxjfrv8G3su7DHJPtrz\nEXX86tC6bNbzkOroWIutra0pH2x2ER8fr8kt/Cxx8uRJ6tSpk+GqwYwZM0z/L1u2zGKdPXv2sGPH\nDvbv32/Kzevt7U29evXYvXu3KXVkTuLi4kKtWrVy/Do5QUxMDA4ODnmthkXy4pnqbSzPfNOaKZtI\neq7cA6gOnMHoRFYbmJ5U5UoaTUkKxbkM8FNKeadVLzRF2ZmeMmkRGQn/+x+sWQNffWVch371VWPq\npbJloVYtiIykQwdImf4yIQE+/dRyl7YGW5Z0XoK3s1btnit7En4n/Em01NHJEaZNm0ZQUBCFChXC\nx8eHjh07cu7cOU2dBg0a0L17d77++mtKly6Nk5MTgwYN4osvvuDs2bOmJe9BgwZp2m3ZsoUqVapQ\nsGBBGjZsyMmTJzXnExMTmTRpEmXKlMHBwYHAwEAWLFigqbN7924aNGhAoUKFKFSoENWrV+fnn38G\nwM/Pj7t37/Luu+9iMBjSXUoGOHfuHB06dMDV1RVXV1c6duxoyuqUkJCAwWBg9+7dLF26FIPBQLly\n5Z54XMG4YlC8eHGTEQaoU6cOfn5+bNy4Mc12yWO6cuVKBg0ahJubG35+fnz4ofmK2pEjR2jVqhWu\nrq4UKlSIbt26ERkZaTpvaWn61q1bdOnSBRcXF/z8/Pjss88YMWIEZcuWNev/zJkzNG/eHBcXFypW\nrMiaNWss6vz1119TsmRJnJycaN++PVeuaL/ar1+/Tq9evfD09MTZ2ZmmTZvyxx9/aOr4+fnx1ltv\n8cEHH1C8eHE8PT0BOHr0KC1btsTDw4OCBQtSqVIl5syZk+b4pWbnzp2EhoaaSnaQ3tK0GUopH8Af\nMPtZISK7rezmOJa3O1UEMgwhJSKrkma35YA4ETmvlJoFXBSRS1bqkCah8+fDpUvmJcWbMUscOgRf\nfonho48YP95oo5OZOxfefx98fc2b+Rb0ZXHnxTSd39SUHOJ2zG1CloXwa99f9eQQ+Rw1MeeX7WRC\n9uxDT0jQ+ieknM1eunSJN954g4CAAO7evcusWbOoX78+f//9N87OzqZ6u3bt4syZM0ybNg0HBwee\nf/55Hjx4wL59+1i+fDkiQpEij/PLnDt3jvHjxxMaGoq9vT0jR46ke/fumi/f119/ncWLFxMaGsrz\nzz/P5s2b6d27N0WKFOHFF18kKiqK9u3bExISQmhoKCLCkSNHTM9Y165dS8OGDenZsyd9+vQBSHMp\nOTY2libVybPoAAAgAElEQVRNmuDs7Mz333+PUor33nuPxo0bc/ToUVxdXQkLC2PQoEF4e3vz0Ucf\nUcCKx1bpcfLkSQIDA83kFSpUMPtRYonRo0cTEhLCihUr2LJlCxMmTKBKlSp07NgRgNOnT9OgQQPq\n1KnDTz/9RFxcHO+88w4vvfQSe/fuNfWTeom5V69eHDx4kJkzZ+Ll5cW0adM4c+aM2exTROjRoweD\nBg1i3LhxfP7553Tr1o3z58/j7f14krF7925OnDjBF198wYMHDxg7diydO3fW6NCuXTsuXbrEF198\ngZubG1OmTKFx48YcPnxYs2w+f/58nnvuOWbPnm1637Zt25bq1auzePFi7OzsOHnyJHfv3s1w/JJp\n3LgxjRs3Nh1PnGhpw04msSZpMVAMYwrEBAslEUiwNgEy8CZGh6uSKWQlk2TDM5tQGSgK3ATGZlDP\nBvgdOJ9OHUmTmBiRc+dEdu8W+eknkalTRYYNE3n5ZZFatUSKFhVRSsQYLCv90qqViIjExYmULKk9\nNXp02iqIiHyy5xMhFE0ZvHZw+o108px031siZq9pTpSsEhoaKkopTTEYDLJ9+3aL9RMSEuTBgwfi\n7OwsixYtMsnr168vzs7OcvPmTU394cOHS9myZc366dmzp9jb20t4eLhJtnz5cjEYDHL27FkRETl1\n6pQopTTXERHp0aOH1K1bV0REwsLCxGAwSHR0dJr36ObmJpMmTcpgJET++9//ir29vVy8eNEki4iI\nEDs7O5k2bZrmXrt3755hf9boEBwcLCEhIWbybt26SaNGjdLs78yZM6KUkgEDBmjklStXll69emn6\nqVSpkiQkJJhkJ0+eFBsbG9myZYuIiGzbtk0MBoOcOnVKREQOHz4sSilZvXq1qc2DBw/E3d1d81p+\n++23YjAYZMGCBSZZZGSkGAwG+e6770yy+vXrS4ECBeSff/4xyXbt2iVKKdP7bO3atWIwGGT//v2m\nOvfv3xcPDw8ZMmSISVa8eHHx8/OTR48emWRXr14VpZScPHkyzfGyRHqf36RzmbJbqYu1S9OzgCrA\nWKAV0CRFCU76ay3fAOHAaqVU+6RIVz8DEYBpfUAp5a+UeqSUejeFzFYpNV0p1UEpFayUGorRIeso\nj5enUUp1U0otUEr1UEo1Ukp1w7jSXDXpHjJPgQIQEAANGkD37jBmDHzxBaxYAb/9BpcvQ2wsXLgA\n+/YZnb6mT4eRI6F1que4SctXdnYwNpU2s2bBrVtpqzG23lg6lNc6f3/9+9f8eNiCp5eOTjbj5ubG\n77//zqFDhzh06BAHDx7ULJXu27eP5s2bU7hwYWxtbXFxcSE6OtrMy7ZWrVp4eHik7j5NSpcuTYkS\nJUzHFStWRES4dMm4CLZt2zbs7e1p3749CQkJptKkSRPTrLls2bI4OzvTrVs31q5dm6lZUGoOHjxI\nUFAQxYsXN8n8/f154YUXstXrOjtp3ry55rhixYqm8QPjsvPLL7+MiJjGr3Tp0hQvXpxDKT1LU3Dw\n4EFsbGxokyJSkZOTE02bNs1QBy8vLwoXLqzRASAoKAjfFMuCDRs2xMPDgwNJvjkHDx7E19eXF154\nwVTH2dmZNm3amI19s2bNNCs2Xl5eFC9enEGDBrFs2TKuX386toJaa4gbACNF5DMR2SIiu1IXay8o\nxn2/TYDTwHzgR4zboJomnUtGpSim5hijcH0NbMDouPUt0FJEUu4vOg/4YAy9uQVjbOxooIWIWPaE\nyA7s7IwOWXXqGANLjxgBn31m7g4dHm4KMt23L6RYleHBA/jyy7QvoZTih44/UNpdu1PrtXWvcfTa\n0Wy6ER0dy9ja2lKtWjWqV69uKslLzuHh4bRs2RJbW1u++eYb9u3bx6FDh3B3dycmJkbTT8qlSGtw\nc3PTHNvbG+MLJfd748YN4uLicHFxwc7OzlQGDhxIXFwckZGReHh4sHnzZmJjYwkJCaFw4cK0b9+e\niIiITI/DlStXLN6Dt7c3t9L7JZ0F3N3diYoyj0d0+/Zt3N0z2nBieQxTvi43b95k0qRJmvGzt7fn\n4sWLXLx40WKfV69epVChQmbOdl5eXk+kA6B5JJFSlvycODNjn7qewWBgy5YteHl50a9fP3x9fWnU\nqBFHjhyxqG9uYe0z4mggmx6Sghif5YZkUCcC43JySlkCxoAgGfX/G9AsKzpmK+7u4OoKyb/AY2Lg\n2jXw8cHBwbhtOeXM+MsvjbKCBS135+bgxvIuy6nzXR1iHhnfxNGPoum0tBOHBh3SBAHRyR9k1/Pb\nvGTjxo3ExcWxevVqk6GMj4/nzp07ZnWzeyuLh4cHBQoU0DxHTEmyo06dOnXYuHEjMTExbN26lREj\nRtCrVy9277bWxcWIr6+vmRMawLVr10zXym4sOZ+B8dlx9+7ds9y/u7s7PXr0oG/fvmZx7dMyrD4+\nPkRFRZGQkKAxxlmZaUZa8MeJjIw0zZJ9fX0t1rl27ZrZKoul91lgYCDLly/n0aNH7NmzhzFjxtCu\nXbsn+kGWXVg7I/4GY1xonSdBKeOydkrOmwKLMXgwpPyhePs2zJ6dfpdVfaoys/VMjezvW3/Tb3U/\nPTmETp4QHR2NjY2N5gt50aJFJCYmptPqMZZmR9bSpEkT4uLiuHfvnma2nlxSz9gcHBxo164dffr0\n4a+/HvuIWqtD7dq1OXDggGZZ9cKFC4SFhdGgQWbCKlhPq1atuHTpkmmJFiAsLIwLFy7QOvXjryeg\nadOmHDt2zGzFo3r16vj5Wc7JExQUREJCAmvXrjXJHjx4wPbt259Yj4MHD2q8pHft2sWtW7dMj0Bq\n167NP//8Q1hYmOaaGzZsyNTY29raEhwczPDhw7l06RL379/PuFEOkeaMWCnVL8XhJaCXUmo7sBFj\n8A0NIjI3tUwnBSVLwuHDj4/Dw41L2BhnvsOGwQcfPD792WcwZAikt+2tX7V+7L2wl7l/Ph76FSdW\nMCNsBiPqjMhe/XV0MqBp06aMGzeOPn360LdvX44cOcKMGTOsDvgRGBjIP//8w4IFC6hQoQJeXl74\n+/tb1bZixYoMGDCAzp07M3bsWGrUqEF0dDTHjx/n/PnzzJo1izVr1rBgwQI6dOiAn58fFy9e5Jtv\nvtE8zwwMDGTdunU0bdoUFxcXAgMDNd7eyfTv35+pU6fSsmVL0xaW0NBQihYtyoABA6zSOSUREREc\nOnQIESE+Pp5jx46xYsUKXFxcaNGiBQD169enSZMm9OzZk6lTpyIijBs3juDg4Gwx/h988AG1a9em\nXbt29O3bF09PTy5dusTWrVsZOHAg9erVA9D80H/uuedo1aoVAwcO5Pbt23h5eTF9+nQKFiyIwfBk\nu2O9vLxo3bo1EyZM4MGDB4wbN44XXniB4OBgAFq3bk2tWrUICQlh8uTJuLm58emnn/Lo0SNGjhyZ\nbt9//PEH48ePp2vXrgQEBHDz5k0+/fRTatasiYuLyxPpmy2k5cWF0Rva2mK11/TTXMjAszVLDB+u\ndY9O5RV544aIs7O2yqxZGXf7MO6hVP26qsY71maijSw7viyHbkTnScjR91YuERoaKl5eXunWmTdv\nnpQuXVqcnJykXr168vvvv4ufn5+MHz/eVKd+/frSo0cPs7bR0dHSp08fKVKkiBgMBhk4cKCIGL2m\n69Spo6l75swZMRgMsnnzZo38888/l0qVKomDg4MUKVJEgoODZeHChSIicuLECencubP4+/uLg4OD\n+Pv7yxtvvCFRUVGm9gcPHpQXXnhBXFxcxGAwyN69e9O813PnzkmHDh3E1dVVXF1dpWPHjnLu3DlN\nnbTuNTXffvutyQs9ZUntRX7nzh3p3bu3uLm5iZubm7z66qty+/btdPtOa6wsjeuJEyekU6dO4unp\nKU5OTlKuXDl5/fXXTV7Mqb2mRURu3bolXbp0EWdnZ/H19ZXJkydL3759JSgoSHN/BoNBYmNjNddL\n/d5o0KCBdO/eXb766ivx8/MTJycnadeuncaLWkTk+vXr0qtXL/Hw8BAnJydp2rSp/Pnnn2Z9v/32\n2xrZ1atXpVevXlK6dGlxdHSUokWLSq9eveTy5cvpjmF6n1+ywWtaSRrLmEqpEhZPpG3Q826BPZtQ\nSkla45FlvvwS3kwR7GvAAPjmG02VUaOMjtbJlCwJf/8Nthk8yT93+xzVZ1cnKvaxI4dCMbP1TF4P\nej0blNfJKkop/ZGBzr+CR48eUbFiRRo1asQ3qb7j8ivpfX6TzmXJ6SG9EJf53rA+VaSOzRoeblZl\n1Cj4v/+D5Ljo4eGweDH07Jl+16XcSzH/pfl0WPx4W5Mg/GfDf7h6/yqhjUP1OK86Ojo5wpIlS4iM\njKRy5crcuXOH2bNnEx4ezpIlS/JatXzDU5828JkhHWetZIoWNW5nSsnHHxvDXGdE+/LtmddxHjZK\n65Tywe4PeH3963q2Jh0dnRzB2dmZ7777jg4dOtCzZ0+ioqJYv3491apVy2vV8g1pLk1rKil1Hm0m\nppQkAlEYo1Z9KSKWUhzmC3J0afrePeMWpmTs7CA6GlJ5c547ZwxJndL4rloFSVHoMmT96fWELAsh\n+lG0Rv5yhZdZ+PJCHGyfzqDnzzr60rSOTv4lp5emrZ0R78K4p9cXY7CMsKS/RTEub0dg3N97UCmV\nO4lD8xsFC0LK/YXx8cZMTqkoVcoYuCslkyeb4n9kSJtybdjRewcejtr9dCtPrKTFghbciTHf06mj\no6Ojk3dYa4j3YJz1BohIUxHpISJNgQDgLsYtTWWAw0A2RMB+RrFieRrgrbe0xwcPQma25b1Q/AV+\n7fsrfq7avX+7I3bT6IdGXLmXZpIqHR0dHZ1cxlpDPA74QESuphSKyBXgI2CciDwAvgDyZ7LK3CC1\nw1YahrhyZeigDSfNpEmZu1QFrwrs7beXil4VNfIj145Qd25d/r75d+Y61NHR0dHJEaw1xH5AbBrn\nYjBmZwK4DNhnValnltQzYgue08mMH6893rnTmEsiM/gV8mNP3z3U9dM+LQi/E069ufU49I/lQO46\nOjo6OrmHtYb4BDBKKaVJqKmUcgBGJ50H4zPja9mn3jOGlUvTALVrQ+oEJh9/nPlLejh6sLXXVtqU\nbaORX394neB5wWw9uzXznero6OjoZBvWGuKxwAvABaXU90qpKUqp7zE6adUGxiTVq4sx25GOJaxc\nmk7m7be1x+vWaaNkWouTnROruq6iT9U+Gvn9uPu0+akNi48tznynOjo6OjrZglWGWES2AdWB7UBD\nYGjS321AVRHZnlRvmIgMyiFd8z+ZWJoGCA42zoxT8sknT3ZpOxs75rafy7h64zTy+MR4uq/ozpe/\npZN7UUcnBStWrKBp06a4u7vj4OBA+fLlGTVqlClQf0REBAaDgQ0bNuSxpuYsW7aMefPmZVt/IsIb\nb7yBj48PNjY2fJAyYHwKzp49y2uvvcbzzz+Pra0tTZqkncJ98uTJ+Pv74+TkRKNGjTj8JL++s4DB\nYOCrr77KVBtrX/PQ0NA0Mzn9m7E6oIeI/JXkLV1aRJyS/r4iIicybq0DQIlUUUMvXTJuY0oDpcxn\nxUuXGsNePglKKT5p9gnTX5xudu7NTW/yzvZ39L2uOukyatQounbtSpkyZViwYAFbt25l5MiR7Nix\ngyFDhpjqPa2R3JYuXZqthnjlypXMmjWLKVOmEBYWlmbCh+PHj7Np0yYCAwMpX758mv19/PHHTJo0\nifHjx7Nu3TpcXFxo1qyZxbR/OUVYWBghIelmqbWINa+5UuqpfW/kKVkNVv0sFXIjML+Pjzazw5kz\n6VZPSBCpXFnbZMCArKux4PACsf3AVpMsglCk/+r+Ep8Qn/UL6GjIlfdWDrNmzRpRSskPP/xgdi4x\nMVE2bdokIiLh4eGilJL169fntooZ0rlzZwkODs62/j788EPx9PTMFh1iYmKkUKFC8tFHH5lkDx48\nEC8vL3nvvfeyrGtOYu1rbk3ikCclISFB4uLicqTv9D6/ZEPShzRnxEqpuUqpgBT/p1e+y5VfDc8C\nmVyeNhjMZ8Xz5hkn01nhledeYV33dTjbaVO8fffHd3Ra2ono+Og0Wur8W5kxYwY1atSgd+/eZueU\nUqZ0fZZITEwkNDSUEiVK4ODgQOXKlVm0aJGmzl9//UWrVq3w9PTExcWFihUrMmvWLE2d1atXExQU\nhKOjI76+vowbN46EhMfhWy9fvkyXLl3w9vbGycmJMmXKMGHCBAD69u3LihUr2LVrFwaDId2lZDDm\nVx42bBi+vr44OjpSq1Yttm597NwYHBzM+++/z+3bt039XbhwIf1BTId9+/Zx7949zWzUycmJdu3a\nsXHjxnTbBgQEMGbMGGbMmIGfnx8eHh50796du3fvaurdvn2bQYMG4ePjg6OjI/Xq1dPkNwbLS9Pv\nvfce3t7eFCpUiAEDBrB48WIMBoPZ/T58+JDBgwfj5uaGn5+fKUWkpXutUaMGjo6OVKtWjb1792rO\nW/N+6du3L0FBQaxevZrKlSvj6OjIgQMHiIqKYsCAARQrVgxHR0dKlCjBa6+9lu745TlpWWiMkbOe\nT/o/POk4rXIuq78InoZCbsxaevTQTm+/+SbDJvHxIqVLa5sNH5496vx26TfxnOJpNjOuP7e+3Hp4\nK3suopPxjDjli5tTJQvEx8eLg4ODvPvuuxnWtTQ7evvtt8Xe3l4mT54sW7Zskddee02UUrJ48WJT\nnVKlSkm7du1k06ZNsmPHDpk1a5ZMmTLFdH7JkiViY2MjQ4YMka1bt8rXX38tbm5uMmbMGFOd4OBg\nqVu3rqxZs0Z27dol33//vYwbN05ERM6ePStNmjSRGjVqyIEDB+S3335LN/1djx49xNXVVWbOnCmb\nNm2STp06iZ2dnSk14okTJ2TAgAHi7u5u6s+aGVlaM+KvvvpK7OzsJDExUSP/9NNPxcXFJd0+S5Ys\nKf7+/tKuXTvZuHGjfPPNN+Li4iJvvPGGqU5sbKxUq1ZNSpcuLQsWLJDNmzeb0jheu3bNVE8pJTNn\nzjQdT58+XWxsbCQ0NFS2bt0qQ4YMEX9/fzEYDBIRESEij1/zgIAAGT16tGzbtk3Gjx8vSilZtuxx\nStbQ0FBxcnKSUqVKybfffivr1q2T4OBgMx2seb/06dNHChcuLOXLl5eFCxfK9u3b5dKlS9K3b1+p\nUKGCLFu2THbv3i0LFy6U1157LaOXJV3S+/ySDTPiPDd+T1PJFUP89tvaL8d33rGq2Zw52mZOTiKR\nkdmj0snrJ6XE5yXMjHHlryrLpahL2XORfzn53RBfvXpVlFIyZ86cDOumNsS3bt0SZ2dn+fDDDzX1\nWrduLYGBgSIicuPGDVFKybFjx9Lst0SJEtK/f3+NbO7cueLk5CS3bhl/NLq4uMi6devS7MPapekT\nJ06IwWCQH3/80SRLTEyUypUrS8uWLU2yJ1lqTUuHSZMmibu7u5k8OZdvfHzaj4xKliwpZcqUkYSE\nBJNs+PDh4uvrq+mnQIECcvbsWZMsISFBSpcuLWPHjjXJUhrihIQE8fX1laFDh2qu17p1a4uGuE+f\nPpp6VatWle7du5uOQ0NDxWAwaAzq/fv3xcPDw5SX2Jr3i4jREBsMBjly5IimXuXKleX//u//0hyr\nJyGnDbGefSm3ycRe4pS8+qoxO1MyDx8aUxxnB+ULl2df/31UKVJFIz8WeYy6c+ty8sbJ7LmQTr7n\nSRxtjh07RnR0NJ07d9bIu3btyunTp7l58yYeHh74+fnx2muvsXTpUq5fv66pe/r0aS5cuEBISAgJ\nCQmmEhwcTHR0NMeOGXPNVK1albfeeot58+Zx8eLFJ77PgwcPAmh0VkoREhLCr7/++sT95iTBwcEY\nDI+/0itWrEhkZKRp6X779u3UqFGDEiVKmMYvMTGRRo0aceiQ5eA+Fy9e5OrVq7Rr104jb9++vcX6\nzZs31xxXrFiRSxaeo3VMkcXG2dmZ5s2bm5bIjx49muH7JZlixYpRpYr2e6tq1apMnTqVWbNm8feT\nerbmMlYbYqWUs1JqmFJquVLqF6VU2SR5N6VUYM6p+IzxhIa4QAEYPVor++9/ISoqe9QqWrAou/vu\npoF/A438QtQF6s+tz4HLB9JoqfNvwNPTkwIFCjzRM9DkbU3e3t4aefLxrVu3UEqxdetWfH196d+/\nPz4+PjRs2JA///wTgBs3bgDQunVr7OzsTKVUqVIopUxGd+nSpQQFBTFy5EhKlChBtWrV2LFjxxPp\n7OLigoODNluZt7c3Dx8+JD6d3Q5Piru7O/fv309enTNx+/ZtnJycsLVNM308AG5ubppje3t7RITY\nWGNQxBs3brB//37N+Nnb2/PDDz+k+aPl6tWrKKXMthyltQXJkg4xMTEamYuLCwUKaGJDUaRIEdP7\n5OpVYyTl9N4vqWUpmTlzJi+99BIffvgh5cuXp1y5ck99bmSrDLFSyg84AnwKlMW4h7hg0ulgjNG1\ndKwhdVCPDJy1UjJwoDaBU1QUpPJlyRJuDm5s7rmZDuW1ga5vRt8keF4wm85syr6L6WjJjcXpLGBr\na0u9evXYvHlzptv6+voCmG3BuXbNGITPw8OYKaxcuXIsW7aMO3fusH37dmJiYmjbtq2mzjfffMOh\nQ4c05eDBg7Rq1cp0rblz53Lz5k3CwsLw8fGhQ4cO3L59O9M6379/38yIXLt2DScnJ+zs7DI5ChkT\nGBhIQkICZ86c0chPnjxJYGDW5zoeHh4EBQXx+++/m43fqlWrLLbx8fFBRMxWKFIfZ4b79++bfhwk\nExkZaXqfWPt+AcsrNK6ursyYMYN//vmHI0eO8MILL9CzZ09Onnx6V/asnRF/hjHWdDmgBpDy7ncB\nDSw10rGAn5/RFTqZK1eMeYmtwMUF3nxTK5s+3bhMnV042jmyvMtyBlTT7od8GP+QdovasfDIwuy7\nmE6+Yvjw4Rw6dIj58+ebnRORNI10skfrsmXLNPIlS5ZQrlw5PFP+ugRsbGxo3LgxI0eO5MqVK9y5\nc4fy5ctTrFgxzp8/T/Xq1c2Ku7u72XVr1arFhAkTePjwIREREYDlGZolgoKCAFi+fLlGvnz5cho0\nyJmvu7p161KwYEHNOD18+JC1a9fSunXrLPfftGlTzpw5g5+fn9n4VapUyWIbPz8/fHx8WL16tUae\n+jizpDT89+/fZ+vWrdROil6U2fdLelSuXJmpU6eSkJDwVBvi9Nc6HtMcGCQiEUopm1TnLvM46YNO\nRtjbQ7FikHIpKCICrPzFO2QITJ0K9+8bj69fh7lzjfLswtZgy5x2c/Bx8eGjPR+Z5I8SH9FzVU8i\nH0Qyos6I7LugTr6gbdu2jBgxggEDBrB37146dOiAi4sLJ06cYPbs2QQEBFjcwuTu7s7w4cP56KOP\nsLGxoWbNmqxYsYJNmzaxeLExvOrRo0cZPXo0Xbt2pVSpUty6dYspU6ZQtWpV03LnZ599Rq9evYiK\niqJVq1bY29tz9uxZVq9ezYoVK4iLi6NFixa8+uqrlCtXjpiYGKZPn46Pjw8VKlQAjLPONWvWsHr1\naooXL07RokVNM7CUBAYG0r17d4YMGcLdu3cpXbo0c+bM4dSpU8yePTvTYxcdHc2GDRsQES5fvsy9\ne/dYsWIFAG3atMHBwYECBQrw1ltv8dFHH+Hm5kZgYCCfffYZIqIJlvKkvPrqq8yePZtGjRoxevRo\nSpUqxc2bNzlw4AC+vr68mfpXPsatTGPGjGHMmDEULlyYevXqsWbNGtMz+ZTPpK3FwcGBd955h3v3\n7uHr68u0adOIj49n2LBhgHXvl/Ro0KABL730EpUrV0YpxZw5c3BxcaFWrac4MaA1Hl3AA6Bl0v82\nQCJQPem4PXAnq15jT0Mht4IuNGyoXTTcuDFTzceO1Tb38xOJjc0ZVb8M+1JUqDLzqB67ZazZNgud\ntMm191YusHLlSmnSpIm4ublJgQIFpHz58jJ27FjT9pPw8HAxGAya7UuJiYkSGhoq/v7+UqBAAalU\nqZIsWrTIdD4yMlJeffVVKV26tDg6Ooqvr6+88sorcvHiRc21N23aJA0bNhQXFxcpVKiQVKtWTd5/\n/31JSEiQ2NhYGTRokAQGBoqzs7N4eXlJu3btNJ7YN27ckJdfflk8PT3FYDDIxIkT07zP6OhoGTZs\nmPj4+IiDg4MEBQXJ1q1bNXWs9ZpO9io2GAxmJdnzOJnJkyeLn5+fODk5SaNGjeTw4cMZ9h8QEKDx\nfBYR+eGHH8RgMMiDBw9Msrt378rw4cNNr4Ofn5906tRJ9u3bZ6pjMBjkq6++0vT13nvvSZEiRcTV\n1VV69eols2bNEoPBIFFRUab7S/2aixg9m4OCgkzHyeP166+/StWqVcXBwUGqVasmv/76q6ZdRu8X\nS30nM3bsWHnuuefE1dVV3N3dpUmTJqYtZ09Kep9fssFrWokVz46UUvuBYyIyMGlGHA/UFJH/KaVm\nAeVEpGn6vTz9KKXEmvHIMn36GKNyJPPVV/D661Y3v3rV+Kg55WOW7783dpsTLDm2hF6rehGfqHVQ\nCW0UyoTGE3Lmos8YSikzJxwdnfzKgAED2L59O+etdDbN76T3+U06l6W4ndYuTX8KLE96MP5Tkqyi\nUqoD0B/jrFjHWjKZhSk1Pj7Qv7/RfifzySfQqxfYpH5wkA10rdwVTydPXlryEvfj7pvkobtCKeZa\njAHVLcfX1dHRyf8cP36cJUuWULduXZRSbNy4kXnz5jF16tS8Vu2ZwdrsSyuB/wAhGDMuAcwHhgND\nRCRT7rRKqeJJ26DuKKWilFIrkjyzrWlbMqntbaXUfaXUDqVUDQv1lFJqvFLqvFIqWin1p1Lq5czo\nmWNkMsylJcaM0RrdU6cgDcfHbKFZqWbs7L0TD0cPjXzwusGsO70u5y6so6OTpzg7O/Prr7/yyiuv\n0KFDBzZu3MjUqVMZMUL3E8kurFqaNlVWyhmoAxQBbgL7RORepi6olCPGrVDRwDtJ4kmAI/CciKTp\nQqFgaLYAACAASURBVKyU8gCOAlHA+0l9jMboyR0kIqdS1J0EjATeBv4HdAMGAW3S+uGQa0vTu3dD\no0aPj2vWhKQAApkh9Qp3tWrw++/GrE05xb6L+2g6vykxjx57njraOrKj9w5eKP5Czl04n6MvTevo\n5F9yemk6U4Y4O1BKvQlMw/hc+XySrCTwNzBGRGak0/ZdjAa4nIiEJ8mcgHPAThHpliTzAi4Ck0Xk\ngxTttwGFRaRqGv3njiG+cEGbEtHTE5ICFmSGEyegUiXtFtGNG6Fly2zQMR1+PvkznZZ2IlESTTJP\nR0/29d9HOc9yOXvxfIpuiHV08i9PjSFWShmAWoA/4JD6vIiYby603M82oICINEgl32nsRoLTabsW\nKCUilVLJlwGtAFcRSVRK9QJ+wGiwz6ao1wf4LqmPCAv9544hTkgAR0dtLuK7d6FgwbTbpEHnzpC0\nCwKA+vVhz55s0DEDvj70Na+v1zqYlXQryf7++/Fx8cl5BfIZuiHW0cm/5LQhtjayVkXgJLAXWIzR\nyKUs32fimpWAYxbkx4GKGbRNAOIsyGMxLm2XTjquCMSmNMIprqGsuE7OYmMD/v5a2RM8JwYYP157\n/OuvuWOIB9cczLsN3tXIwu+E03pha+7FZupphY6Ojs6/Gmt3Y3+F0cO6CxAIBKQqpTJxTQ/AUry5\nW4B5eBwtp4CySilTPWV05a6dou/kv3fSuEbKenlHFkJdpqRGDUgdQ2Hy5CfqKtN8EPwBfav21cj+\nuPoHnZZ2Ii7B0u8lHR0dHZ3UWLt9qTrQJ8l7Oi/5GhgG/KiUGsZjh6+SSecT02j39PGEyR8s8fbb\nkDK64KZNsGEDZENUvHRRSjG77Wyu3r/KxjOPE5dvPbeV/mv6M7/j/CfK1vMsUqJECX0sdHTyKSVS\n+vTkANYa4htYXhJ+Em5jeeab1kzZhIicV0r1AGYCZwDB6BE9HaP39JUU13Cz0EXyTPiWhXMAhIaG\nmv5v3LgxjRs3Tk+lJycbDXGDBlCvHuzd+1jWsSPMnw/duj1xt1ZhZ2PHspBlBM8L5uA/jz2/FxxZ\nQLGCxfik2Sc5q0A+IfwJVzx0dHSeLnbu3MnOnTuztU9rI2sNBVoDbUUkIUsXVGo7YCciDVPJfwFI\nz1krRV2FMQFFXJJxngW0EpGSSeeTnbXKisi5FO368DQ4awH89BO88srj444ds7QReNs2SJUKFIAv\nvoCkEK45SuSDSOrNrceZW9rMMV+2/JKhtYfmvAI6Ojo6eUCuOWsBXkB54C+l1P8ppT5IVSZm4ppr\ngBeStiwBpu1L9QCrUnokhfg8lWSEi2J8dp0izhSbgEfAK6ma9sQYqtPMCOc62TgjBmjWzGh0U/Pm\nm/DOO1nOgpchRZyLsOmVTXg5afOUvrnpTZb/tTyNVjo6Ojo61s6IM3r2KiJiVXDFpH2/f/5/e/cd\nJlWRNXD4dyYAAxIFkQyCGcQEJkRUJKwgrgFFYcG86IKBz5wQBcy65hwQcRWMqEQFA6DoIiq6BpCg\nEgTJGWbO90fddrp7umfuMN19u2fO+zz3mem6oaqB5vStW1UH93z3Zq94GFANaKuqm73jmuLmBw9V\n1Tu8shzgblzqxfVAa+A63Bzkzqq6M6yekcDluGfIoQU9LgJ6qmrhA83ItqXujnjZMmjYsPB1jRqw\ndm2ZV+MYMwb694edOyPLL7gAnngCSsgtXmZfLv2STi90YtOOTX+VVc6uzOR+k+nYrGMxZxpjTOZJ\n2R2xqmaVsPle4dgLtCcAP+GWyXwJWACcGArCHgnb/jod2Bs3aOt93MCtZ3CZoaJCDzcAd3jHTMSt\nCHZmvCCccnvuCVXCpmOvX+8CcRmdcw689x5UqxZZ/uyzbs6xz9THu+zwhoczrvc4ssOyZW7L38Yp\nr5zCvD9izVozxpiKLeUra6WzlN4RA+y/P4Qnq/7vf+HQQxNy6dmz3ajpP/+MLO/QAd55B2LkUU+o\nF+a+wHlvR05talyjMTPPn0mTmr6WFTfGmLSXymfEJhnKmIWpOO3bu1HU0euGfPopdOwIS5cmrKqY\nBhw8gOEnDI8o+239b3R/uTtrt5b9zt8YY8oLC8RBSkAWpuLsuy/MnAmtW0eWz5sHRx/tMjYl0/Ud\nrufSwy+NKPtu5Xf0+k+viKQRxhhTkVkgDlKCR07H0qiRS/bUoUNk+eLFrmwXkj75JiI81P0h/r7f\n3yPKP178Mf3e7Ed+QZlmwhljTLlggThISeyaDle7NkyeDKecElm+ahUcf7zblyzZWdm8fNrLHNPk\nmIjycd+P48pJV1oiBGNMhRc3EIvIGyLSyvv9HyKye+qaVUEkuWs6XF6ey9J0/vmR5Zs2wcknu2lP\nSas7N493+rzD/nX3jyh/ePbD3DPznuRVbIwxGaC4O+JeFC4J+TyFmY1MosQKxEm8Q8zJgWeecWtT\nh9u50y3yFWtBkESpk1eHiX0n0rB6w4jya6dey+hvRievYmOMSXPFBeIVuLm34ObyWh9iotWpA7vt\nVvh682ZYuTKpVYrA8OGxg+4VV7ggnazvAk1rNmXCuROoUblGRPl5b5/HlAVTklOpMcakueIC8WvA\nAyKSjwvCn4lIfpwtejEN44dISgZsxTJ4sOuOzs2NLB85Ei68sOjKXIlyUP2DeOust8jNKqx4Z8FO\nTnvtNOYsm5OcSo0xJo3FXdDDS6xwBnAAcCsuicLv8S6kqjfH25cpUr6gB0CvXm6FjZBXXkl+yqQw\nkyfDaae5Z8XhevaE//wHqlZNTr3/mfcf+rzeJ6KsfrX6zLpgFi1qt4hzljHGpJdELOgRd+VhLyKN\n9SoaAPxbVb8uS2UmhuiR0ylOl9elC0yb5lbhWrWqsHz8eLdv/PjkrMJ1duuzWbZhGVdNvuqvshWb\nVtB1dFdmXjCTulXrJr5SY4xJQ37Xmm5hQThJAuqaDteunVtxKzr39YwZbhWu3+P2g5TNlUddyVVH\nXhVR9vPqn+kxpgebd2yOc5YxxpQvvucRi0gDEblXRL4QkQXez7tFZM9kNrDcS9Fc4pKEVuFq0yay\nPLQKV/iS2Il0T5d76NM6sov6898/56xxZ7GzwIYeGGPKP1+BWET2Ab7GZTLaCMz2fl4OzBWRvZPW\nwvIuhXOJS9KwoVuF69hjI8uXLHGrcM2enfg6sySL53s9zwktTogof/endxn47kBb8MMYU+75zUf8\nJi7370mquiisvBkwGfhOVU9LViNTJZDBWuvWQa1aha8rVXK5CrOCW/Rsyxbo0wfefjuyvGpVeOMN\n6No18XWu27qOji905JsV30SU33jsjdxxwh2Jr9AYYxIgldmXjgduDg/CAKq6GBjq7Te7ombNyNFQ\n27cnPzVSCfLyYNw4uOCCyPLNm6FHD3j55cTXWbNKTSacO4GmNSPTRQ3/ZDgPzHog8RUaY0ya8BuI\nKwEb4uzb4O03uyqNuqdDcnLg6afhxhsjy3fuhL594cEHE19nw+oNmXjuRHbPi1xN9arJVzHq61GJ\nr9AYY9KA30A8FxgkIhHHe3ONL/X2m12VBiOnYxGBO+6Ahx4quu/KK+GppxJf5/719uf9c9+nWm61\niPLz3z6f8T+OT3yFxhgTML+BeBjQGfifiAwTkYEichvwHXAScFuyGlghpMnI6XgGDXLrjESvwnXp\npTBhQuLra9+oPW+dHbn6Vr7m03tcbz5e/HHiKzTGmAD5nUc8EeiB64a+EXgUuAk3crqHqiYxkV4F\nkIZd09HOPhvee889Pw7Jz4czz4Svvkp8fZ336syY08cgFI6B2LpzKz1f6cnc5dYBY4wpP3wPzVXV\niap6OFAdaAJUV9X2qjopaa2rKNK0azraSSe5O2MJGx8YSqO4ZEni6zvjgDN4oscTEWXrt62n6+iu\n/Pznz4mv0BhjAlDqOTKqullVf1dVW/ooUdK8azpcr15FMzctW+aWyFy7NvH1XXzYxYw4YURE2R+b\n/qDL6C4s3RDs6HJjjEmE4CarmkLRgfi335KX/igBBg1yg7XCffcdnH66m32VaNd1uK7IUpiL1i6i\n6+iurN6yOvEVGmNMClkgTgdVq0L9+oWv8/Ph11+Da48P997rsjaF+/BDuOiixOczFhHu6XIP/dv2\njyif98c8eozpwabtm+KcaYwx6c8CcboIOAtTaWVlwejRcOSRkeWjRsHQoUmoT7J45pRn6LlPz4jy\nWb/N4oyxZ7A9Pwm34sYYkwIWiNNFhgzYCpeX51Ipt2wZWT5sGDz/fOLry8nK4dUzXuXYppGLYU+c\nP5EBbw2gQAsSX6kxxiSZBeJ0kYGBGKBePTeXePfIxbC4+GKYMiXx9eXl5jG+z3ja1m8bUf7KvFe4\nfMLlliTCGJNxSpMG8RAReUNEVonIThE51CsfISLdktfECiLDuqbD7b23uzOuXLmwbOdON3jrm2/i\nn7eralapyaS+k2hVp1VE+SNfPMKwj4YlvkJjjEkiv2kQOwCzgP2AMVHnFQD/LE2lItJYRMaJyFoR\nWScir4tIE5/nNhGRF0VksYhsFpEfReR2EakaddwiESmI2vJF5JTStDVlMvSOOOToo90z4/A5xhs2\nuGlNv/+e+Prq71afyX0n02C3BhHlQz8ayiOzH0l8hcYYkyR+74jvBCYBBwJXRe2bAxzqt0IRyQOm\nAfsA/YC+wN7Ah96+4s6tCnwAdMCt8NUdeBoYAjwbdbgCE4Ejw7ajgI/8tjWlMmgucTxnnAH33BNZ\n9vvvbsGP9esTX1+L2i2Y3G8ytarUiigfNGEQY74dk/gKjTEmCXJ8HncocJqqqohEP4RbBdQrRZ0X\nA82BfVR1IYCIfAv8DFwCFJfX5xigJdBVVad6ZR+JyO7AEBGpoqpbw9umqklIZ58ETZu628nQM86l\nS2Hbtsj+3gxw1VWuV/2RsJvSr792S2G++27R9arLqvUerXn/nPfp/FJnNu8oXGOm/1v9qV2lNt33\n7p7YCo0xJsH83hFvBarG2dcAWFeKOnsCn4WCMICX53gG0KuEc0PpFqPrW4d7L2VKzhyoypWhUaPI\nssWLg2lLGYi4FImnRD0AmDwZBg5M/BxjgKOaHMXrvV8nJ6vwe+XOgp2c/trpzPx1ZuIrNMaYBPIb\niD8FrhCR7LCy0H+pFwAflqLOA4F5Mcq/Aw4o4dypuDvnu0VkfxGpJiInAIOBx1V1S9TxPUVkk4hs\nFZFZIlJSoA9WOeieBsjOhjFj4PDDI8uffRZGjIh9Tll1a9WNUaeOikgSsWXnFk4eczLfrvg2OZUa\nY0wC+A3EN+O6p7/2flegv4hMwz17LU0axDrAmhjlq4HaxZ2oqtuAY4FsXODeAEwBxqvqoKjD3wEG\nAV2Ac4AtwJsick4p2ppaGZCFya9q1VxXdPR3i5tucoO6kqFPmz488rfIgVprt66l6+iu/LLml+RU\naowxZeQ3DeLXQEdgBW6QlAD/8nYfp6o/Jqd5kUSkMvAasAdwrtemq4GzReSxqDZfrqqjVXWGqr6B\ny6f8JZCke7IEyPCR09Hq13dzjGtHfb06/3yYNi05dV7a7lJu6xT5vXDZxmV0eakLyzcuT06lxhhT\nBn4Ha6Gqc4ATRaQK7q527S5mYFpD7DvfeHfK4S7EBd9WYc+YPxWR9cCTIvK4qsbsh1TVAhEZC9wp\nIvVVdUWs44aGrc/YqVMnOnXqVEKTEqicdE2H228/eOstl0IxlBBixw74+99hxgw48MDE13lzx5tZ\ntXkVD89++K+yBWsW0G10N6YPmF5klLUxxvg1ffp0pk+fntBrip+ViEQkF6ikqkVW1xeRasB2Vd3h\nq0KRD4BcVe0YVT4NQFWPL+bcx4Heqrp7VPlBwFzgbFV9rZjzr8ZNxWoYKxCLiAa6MtP06XB82Ntv\n3x4+/zyw5iTSK6/AOVEPBZo2hc8+gwYNYp9TFgVaQL83+xWZxtShaQcm9Z1E1dx4Yw+NMcY/EUFV\nyzRQ2O8z4mdw83VjedLb/HoHOFJEmocKvN+PAd4u4dzlQC0R2Suq/Ejcc+u4S0d4A83OBpbEuxsO\nXDnrmg7Xpw+MHBlZtmQJ9OgBGzcmvr4syeKFXi/QvVXk9KVPl3zKWePOYke+r++NxhiTdH7viJcA\nV6vqqzH29QbuUdVmvip0i3LMxQ2eutkrHgZUA9qGurtFpCnwCzBUVe/wyprhBowtxz3rXQK0A24C\nflDVI7zjzgZ6AO/jgnMD4DLgaNxd89g4bQv2jnjnTqhSxaVBDNm40Y18KgdU4Z//hKeeiiw/+WTX\nfZ3j+0GJf5t3bKbLS12Y8euMiPK+B/XlxVNfJEtsuXVjzK5L5R3xHsAfcfatBOrH2VeEF2hPAH4C\nRgEvAQuAE6OeOUvYFjp3Me7udy5wO/AebvrUE7jR0SELgT2B+4DJwGO4wN81XhBOCzk5rr82XAaP\nnI4mAo8+Ct2j1th47z0YNCg5c4yr5lZlfJ/xtNmjTUT56G9Gc9WkqyxJhDEmcKW5I75XVR+KsW8w\ncK2qNip6ZmYJ/I4Y4MQT4cOwadnjx7v+23JkwwY47jj46qvI8rvugmuuSU6dyzYs45jnjmHh2sju\n/sHtB3NTx5uoV600i8MZY4yTyjvid4GbvUFR4Q1og5vONL4sjTBhMjgLk1/Vq7s5xk2i0nxcey28\nWuThR2I0qN6AKf2mUL9aZOfNQ7MfoumDTblk/CX8uCols/CMMSaC30B8C7AW+K+IzBSR10RkBi7h\nwzrcM1qTCOV4wFa4hg3h/fehRo3I8n/8Az75JDl1tqzTkkl9J1Gzcs2I8q07t/LUnKfY79H96PlK\nT6Yvmm5d1saYlPG7oMcq3KCokbhntgd7P4cD7bz9JhHK4VzieFq3hjffjEwEsX079OoFPybp5rTt\nnm1575z3qFc1dlf0uz+9y/EvHs/hTx/OmG/H2OhqY0zS+XpGXFGkxTPiGTOgQ4fC14ccAnPmBNee\nFBg1Cvr3jyxr0QJmzXKrcyXD+m3reWbOM/z783+zZN2SuMc1qdGEwUcM5qJDL6JmlZpxjzPGVEyJ\neEZsgThMWgTipUsjszDVqgVrSlpwLPMNGwa33hpZdthhbkR1soIxuCxN474fx32z7uPLpV/GPa56\npepceOiFXH7E5TSr5WumnjGmAkhpIBaR/kAfoClQJWq3qmrLsjQkHaRFIC4ogKpVXS7ikDVrXEAu\nx1Thggvg+ecjy5s0cXOMDz002fUrnyz5hPtn3c87P76DEvvfQbZkc/oBpzPkqCG0b9Q+uY0yxqS9\nlAViEbkZl2Fpnrdtiz5GVc8rS0PSQVoEYoB994Wffip8/dVXcPDBwbUnRXbscIt7TJkSWV6lCjz3\nnFudKxV++vMnHvzsQV6Y+wJbdkZn1izUoWkHhhw1hJ779CQ7KzvuccaY8iuVgXgR8KaqXlmWytJd\n2gTibt1g0qTC12+84bIkVADr18Npp8EHHxTdd+21MHy4y3ecCqs2r+KJL5/gkdmPsGJT/FVRW9Vp\nxZVHXsmAgwfYGtbGVDCpnEe8OzZXOHUq0MjpaDVqwMSJcMUVRffddRf07Alr16amLXWr1uWmjjex\n6IpFPHvKsxxYL3aqqPmr53PZ+5fR5IEm3PThTZZu0RhTKn4D8UdA22Q2xISJnktcDhf1KE5ODjzw\ngHteXKlS5L4JE+CII+CHH1LXnio5VTj/kPP5duC3TDh3Ap336hzzuNVbVjP8k+E0e7AZ5799PvP+\nmJe6RhpjMpbfQHwFcJ6I/ENE6opIVvSWzEZWOBVkUY+SDBgAH31UNE3iTz+5YPzee6ltj4jQrVU3\npvSbwtxL5tK/bX9ys3KLHLc9fzvPz32eNo+3odvobny65NPUNtQYk1H8PiMu8H6Nd7CqahJy56RW\n2jwjnj3bRZqQAw+EeRX37mrpUveIfPbsyHIRGDHCPTuWMj2hKUPbNizlkdmP8MSXT7Bma/xpZj32\n6cHIE0fSeo/WKWydMSbZUjlYayjxgzAAqnpbWRqSDtImEK9cCXvsUfi6WjWXKSGoaJMGtm51KRRf\nfLHovrPPhmefdbO+grJx+0ZemPsCD3z2AL+s+SXmMYLQr20/hnUaZnORjSknbEGPBEubQKzqMiNs\n2lRY9scfUK9iZwhShX//G4YMcdOtwx1yiJtvHJ1FMtXyC/J5+8e3uW/Wfcz8dWbMYyplV+Kydpdx\nw7E3ULdq3RS30BiTSBaIEyxtAjG4hZi/+67w9ezZ0K5dcO1JI1OnQu/eRRccq1cPXn8djj02mHZF\n+2TxJ1z3wXVxA3KNyjW4+uirufLIK6lWqVqKW2eMSYRUr6xVCegO7EvslbVuL0tD0kFaBeKePV2u\nwJBXX3XRxwAwf75LDvH995HlOTnwyCNwySXBtCuaqjL+p/Fc/8H1fL/y+5jH1K9Wn1uOu4WLDr2I\n3Oyig7+MMekrlc+IGwKfAs1xz4pDlf51sqpm/NJCaRWIBw+Ghx8ufH3nnW5UkvnLhg3Qrx+8/XbR\nff/8p+vGjp7+FJT8gnxe+uYlbpl2C7+u/zXmMS1rt+SOE+6g94G9ybKJCMZkhFQu6HEPsBK3zrQA\nRwB74dIgzvd+N4kUvahHBZtL7Ef16m7RsVtuKbrviSegc2f3aD0dZGdlM+DgAfw06CfuPele6uTV\nKXLMgjUL6PN6H9o93Y4pC6bEuIoxpjzyG4iPBe4DlnqvC1R1kareAowDHkpG4yo0m0vsS1YW3HYb\njBvnBpeH++QTOPxwt1R3uqiSU4UhRw9hweAF3NDhBvJy8oocM2fZHLqM7kLnUZ2LzQhljCkfSrPE\n5TJVLQA2AbXD9n0IdEpwu0wFXuZyV5x+OsycWfSP7ddf4Zhj4D//CaRZcdWqUovhJw5n/uD5XHLY\nJWRL0Sc7Hyz8gHZPt6P32N78/OfPAbTSGJMKfgPxb0BoYusCoEvYvvbA1kQ2ylD0jnjx4qJzdkyE\ngw6CL76A44+PLN+yxWVuuv56yM8Ppm3xNKzekCd6PMH3l33PmQecGfOYsd+PZf9H92fguwNZtmFZ\niltojEk2v4O1ngC2qerlIjIQeBSYCuwAugJPquplSW1pCqTVYC2A2rUjMxz8/js0bBhcezLEjh3w\nf/8HD8V4YPK3v8GYMVCzZurb5ceXS7/kuqnX8cHCGOmngKq5VbniiCu45phrqFklTd+EMRVIKkdN\n1wXqqOpP3utBwFlAVWAiMExVM/6uOO0C8SGHwNy5ha8//dT1sxpfnnsOBg6E7dsjy/fd14203nff\nYNrlx5QFU7jug+uYs2xOzP118upwQ4cbuKz9ZVTJiZ5NaIxJFVvQI8HSLhCfdhq8+Wbh69Gj4dxz\ng2tPBpo1y/0xLo/KTFizJrzyCnTvHky7/CjQAsZ+N5YbP7yRBWsWxDymSY0mXNfhOhpVb5TUtmRn\nZZOXk0debh55OXlUza361++hn9lZGT+D0ZhSS+Ud8YfApapaJPmciOwDPKGqJ5SlIekg7QLxkCFw\n//2Fr2+/HW66Kbj2ZKjff3dJI774IrJcxE3NvvpqqFN0NlHa2J6/nWfmPMOwj4axYtOKoJsTV25W\nbrGBOmJfjPLGNRpzQosT2L3q7kG/FWN8S2UgLgCOVNXZMfYdBsy2BT2S4OGH3cIeIeef77IbmFLb\nsgUuvth1KkSrXh3+9S+46iqom8ZLP2/cvpEHP3uQu2fczYbtG4JuTlJkSRbtG7WnW8tudN+7O4c3\nPNwWNzFpLdWB+AhV/SLGvt7A06qa8SNH0i4Qv/uuW+oy5IQT4IPYg3hMyVThgQfcHXCsAejVqsGl\nl7qOiPr1U98+v1ZtXsWIT0bw6BePsj1/e8knZLC6VevStWVXurXqRteWXalXrWInPjHpJ6mBWETO\nA87zXh4DfANEfw3PA1oDH6hqD9+VijQGHgQ641bqmgpcoaqx1/6LPLcJcAdu7nI94FfgNWCkqm4O\nO06A64CLgT2BH3GDyt4o5trpFYi/+84lfwhp0QJ+iZ1iz/g3eTL07euyTcaSl+fWqr766vQepL54\n7WIe//Jx/rfqf0mva0f+Drbs3MKWHVti/ty8Y3PJFykjQTi84eF0b9Wd7nt3p13DdvZc2gQu2YG4\nPzDAe3kc8BWwPuqwbcD3wF2q6uvhlYjk4YL6FuBGr3g4LqgfpKpbijm3KjAXyAZuxQXhdsAw4G1V\n7RN27HDgKuAGYA5wNi4on6yqE+NcP70C8caNrt80JCfH9bHm5ATXpnJiwwZ47DG47774AblyZbjo\nIrjmGmjSJLXtyzSqyrb8bcUG6uL2bdi2gRm/zuDrFV/7rrNOXh26tOxC91bd6dqyK/V3S+NuDFNu\npbJrehowMNZgrVJXKHI5cC+wj6ou9MqaAz8DV6vqg8WcexJuulRXVZ0aVj4SGALUUNWtIhK6Ux6h\nqsPCjpsK1FXVg+NcP70CMcAee0RGikWLoJkllU+UTZvgySfh7rthRZyvkrm57vH8ddcVXbnLJNbS\nDUuZOH8iE+ZPYMqCKazbts73uYc2ONTdLbfqzhGNjyAny76wmuQLfPqSiOyuqn+W8pypQGVVPTaq\nfDouneLxMU90x5wMvIMbOPZFWPl1uO7q6qq6RUT6AS/ggv2CsOMGAM8Ce6nq4hjXT79AfMQRLhdx\nyLRp0KlTYM0pr7ZsgWeecUmuli6NfUxODvTv71boatkyte2riHYW7OSz3z5jws8TmDB/Al8t979o\neK0qtejSsgvdWnajW6tuNKjeIIktNRVZKu+ILwJqqeo93us2wASgAa7LuoeqLi/mEuHXWga8paoD\no8ofBc5Q1bj9SyJSGfgaWAZcCizBZYIaDbyuqoO840YCl6tq1ajz2wGf47qnJ8S4fvoF4rPOgtde\nK3z9/PMwYEBgzSnvtm51f8QjR7p1qmPJznbTuW+8EfbZJ7Xtq8iWb1zOpPmTmDB/ApMXTGbN1jW+\nzz14z4Pp3qo7beu3xQ0fSZ6crBwqZVcqsuVm5cYsD205WTlJb5tJvEQEYr99N4OAp8Je3w+sshZD\nbwAAH91JREFUBe4CBuOe0V7s81p1gFifoNVEJpMoQlW3icixwOvAd6Fi4JlQEA6rY230+V4dof2Z\nwbIwpVSVKm41rgsugFGjYMSIon/k+flu3+jRcPbZLiAfcEAw7a1I9txtT/of3J/+B/dnZ8FOZv8+\n+69u7JKyVM1dPpe5y+cWe0w6KC5Qh282pat88RuImwE/AIhITdzgrVNV9X0R+RMYmaT2RfDuiF/D\nJaA4F/ccuD1wq4jkq+qlqWhHSlkWpkBUqgQXXui6ol9+GYYPh/nzI48pKHDrVr/yCpxxhltr5aCD\ngmlvRZOTlcPRTY7m6CZHM+z4Yfyx6Q8mL5jMhPkTmDR/En9uKdUTs7SxPX97uZ+SZoryG4izgNDM\nyw64u9Dp3utfKczM5McaYt/5xrtTDnch0BFoFRroBXwqIuuBp0TkcVX91rtOrTh1QOGdcRFDhw79\n6/dOnTrRKejnsdF3xIsWBdKMiio31z0J6NsXXn0V7rgDfogasqgKY8e67dRT4eab4dBDA2luhbVH\ntT3oe1Bf+h7Ul/yCfL5c+uVfd8uzf5+NkmaPnEzmWggsSuwl/T4jngNMU9UhIvIS0Dg0qEpEzgLu\nV1Vfi92KyAdArqp2jCqfBlDCYK3Hgd6quntU+UG4aU1nq+prYYO19lbVX8KOG0CmDdb66afI7ASN\nG8d/eGmSLj8fxo1zAXnevPjH9ejhAnL79qlrm4lt1eZVTF4wmWkLp5VqFPauUJT8gvy/7mxLs+Vr\nmuXoNP4MJWWDtc4BXqLwbvbM0MIYXorEZqrqa/l8b/rSPbgRzYu8subAT8A1JUxfuhW4haIB9mLg\ncaCjqs7wpi/9BtyhqreHHTcVqKeqbeNcP/0C8datboWJEBE3xLdy5eDaZCgogLfegmHD4Otipr52\n7eq6tQ87LHVtM5kpvyCfHQU7YgbpHfmF5dvyt5F2/09VYJ1adErd9CUR6YAbofyFqn4cVn4b8Lmq\nvu/zOqFFObYAN3vFw4BqQNvQ6lgi0hT4BRiqqnd4Zc1wo6aXAyNwo6bbATcBP6jqEWH1jAQuxy0a\nElrQ4yKgZ6wR09456ReIARo1ipxT8/PP0KpVcO0xf1F1K5EOGwZfxhkvJOKeNw8fDvVshUZjypXA\n5xHvcqVuicsHgJMoXOLySlVdEnZMMwoDcfhd7X7AUOAooC7uGfXbuMU71oUdJ8D1uOAbWuLyNlUN\nyytYpF3pGYg7dIAZMwpfT54MJ50UXHtMEaowcaILyJ99FvuYWrXc/oEDbXE0Y8qLZC9x2RRYpqo7\nvN+LFR5EM1XaBuK+fd3Q3ZAnn3SphEzaUXV5OW67DT79NPYxrVvDQw/B8XFHQxhjMkUiAnFxk9EW\nAod4vy/yXhe3mWSxkdMZQwQ6d4aPP3Z3yOHj7ELmzXOJtHr3hiUZ//XVGFNWxXWQnQ8sCPs9DW8V\nKwhb1CPjiLiBWt984+5+b7vN5fAIN3ase758ww3wf//nFhMxxlQ8gTwjTldp2zX94Ydw4omFr484\nIv6DSJOWli1zSSNGjYq9v0ULlyv5lFNcEDfGZIZkd02bdGFd0xmvQQN48UU35i7WYh8LF7rFQLp3\nL7pgiDGmfCtusNZzpbiOquoFiWlScNL2jnjnTtdvmR824X/TJqhaNf45Jm3l58Nzz7ku6VWriu7P\nyYErrnALgtSokfr2GWP8S/ao6UVEPheuBdQEdgJ/ArvjnjGvA9ao6l5laUg6SNtADG7N6cVhi4F9\n/z3sv39gzTFlt2YN3HorPPqoWyAk2p57wl13uUHzWdZ3ZUxaSmrXtKo2V9UWqtoC6AdsxC2Kkaeq\nDYA8oA+wAehblkYYH2zAVrlTu7YbyDV3Lhx3XNH9y5e7pBMdOsB//5v69hljUsPv9+z7gZGq+pqq\nWxBVVfNV9VVcKsS4y1KaBLFAXG61aQPTprmkEo0bF90/axa0a+emjq9cmfr2GWOSy28gbgPMj7Pv\nZ6B1Yppj4opOh2gDtsoVETev+IcfXDrF6KXEVeHpp2GffeDhh92wAWNM+eA3EC8HesfZdzawIjHN\nMXHZHXGFUK0a3H67GwLQq1fR/WvXwuDBcMghMH16yptnjEkCv4H4QeB8EXlPRAaISHfv5/tAf1zX\ntUmm6DtiC8Tl2l57uexOEya4u+Bo8+a5JTLPOstW5zIm05Um+9IFwK1A+FOsX3GJFEoz1SltpfWo\n6d9+gyZNCl/XqQN//hlce0zKbN8ef3UucN3aubnJbUNeHtSv77Y994z8Gf27Zeg0FUnKsy95GY0a\nAw2AZcBv6Ru5Si+tA3FBgZtLvGNHYdm6dTbRtAJZtgyuvRZeeinolhSvVq3iA3X475UqBd1aY8om\nY9Mgpqu0DsQAe+8N88PGzM2dC23bBtceE4iZM2HQIJgzJ+iWlF3t2oXBuXZtd+ddpYr7GdqiX/st\nq1TJlgs1yWeBOMHSPhB36QJTphS+fuut2CN6TLmXnw/PPgt33w0LFpR8fEUkUjQ4pyIPdKVKbtDd\nbru5n363WMdXqWJfJtJdIgKxpSfPJDZy2niys9284osvhm3bkluXqns2vWKFW2RkxYrI38N/rlwZ\nuRJrkFRhyxa3ZaqsLLeSbXSATsUXCpM69teZSWzktIkhFYOjqlSBunXhwAOLP66gwI0hjBWkowP4\nypWxl/Y0hQoK3JegWIP0TPlhgTiTWBYmk+aysqBePbe1aVP8sfn5LulFKDCvXw9btxbexYa26DK/\nr8PHNRqTziwQZxLrmjblSHZ24ejpZMjPLxqok91truoeFWza5LaNGwt/97uFn7N9e3Lba9JDaeYR\nNwKGAB2BOsApqjpPRK4AZqnq58lrZmqk/WCtFSvc8NKQ6tXdFCYbzWFMubRzZ+xgbV366aNjxxQN\n1hKRA4FPgHxgFnAIEJoB2AxoD5xTloYYH/bYw43c2LzZvd6wAVavht13D7ZdxpikyMmBmjXdZsov\nv0tc3gf8D2gBnAaER/+ZwJEJbpeJRcQGbBljTDnjNxB3AO5U1Y1AdN/tCmDPoqeYpLAsTMYYU674\nDcTFPZGoC2TwTL0MYwO2jDGmXPEbiGcD58XZ1xuYkZjmmBJZ17QxxpQrfqcv3Q5MFZHJwBhc93Rn\nEbkc+DtuJLVJBZtLbIwx5YqvO2JV/Qg4FTdY6zncYK07gWOBU8vD1KWMYV3TxhhTrvjtmkZV31PV\nvYF9cIO39lfVvVR1QmkrFZHGIjJORNaKyDoReV1Emvg471YRKYizbY46dlGMY/JF5JTStjetxBqs\nlc5zn40xxhQr5dmXRCQP+AY3wOtGr3g4kAccpKpxB36JSENcPuRw1YBJwOuq2ifs2IW4KVdDo47/\nUVXXxbl+ei/oAS7o1qrl1gMMWbYscqEPY4wxKZHS7EsiUgP4G9AUqBK1W1X1dp+XuhhoDuyjqgu9\na38L/AxcAjwY70RVXQosjWpXPyAbeDHGKatUdbbPdmUGEdc9/fXXhWULF1ogNsaYDOV3Za1jgPFA\nrTiHKG5Alx89gc9CQRhAVReJyAygF8UE4jj64+YyTy7leZmrefOigfioowJrjjHGmF3n9xnxg8Ai\noB1QRVWzorbsUtR5IDAvRvl3wAGluA4i0hjoBIxW1VhznXuKyCYR2Sois0SkV2mun7Zs5LQxxpQb\nfrum9wd6q+p/E1BnHWBNjPLVQO1SXqsfbgT3qBj73gG+ABYC9YF/AW+KSF9VHVPKetKLjZw2xphy\nw28gXgKkIP14qfUDvlLVInfYqnp5+GsReQv4DBiBmwuduWyZS2OMKTf8BuLbgOtE5ANVXV/i0cVb\nQ+w733h3yjGJSHtgP2Cwn+NVtUBExgJ3ikh9VV0R67ihQ4f+9XunTp3o1KmT3yaljt0RG2NMIKZP\nn8706dMTek1f05dE5CXc4h3VcWkQV0cdoqra31eFIh8AuaraMap8mneh431e51HgAqCRqv7p85yr\ncQuRNIwViDNi+hK49Ic1ahS+zs11Wc+zS/Oo3hhjTFmlcvpSB9zI6PW4wVbRShO93gHuEZHmqroI\nQESaA8cA1/i5gIjkAmcB75ciCGcDZwNL4t0NZ4zq1V0O4j+9t75jByxdCk1KXBPFGGNMmvEViFW1\nRclH+fY0cBnwtojc7JUNAxYDT4UOEpGmwC/AUFW9I+oaPXFd2bHmDiMiZwM9gPeB34EGXp0H44Jx\n5mvRojAQg+uetkBsjDEZx/cSl4miqpuBE4CfcKOdXwIWACd6+0IkbIv2D2AV8F6cahbiciTfh5tf\n/BhuJa+uqjo2AW8jeJaFyRhjyoW4d8TeHekyVd3h/V4sVV3it1JV/Q04s4RjFuNWzIq179QSzv0c\n6Oy3PRnJ5hIbY0y5UFzX9ELgKFwu4kWU/BzYRgqlko2cNsaYcqG4QHw+rss49HsGDCeuQKxr2hhj\nyoWUZ19KZxkzfQnghx9g//0LXzdtCosXB9ceY4ypgBIxfWmXA7GIHIBb+nKWlxUp42VUIN6yBapW\nLXydlQVbt7o5xcYYY1IiEYHY16hpEXlERJ4Ie30a8DUwFvheRNqVpRFmF+TlRaY+LCiAJb7Hyxlj\njEkTfqcvdQdmhr2+DXgXaIsbzHVrgttl/LCR08YYk/H8BuIGuJHTodSDBwIjVfVb4CFcekSTajZy\n2hhjMp7fQLwZ2M37/TjcUpdfeq834tagNqlmI6eNMSbj+V1reg5wmYgswS0VOUVVC7x9LYBlyWic\nKYF1TRtjTMbzG4hvBCbiBmitBf4Ztu9U3HNik2rWNW2MMRnPb9KHL7xlLvcDfo7KSfwU8HMyGmdK\nEN01bXfExhiTcWxBjzAZNY8YXPrDKlXc1KWQzZvd1CZjjDFJl7J5xF5lbURknIisFJGd3s/XRKR1\nWRpgyiA3Fxo3jiyz1bWMMSaj+F3Qox3wOXA8bv7wPd7PE4DPReSwpLXQFM+6p40xJqP5Haw1EpiH\nyxm8IVQoItWBqd7+LolvnilRixbw8ceFr23AljHGZBS/XdNH4hbw2BBe6L2+C5cu0QTB5hIbY0xG\n8xuISxrBlEEjnMoZm0tsjDEZzW8g/hy4weuK/ouIVAOuBT5LdMOMTzaX2BhjMprfZ8Q3ANOBxSLy\nLm4lrT2BvwFVgU7JaJzxwbqmjTEmo/meRywiBwG3AMcCdYDVwEfA7V7yh4yXcfOIAfLz3bzhHTsK\ny9avh+q2/LcxxiRbIuYR24IeYTIyEAO0agULFhS+/uYbaNMmuPYYY0wFkdQFPUQkS0R6Frdgh7fI\nR8+yNMAkgHVPG2NMxipusNa5wCu4NIfxbABeEZE+CW2VKR0bOW2MMRmruEDcD3heVRfFO8Db9yzQ\nP7HNMqViI6eNMSZjFReIDwUm+7jGVODwxDTH7BJb5tIYYzJWcYG4OrDGxzXWeMeaoNgdsTHGZKzi\nAvEqoJmPazT1jjVBiRWIM3H0tzHGVEDFBeJP8ffsd4B3rG8i0thLqbhWRNaJyOsi0sTHebeKSEGc\nbXPUsSIi14vIQhHZIiJzReS00rQzY9Sv7/ISh6xfD2vXBtceY4wxvhUXiB8EThSRB0SkUvROEckV\nkQdxqRAf8FuhiOQB04B9cAPC+gJ7Ax96+4rzNC4BRfh2IrATeDvq2DtwC5A8BHQDZgFjRaSb37Zm\nDBGbwmSMMRkq7hKXqjpLRIYA9wHnishkIJR1vhlwErA7MERVS7PW9MVAc2AfVV0IICLfAj8Dl+C+\nAMRr01JgaXiZiPQDsoEXw8rqAUOAEaoa+pLwkYjsDdwJTCxFezND8+bwww+Fry+5BOrVC6w5xhhj\nfFLVYjegI/AesAko8LZNXtmxJZ0f43pTgU9ilE8Hpu3i9ZYCWWFl/YB8oGXUsQO88mZxrqUZa+BA\nVfdkWKd5PzN5Kw/vwd5H+m32PtJrKw/vw4sblGUrMfuSqn6sqifjRkbv6W01VPVkVf1kF2L/gcC8\nGOXfAQeU5kIi0hiXcGK0qhaE7ToA2KaqC6JO+Q6Q0taTEfbb769fpwfXioSZHnQDEmR60A1IkOlB\nNyBBpgfdgASZHnQDEmR60A1IE37TIKKqBar6h7fll6HOOsSeFrUaqF3Ka/XDBdZRMeqINVppddj+\n8uWss6BZs6BbYYwxppT8pkFMV/2Ar1Q11h12xVK/PsybB198Ac88A+eeG3SLyubllzP/PYC9j3Rj\n7yO9lIf3cfLJZb5EyrMvichy4E1VHRhV/ihwhqrW93md9sBnwGBVfSRq351eedWo8nbA58DJqjoh\nxjVT+4dhjDEm42kZsy8FcUf8He45cbQDgO9LcZ3+wHZcYopYdVQWkb1U9Zew8gNxD9dj1lPWP0xj\njDGmtHw/I06gd4AjRaR5qMD7/RiKzgWOSURygbOA91X1zxiHTMTNLY7u8+gLzFPVxUVPMcYYY1Iv\niED8NLAIeFtEThGRU4C3cHOUnwodJCJNRWSniNwU4xo9cQOuXoyxD1VdCdwPXC8iV4rIcSLyOG6E\n9XWJfDPGGGNMWaS8a1pVN4tIaDWuUbhRz1OBK1U1fJlKCdui/QO3vvV7xVR1Ay5f8mDclKsfgTNj\nPRs2xhhjghLEHTGq+puqnqmqtVS1pqqerqpLoo5ZrKrZqnp7jPNPVdU9VHVnMXWoqo5Q1Raqmqeq\nB6vqm9HH7eq61+lERM4QkTdFZImIbBaRH0RkhIjsFnTbykJEJnrriA8Lui2lJSJ/E5GPRGSD9+9q\ntoh0CrpdpSEix4jIJBFZISLrReS/InJe0O2KR0QaicjDIjJTRDZ5/3aaxjiulog8IyIrRWSjiEwR\nkdZBtDkWP+9DRE4UkZdF5BfvMz9fRB7zVhVMC37/PqLOecI7LnpKamBK8z5E5EgRmSAia7x/W1+L\nSO+S6ggkEKeLMq57nU6G4J6JX4dbV/sxYCD+8kmnJRHpAxyEG1yXUUTkEtzjli+AU4EzgLFA1eLO\nSyci0gaYgus1uxD4OzAbeNZ7f+moFe7PejXwMfH/7bwLdAEuA04DcoFpItIwFY30wc/7uASoi1tT\nvyswAjgFmCUi6fLvzO/fB+C++OHG9axLftNKxdf7EJGTgY9wKz32wf19PA1UiXV8hLIuzZXJG3A5\nsANoEVbW3Cu7Iuj2leJ97B6jLLTMZ6eg27cL76c2sAw3IK8AGBZ0m0rR9mbAZmBQ0G0p4/sYAWwF\n8qLKZwIzgm6fj/Zf4P37bxpV3ssr7xhWVgP4E3gw6HaX4n3E+swf631eBgTdbr/vI2x/DvAtcC2w\nEBgVdJtL+fexG7ACuG9Xrluh74hxg74+Uy/5BICqLgJm4D6wGUFjjxz/Avd8vVGKm5MIdwHfqOqr\nQTdkF4Q+qE8G3ZAyygW2q+qWqPJ1ZHZPWk9gqap+HCpQ1fXAeMrHZx4y8zN/De7f1b1BN2QX9cb1\nUNy/Kydn8gcqERK27nUa6oTrQvlfwO0oFRHpgHtEcFnQbdlFxwA/AH2853Y7RORnEbk06IaV0gu4\ntN4PiUgDEakpIhfh0p7u0n82aaK4z3zTNOrW3RWdvJ+lWY8hcCLSCrgRGKhlWz45SMfguq4PEpFv\nvM/9EhG5RURKjLOZvsRlWSVy3eu0ISKNgNuAKao6J+j2+OXND38CuEdV5wfdnl3U0NvuBq4HfgHO\nBB4RkWxVfTjIxvmlqt+JyPHAm8C/vOLtwD9VdWxwLSuzOriuz2ihdehr4x4tZBRvYOaDuC8UvtZj\nSCOPA+PCeykyUEOgGvAyMAyYA3QGbgZq4sbxxFXRA3G5IyLVcB/E7cD5ATentK7FDWwYEXRDyiAL\n97zoH6oa+g9xuoi0wAXmjAjE3l3K67jndhfjnhf3Ap4Uka2qGmtFOxMAEckG/gM0AI7WyEx0aU1E\n+gKH4QY3ZbIsoDJwvar+2yv7WETqApeJyFBV3VDcyRXZGmLf+ca7U05rIlIFNyK0OdBVVZcG2yL/\nvCljN+C+QVbxukJrebsre68z4d9r6Nnd1KjyyUB9EfG1lnoaGIn7MneKqk5Q1WmqegXwGvDv4k9N\na8V95kP7M4aIhLLPnQD0UtXvAm6Sb95Nw324MSE7wj7zWUCu9zpTbhaL+9znUsKjzkz4jy2ZErXu\ndeC8f7CvA4cC3VU1o9oP7IX7Rjka95/hGlx3oQJXe7+nzVzPYmTMf4QlaI0bMBc9V382sLuI7BFA\nmxKhuM/8Eo1cVCgTPIl79HGWqk4PuC2lVReoh+sBC//MN8bNmFgN/C2w1pVOmT73FT0Ql3nd63Tg\nfSsegxus0UtVvyj+jLT0FXC8t3UK2wR4yfs9E54bhxaN6RpV3h34TVVXpLg9u2o5buBJ9B3Jkbhu\n6tVFT8kI7wCNROTYUIGI1MCNps6YzzyAiNyHe/w0QFXHB92eXbAc97mO/sz/gZvD3gn4NIiG7YK3\ncP9Xxfrcb8U94okrU277k+Vp3Ojct0XkZq9sGFHrXmeAx3ATzu8AtojIEWH7flPV34Npln/eFJIi\ngzXcdwwWq+onKW/ULlDV90VkOu5Zaj3cYK3euIEbAwJsWmk9guuGfldEHgO24J4RnwXcH+NOOS2I\nyOner4fj/mP8m4isBFZ6g4HewaVPHS0i1wBrcc/uAe5JdXvjKel9iMi1wJXAs8CCqM/8So3MOhcY\nH38fsT7zW4EV6fSZL+l9eIMbXwCGec/s5wAn4b4oDSuxpyXoCdJBb7hukLG4D+Q6XPduzEnn6brh\nRoHmx9luCbp9ZXxv+cBtQbejlG3eDTcoaxnu2/BcXNdh4G0r5fvoCnyIW6hgnfefyyV4eczTccMt\naBHrc/Bh2DG1gGdw69VvxD3Hax1020vzPnArAsb7zD8XdPtL8/cR45xfgBeDbvsu/LvKofBGbitu\nGuO//FxfvAsYY4wxJgAV/RmxMcYYEygLxMYYY0yALBAbY4wxAbJAbIwxxgTIArExxhgTIAvExhhj\nTIAsEBtjjDEBskBsTIKJyKki8pGIrBCRzSKySETeFJHo5e/Sgog0E5ECEUmrbF0iMsBrV9OwsoUi\n8lyQ7TIm0Sr6EpfGJJSIDMblhX0Gl5N4E9ASOBm3pu6k4FqXcdTbwp0KrA+gLcYkjQViYxJrCPCG\nql4cVjYdtyZwSolIJVXdnup6k1m3qn6d6GsaEzTrmjYmserg1mYukYg0F5GXReQPEdkqIl+JyKlR\nx7QUkVEi8ovXzb1ARB4Ly9UcOu4FEflVRI4UkRkishmX5zW0/yIR+a93jdUiMk1EjoxqUraI3CYi\nS0VkjYi8IyKNfLyP6SLyiYj0EJE5IrIFGOjtu0xEZorIn941Z4lIkdR2ItJCRN4TkU1el/6DuLSY\n0cctCu+aFpGhIlIQ47gXRGRh2OtsEbldROaLyBYRWSkiH4vI0SW9P2OSze6IjUms2cAALwi8rao/\nxzpIRBp7xy4HLsclIDgLeF1Eeqnqu96hDYHfcZl2VgMtgBuA93DpOkMUqAm8AtyLyyi0xavrXuAq\nXLaxW3AL2B8JNMVlIgq5HpgJnAfsAdyPS0F5QgnvWYF9gH8Dt+MW7Q+lSWwOPA8sALJx6QbHi0h3\nVZ3stS8Xl1C9Mi6Ar8QllzgtTl3Rr2MtmB9dfh3uz/kG4GugBi6TTp0S3psxyRd0VgvbbCtPG7A3\nLttSPi7grcTlij4p6rhncXfOtaLKJwNzirl+Ni4A5wNtw8qf98p6RB3fEtgJ3FPMNZt5bf0gqnyI\nd809S3jP07w62pRwnHjtnwS8GVZ+kVdPu6hj53nlTcPKFxKWXQi4FciPUdfzwC9hr8cD44L+92Gb\nbbE265o2JoHU3QEfAhyHyw/9FW6A0SQRuTHs0K7A+8AGr9s0W0RycIG4rYjsBu5uUURuEJH/ed3N\nO4BQntZ9o6rfgbtTDtcZF9Se9tH8CVGvQ8nMm0YfGMMiVS2S/FxEDhORd0VkOS5Y78DlaQ1v+5HA\nr6r6RahAVRWXDzlRvsDlkL1DRI7x7sKNSQsWiI1JMHU+VdVbVLULsBcuqN0iIjW9w/YA/oELTKFt\nO26kNcDu3s87cd3Jo4C/Ae2Av+OCa5Woqld6ASxc6Dq/+Wj66qjX27yf0fXEsiy6wOt+n4rL//sv\n4Chcd/DEqGs2IPZzdV/P2n0ajrt77olLRv+niDwnIrsXf5oxyWfPiI1JMlVdLiLP4KY17Q18CfyJ\nCwh34oJqtKXez7NwSdJHhnaISPV4VcUoW+X9bATEfF6dILHq7oZ7Fnumqv4VqEWkatRxy4ADYpy/\np496t3rXzFHVnWHlEQFWVfOBe4B7RGQPoAfwAJAH9PFRjzFJY3fExiSQiMQLHvt7P5d7PycCBwHf\nq+qcGNsO77iquC7dcOcTO/DFMtU79uKSDkyCUMD9q/0isg+Rg8wAZgFNRKR92HEC9PZRx2LvZ+uw\nc2sBcUdDq+ofqvoc7s+mdbzjjEkVuyM2JrHmichU3PPfhbg7wpNxo4BfVdVQF/EtwOfAJyLyCLAI\nqI0LDC1U9ULvuIlAfxGZB8zHjSQ+ym9jVPUXEXkAuFJEagDv4AZAtQf+p6pjS7hErLt1v6Z6db0k\nIvfhRoAPxQXP8JuAF3Gjmt/wnqP/AfwTiHfnH24CboGPp0VkKK7L+2pgY8SbEHkLN1p6DrAGOBR3\nx/74rr01YxLHArExiXUD7lnubUB9XCD6CbgGN70HAFX9VUQOxwWm4UA9XHf1PFxgChnk/bzD+/ke\ncDZu6lO0mHfJqnq1iPwMXIp7Lr0J+IbIVb7i3WH7vfMucpyqfi8i5wDDgLdxU5iuBboDHcOO2yEi\nnYFHgEe99o0B3gWeiFGPhp27TkROxnUzv4p7Fj4MN0itU9h5HwFn4v4MqgJLcI8FRvh8f8YkjRQd\n22GMMcaYVLFnxMYYY0yALBAbY4wxAbJAbIwxxgTIArExxhgTIAvExhhjTIAsEBtjjDEBskBsjDHG\nBMgCsTHGGBOg/wdoY2V3z9WJRgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x55e2a5c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(7,4.5))\n",
    "plt.plot(num_candidates_history, linewidth=4)\n",
    "plt.xlabel('Search radius')\n",
    "plt.ylabel('# of documents searched')\n",
    "plt.rcParams.update({'font.size':16})\n",
    "plt.tight_layout()\n",
    "\n",
    "plt.figure(figsize=(7,4.5))\n",
    "plt.plot(query_time_history, linewidth=4)\n",
    "plt.xlabel('Search radius')\n",
    "plt.ylabel('Query time (seconds)')\n",
    "plt.rcParams.update({'font.size':16})\n",
    "plt.tight_layout()\n",
    "\n",
    "plt.figure(figsize=(7,4.5))\n",
    "plt.plot(average_distance_from_query_history, linewidth=4, label='Average of 10 neighbors')\n",
    "plt.plot(max_distance_from_query_history, linewidth=4, label='Farthest of 10 neighbors')\n",
    "plt.plot(min_distance_from_query_history, linewidth=4, label='Closest of 10 neighbors')\n",
    "plt.xlabel('Search radius')\n",
    "plt.ylabel('Cosine distance of neighbors')\n",
    "plt.legend(loc='best', prop={'size':15})\n",
    "plt.rcParams.update({'font.size':16})\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some observations:\n",
    "* As we increase the search radius, we find more neighbors that are a smaller distance away.\n",
    "* With increased search radius comes a greater number documents that have to be searched. Query time is higher as a consequence.\n",
    "* With sufficiently high search radius, the results of LSH begin to resemble the results of brute-force search."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quality metrics for neighbors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above analysis is limited by the fact that it was run with a single query, namely Barack Obama. We should repeat the analysis for the entirety of data. Iterating over all documents would take a long time, so let us randomly choose 10 documents for our analysis.\n",
    "\n",
    "For each document, we first compute the true 25 nearest neighbors, and then run LSH multiple times. We look at two metrics:\n",
    "\n",
    "* Precision@10: How many of the 10 neighbors given by LSH are among the true 25 nearest neighbors?\n",
    "* Average cosine distance of the neighbors from the query\n",
    "\n",
    "Then we run LSH multiple times with different search radii."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def brute_force_query(vec, data, k):\n",
    "    num_data_points = data.shape[0]\n",
    "    \n",
    "    # Compute distances for ALL data points in training set\n",
    "    nearest_neighbors = graphlab.SFrame({'id':range(num_data_points)})\n",
    "    nearest_neighbors['distance'] = pairwise_distances(data, vec, metric='cosine').flatten()\n",
    "    \n",
    "    return nearest_neighbors.topk('distance', k, reverse=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following cell will run LSH with multiple search radii and compute the quality metrics for each run. Allow a few minutes to complete."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 / 10\n",
      "1 / 10\n",
      "2 / 10\n",
      "3 / 10\n",
      "4 / 10\n",
      "5 / 10\n",
      "6 / 10\n",
      "7 / 10\n",
      "8 / 10\n",
      "9 / 10\n"
     ]
    }
   ],
   "source": [
    "max_radius = 17\n",
    "precision = {i:[] for i in xrange(max_radius)}\n",
    "average_distance  = {i:[] for i in xrange(max_radius)}\n",
    "query_time  = {i:[] for i in xrange(max_radius)}\n",
    "\n",
    "np.random.seed(0)\n",
    "num_queries = 10\n",
    "for i, ix in enumerate(np.random.choice(corpus.shape[0], num_queries, replace=False)):\n",
    "    print('%s / %s' % (i, num_queries))\n",
    "    ground_truth = set(brute_force_query(corpus[ix,:], corpus, k=25)['id'])\n",
    "    # Get the set of 25 true nearest neighbors\n",
    "    \n",
    "    for r in xrange(1,max_radius):\n",
    "        start = time.time()\n",
    "        result, num_candidates = query(corpus[ix,:], model, k=10, max_search_radius=r)\n",
    "        end = time.time()\n",
    "\n",
    "        query_time[r].append(end-start)\n",
    "        # precision = (# of neighbors both in result and ground_truth)/10.0\n",
    "        precision[r].append(len(set(result['id']) & ground_truth)/10.0)\n",
    "        average_distance[r].append(result['distance'][1:].mean())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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q4yZ7+AR4UlWLMtZ0wirriTgzEzp0cKNsBVSvDkuXQtOm3sVljDGJKq6JuCwo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\n2BhjjOkh/wCO3raQsKfb0AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x54195b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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R9JgxA/73v8rtjh01m5aI5IZUE3ETguULAQ4lGP5UXs/4iGAKSpGcE98sfcwx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\n+16KqGoxfgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x5460c898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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gmnhEolJeXk55eXlWz5nphB6HAHeyMoke4O7/jm27Cejm7rtndEGz54Hm7r5j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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x5d3e5588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(7,4.5))\n",
    "plt.plot(range(1,17), [np.mean(average_distance[i]) for i in xrange(1,17)], linewidth=4, label='Average over 10 neighbors')\n",
    "plt.xlabel('Search radius')\n",
    "plt.ylabel('Cosine distance')\n",
    "plt.legend(loc='best', prop={'size':15})\n",
    "plt.rcParams.update({'font.size':16})\n",
    "plt.tight_layout()\n",
    "\n",
    "plt.figure(figsize=(7,4.5))\n",
    "plt.plot(range(1,17), [np.mean(precision[i]) for i in xrange(1,17)], linewidth=4, label='Precison@10')\n",
    "plt.xlabel('Search radius')\n",
    "plt.ylabel('Precision')\n",
    "plt.legend(loc='best', prop={'size':15})\n",
    "plt.rcParams.update({'font.size':16})\n",
    "plt.tight_layout()\n",
    "\n",
    "plt.figure(figsize=(7,4.5))\n",
    "plt.plot(range(1,17), [np.mean(query_time[i]) for i in xrange(1,17)], linewidth=4, label='Query time')\n",
    "plt.xlabel('Search radius')\n",
    "plt.ylabel('Query time (seconds)')\n",
    "plt.legend(loc='best', prop={'size':15})\n",
    "plt.rcParams.update({'font.size':16})\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The observations for Barack Obama generalize to the entire dataset."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Effect of number of random vectors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us now turn our focus to the remaining parameter: the number of random vectors. We run LSH with different number of random vectors, ranging from 5 to 20. We fix the search radius to 3.\n",
    "\n",
    "Allow a few minutes for the following cell to complete."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "num_vector = 5\n",
      "num_vector = 6\n",
      "num_vector = 7\n",
      "num_vector = 8\n",
      "num_vector = 9\n",
      "num_vector = 10\n",
      "num_vector = 11\n",
      "num_vector = 12\n",
      "num_vector = 13\n",
      "num_vector = 14\n",
      "num_vector = 15\n",
      "num_vector = 16\n",
      "num_vector = 17\n",
      "num_vector = 18\n",
      "num_vector = 19\n"
     ]
    }
   ],
   "source": [
    "precision = {i:[] for i in xrange(5,20)}\n",
    "average_distance  = {i:[] for i in xrange(5,20)}\n",
    "query_time = {i:[] for i in xrange(5,20)}\n",
    "num_candidates_history = {i:[] for i in xrange(5,20)}\n",
    "ground_truth = {}\n",
    "\n",
    "np.random.seed(0)\n",
    "num_queries = 10\n",
    "docs = np.random.choice(corpus.shape[0], num_queries, replace=False)\n",
    "\n",
    "for i, ix in enumerate(docs):\n",
    "    ground_truth[ix] = set(brute_force_query(corpus[ix,:], corpus, k=25)['id'])\n",
    "    # Get the set of 25 true nearest neighbors\n",
    "\n",
    "for num_vector in xrange(5,20):\n",
    "    print('num_vector = %s' % (num_vector))\n",
    "    model = train_lsh(corpus, num_vector, seed=143)\n",
    "    \n",
    "    for i, ix in enumerate(docs):\n",
    "        start = time.time()\n",
    "        result, num_candidates = query(corpus[ix,:], model, k=10, max_search_radius=3)\n",
    "        end = time.time()\n",
    "        \n",
    "        query_time[num_vector].append(end-start)\n",
    "        precision[num_vector].append(len(set(result['id']) & ground_truth[ix])/10.0)\n",
    "        average_distance[num_vector].append(result['distance'][1:].mean())\n",
    "        num_candidates_history[num_vector].append(num_candidates)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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NWxIu2aKRiOOAPUHKdwNV82i7FmjkTaoAiIgA7f3OnZPnvX8+G2KcxhgTMe++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\nIAiCAglFHARBEAQFEoo4CIIgCArk/wEu7yrQjCLXXgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x61e1ef98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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btk2vvvpqrVWrltaoUUP79++vmzZtKvD/O1dhP1/EYNR0wldfEpG9wChVvTuk/CFguKoW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\nfwD/M3RbciprMQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x54623a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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+CTgvwH7II3AjqgeSs8TllcGSsCm4kSOhVCkYPjynbN8+6NrVrUftvzSmMcaY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\nva2q14Y5tqizrmljgtu8Gc4/H5Yv9y2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1HjVi1m0pfdNvU3MA1AyStsFHUxxrvmhMPdIb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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x55e208d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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InxH/H24O7i+4Va12ELQzk6q+VBABxovC8Iw4w5YtbgT1Cb+lS956Cy67zLuY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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x54cbe048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(7,4.5))\n",
    "plt.plot(range(5,20), [np.mean(average_distance[i]) for i in xrange(5,20)], linewidth=4, label='Average over 10 neighbors')\n",
    "plt.xlabel('# of random vectors')\n",
    "plt.ylabel('Cosine distance')\n",
    "plt.legend(loc='best', prop={'size':15})\n",
    "plt.rcParams.update({'font.size':16})\n",
    "plt.tight_layout()\n",
    "\n",
    "plt.figure(figsize=(7,4.5))\n",
    "plt.plot(range(5,20), [np.mean(precision[i]) for i in xrange(5,20)], linewidth=4, label='Precison@10')\n",
    "plt.xlabel('# of random vectors')\n",
    "plt.ylabel('Precision')\n",
    "plt.legend(loc='best', prop={'size':15})\n",
    "plt.rcParams.update({'font.size':16})\n",
    "plt.tight_layout()\n",
    "\n",
    "plt.figure(figsize=(7,4.5))\n",
    "plt.plot(range(5,20), [np.mean(query_time[i]) for i in xrange(5,20)], linewidth=4, label='Query time (seconds)')\n",
    "plt.xlabel('# of random vectors')\n",
    "plt.ylabel('Query time (seconds)')\n",
    "plt.legend(loc='best', prop={'size':15})\n",
    "plt.rcParams.update({'font.size':16})\n",
    "plt.tight_layout()\n",
    "\n",
    "plt.figure(figsize=(7,4.5))\n",
    "plt.plot(range(5,20), [np.mean(num_candidates_history[i]) for i in xrange(5,20)], linewidth=4,\n",
    "         label='# of documents searched')\n",
    "plt.xlabel('# of random vectors')\n",
    "plt.ylabel('# of documents searched')\n",
    "plt.legend(loc='best', prop={'size':15})\n",
    "plt.rcParams.update({'font.size':16})\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see a similar trade-off between quality and performance: as the number of random vectors increases, the query time goes down as each bin contains fewer documents on average, but on average the neighbors are likewise placed farther from the query. On the other hand, when using a small enough number of random vectors, LSH becomes very similar brute-force search: Many documents appear in a single bin, so searching the query bin alone covers a lot of the corpus; then, including neighboring bins might result in searching all documents, just as in the brute-force approach."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}