4. Topic Modeling.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"width: 100%; overflow: hidden;\">\n",
    "    <div style=\"width: 150px; float: left;\"> <img src=\"data/D4Sci_logo_ball.png\" alt=\"Data For Science, Inc\" align=\"left\" border=\"0\"> </div>\n",
    "    <div style=\"float: left; margin-left: 10px;\"> \n",
    "        <h1>Natural Language Processing</h1>\n",
    "        <h1>Topic Modeling</h1>\n",
    "        <p>Bruno Gonçalves<br/>\n",
    "        <a href=\"http://www.data4sci.com/\">www.data4sci.com</a><br/>\n",
    "        @bgoncalves, @data4sci</p></div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import string\n",
    "from collections import Counter\n",
    "from pprint import pprint\n",
    "import gzip\n",
    "\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt \n",
    "\n",
    "import nltk\n",
    "from nltk.text import TextCollection\n",
    "\n",
    "import numpy as np\n",
    "from numpy.linalg import svd\n",
    "from numpy import diag\n",
    "\n",
    "import sklearn\n",
    "from sklearn.metrics.pairwise import cosine_similarity\n",
    "from sklearn.decomposition import NMF\n",
    "from sklearn.cluster import AgglomerativeClustering\n",
    "from scipy.cluster.hierarchy import dendrogram\n",
    "from sklearn.decomposition import LatentDirichletAllocation\n",
    "\n",
    "import watermark\n",
    "\n",
    "%matplotlib inline\n",
    "%load_ext watermark"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "List out the versions of all loaded libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Python implementation: CPython\n",
      "Python version       : 3.8.5\n",
      "IPython version      : 7.19.0\n",
      "\n",
      "Compiler    : Clang 10.0.0 \n",
      "OS          : Darwin\n",
      "Release     : 20.5.0\n",
      "Machine     : x86_64\n",
      "Processor   : i386\n",
      "CPU cores   : 16\n",
      "Architecture: 64bit\n",
      "\n",
      "Git hash: ada0d41c33546e250d7a5ace74624d6ece6f91ef\n",
      "\n",
      "json      : 2.0.9\n",
      "numpy     : 1.19.2\n",
      "matplotlib: 3.3.2\n",
      "watermark : 2.1.0\n",
      "nltk      : 3.5\n",
      "sklearn   : 0.0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%watermark -n -v -m -g -iv"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set the default style"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.style.use('./d4sci.mplstyle')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Preprocessing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load a standard list of stopwords from a file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "stopwords = nltk.corpus.stopwords.words('english')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['i', 'me', 'my', 'myself', 'we', 'our', 'ours', 'ourselves', 'you', \"you're\"]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(stopwords)[:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since we'll be using tweets, we start by instantiating the TweetTokenizer. This will ensure that we preserve #tags, @usernames, etc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "tokenizer = nltk.tokenize.TweetTokenizer()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Process the data from the file. File was obtained from crowdflower (https://www.crowdflower.com/data-for-everyone/) and contains a list of tweets about Apple from 2014 and some information about their sentiment. For our purposes, we only care about the text of each tweet that is located in the last column of the csv file.\n",
    "\n",
    "We treat each tweet as an individual document, and limit ourselves to only the first 200 tweets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "tweets = []\n",
    "line_count = 0\n",
    "\n",
    "for line in open(\"data/Apple-Twitter-Sentiment-DFE.csv\", \"rt\"):\n",
    "    fields = line.strip().split(',')\n",
    "    \n",
    "    line_count += 1\n",
    "    \n",
    "    # Skip the first line of the file which contains the header\n",
    "    if line_count == 1:\n",
    "        continue\n",
    "    \n",
    "    text = \",\".join(fields[11:])\n",
    "    \n",
    "    if len(text) == 0:\n",
    "        continue\n",
    "    \n",
    "    words = tokenizer.tokenize(text.lower())\n",
    "    clean_words = []\n",
    "    \n",
    "    for word in words:\n",
    "        if word in stopwords\\\n",
    "        or word in string.punctuation\\\n",
    "        or \"/\" in word:\n",
    "            continue\n",
    "            \n",
    "        clean_words.append(word)\n",
    "    \n",
    "    if len(words) > 0:\n",
    "        tweets.append(clean_words)\n",
    "        \n",
    "    if len(tweets) == 500:\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[['cat', 'chews', '@apple', 'cords', '#applesnob'],\n",
       " ['nobody', 'expects', 'spanish', 'inquisition', '#aapl'],\n",
       " ['#aapl',\n",
       "  '5',\n",
       "  'rocket',\n",
       "  'stocks',\n",
       "  'buy',\n",
       "  'december',\n",
       "  'gains',\n",
       "  'apple',\n",
       "  '...'],\n",
       " ['top', '3', '@apple', '#tablets', 'damn', 'right'],\n",
       " ['apple', 'inc', 'flash', 'crash', 'need', 'know', '#aapl']]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tweets[:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define the function to calculate the Inverse Document Frequency for each word and the TFIDF matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "corpus = TextCollection(tweets)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Text: cat chews @apple cords #applesnob nobody expects spanish...>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "corpus"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Get the TFIDF matrix for our corpus of tweets. We should note that while we call it a matrix, this is effectively a list of dictionaries, which we can consider to be a sparse representation of a matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "TFIDF = []\n",
    "\n",
    "for tweet in tweets:\n",
    "    score = {}\n",
    "    \n",
    "    for token in set(tweet):\n",
    "        score[token] = corpus.tf_idf(token, tweet)\n",
    "        \n",
    "    TFIDF.append(score)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[{'@apple': 0.090511343128403,\n",
       "  'cords': 1.1042921835724493,\n",
       "  'chews': 1.2429216196844384,\n",
       "  'cat': 1.1042921835724493,\n",
       "  '#applesnob': 1.2429216196844384},\n",
       " {'nobody': 1.2429216196844384,\n",
       "  'spanish': 1.2429216196844384,\n",
       "  '#aapl': 0.21458890838390637,\n",
       "  'expects': 1.2429216196844384,\n",
       "  'inquisition': 1.2429216196844384},\n",
       " {'5': 0.4742997721518754,\n",
       "  'stocks': 0.6134956575402495,\n",
       "  'apple': 0.19177463652111687,\n",
       "  '#aapl': 0.11921606021328131,\n",
       "  'december': 0.5364793041447001,\n",
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       "  'top': 0.852665968292347,\n",
       "  '#tablets': 1.0357680164036984,\n",
       "  'damn': 0.8047189562170503},\n",
       " {'know': 0.6578814551411559,\n",
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       "  '#aapl': 0.08941204515996098,\n",
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       "  '#iwatch': 0.5178840082018492,\n",
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       "  'engine': 0.5178840082018492,\n",
       "  'search': 0.3685707190995114,\n",
       "  'tops': 0.5178840082018492,\n",
       "  'list': 0.5178840082018492},\n",
       " {'#apps': 0.9202434863103743,\n",
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       "  'best-designed': 1.0357680164036984,\n",
       "  'world': 0.689194426123726,\n",
       "  '#iphone': 0.5736698960304017},\n",
       " {'pretty': 0.44390057845872793,\n",
       "  '@apple': 0.03232547968871535,\n",
       "  '..': 0.3448795526644501,\n",
       "  '@peterpham': 0.44390057845872793,\n",
       "  'rt': 0.14250717094614893,\n",
       "  'bought': 0.36542827212529155,\n",
       "  'store': 0.25539648348620947,\n",
       "  'match': 0.36542827212529155,\n",
       "  'logo': 0.36542827212529155,\n",
       "  'good': 0.28695596579185517,\n",
       "  \"can't\": 0.28695596579185517,\n",
       "  'wait': 0.44390057845872793,\n",
       "  'install': 0.39439006556158895,\n",
       "  '@augustsmartlock': 0.44390057845872793},\n",
       " {'screwed': 0.39439006556158895,\n",
       "  '@apple': 0.03232547968871535,\n",
       "  'seriously': 0.44390057845872793,\n",
       "  'stable': 0.44390057845872793,\n",
       "  '#icloud': 0.44390057845872793,\n",
       "  '#isync': 0.44390057845872793,\n",
       "  'contact': 0.44390057845872793,\n",
       "  'sync': 0.44390057845872793,\n",
       "  '8': 0.32894072757057796,\n",
       "  'used': 0.36542827212529155,\n",
       "  'ios': 0.29536903976731116,\n",
       "  'yosemite': 0.3448795526644501,\n",
       "  'much': 0.31591775922815263,\n",
       "  'past': 0.44390057845872793},\n",
       " {'twitter': 0.27089236388165244,\n",
       "  'non': 0.3655651822601289,\n",
       "  'dummies': 0.3655651822601289,\n",
       "  'factual': 0.3655651822601289,\n",
       "  'stock': 0.23631667771093953,\n",
       "  'minute': 0.3655651822601289,\n",
       "  '#rumors': 0.3655651822601289,\n",
       "  'thanks': 0.4602380006386054,\n",
       "  '#aapl': 0.06311438481879598,\n",
       "  'drops': 0.3655651822601289,\n",
       "  'points': 0.3655651822601289,\n",
       "  'followers': 0.3655651822601289,\n",
       "  '3': 0.2840184551354295,\n",
       "  'one': 0.23631667771093953,\n",
       "  'dumb': 0.3655651822601289,\n",
       "  '@applenws': 0.3655651822601289},\n",
       " {'iphone': 0.5240733796812705,\n",
       "  'network': 0.5649643725838356,\n",
       "  '@apple': 0.041141519603819544,\n",
       "  'cannot': 0.5019509925329315,\n",
       "  'use': 0.3652166837350884,\n",
       "  'unlocked': 0.5649643725838356,\n",
       "  '5s': 0.5649643725838356,\n",
       "  'buy': 0.3187779906654529,\n",
       "  'verizon': 0.46509052815946206,\n",
       "  'warning': 0.5649643725838356},\n",
       " {'sign': 0.5521460917862246,\n",
       "  '@apple': 0.0452556715642015,\n",
       "  'days': 0.4135166556742356,\n",
       "  'abandoned': 0.6214608098422192,\n",
       "  'isis': 0.6214608098422192,\n",
       "  'cantlie': 0.6214608098422192,\n",
       "  '739': 0.6214608098422192,\n",
       "  'prisoner': 0.6214608098422192,\n",
       "  'show': 0.5115995809754083,\n",
       "  'john': 0.6214608098422192},\n",
       " {'running': 0.47804677680170704,\n",
       "  'appointments': 0.4247277629124805,\n",
       "  'checkin': 0.47804677680170704,\n",
       "  '@apple': 0.03481205504938577,\n",
       "  'store': 0.27504236683130256,\n",
       "  'thanks': 0.30092484657139584,\n",
       "  'almost': 0.4247277629124805,\n",
       "  'xtra': 0.47804677680170704,\n",
       "  '50': 0.47804677680170704,\n",
       "  'upper': 0.47804677680170704,\n",
       "  'minutes': 0.4247277629124805,\n",
       "  'late': 0.35424386046062245,\n",
       "  'westside': 0.47804677680170704},\n",
       " {'would': 0.31591775922815263,\n",
       "  'stock': 0.28695596579185517,\n",
       "  'money': 0.30490699638334845,\n",
       "  'today': 0.279430214673439,\n",
       "  'analysts': 0.39439006556158895,\n",
       "  '#aapl': 0.07663889585139512,\n",
       "  'crash': 0.30490699638334845,\n",
       "  'make': 0.29536903976731116,\n",
       "  '...': 0.17199611490370512,\n",
       "  'nothing': 0.44390057845872793,\n",
       "  'widel': 0.44390057845872793,\n",
       "  'morning': 0.44390057845872793,\n",
       "  'suggested': 0.44390057845872793,\n",
       "  'mini-flash': 0.44390057845872793},\n",
       " {'..': 0.5364793041447001,\n",
       "  '#aapl': 0.11921606021328131,\n",
       "  'equity': 0.6905120109357991,\n",
       "  'aapl': 0.25148493109341824,\n",
       "  '...': 0.26754951207243016,\n",
       "  'aberration': 0.6905120109357991,\n",
       "  'world': 0.45946295074915067,\n",
       "  'momentarily': 0.6905120109357991,\n",
       "  'dip': 0.6905120109357991},\n",
       " {'newly': 0.5019509925329315,\n",
       "  'staff': 0.5019509925329315,\n",
       "  'issued': 0.5019509925329315,\n",
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       "  '@apple': 0.041141519603819544,\n",
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       "  'ipad': 0.3250500698915394,\n",
       "  '#txed': 0.3880634499424435,\n",
       "  'macbook': 0.3022033036841843,\n",
       "  'mini': 0.3759242324311233,\n",
       "  'jh': 0.5019509925329315},\n",
       " {'look': 0.4263329841461735,\n",
       "  '@apple': 0.03771305963683458,\n",
       "  '@samsung': 0.4263329841461735,\n",
       "  'need': 0.2979625640672444,\n",
       "  '@robconeybeer': 0.46012174315518717,\n",
       "  'defend': 0.4263329841461735,\n",
       "  'big': 0.3837641821656743,\n",
       "  'court': 0.3837641821656743,\n",
       "  'companies': 0.3685707190995114,\n",
       "  'ip': 0.46012174315518717,\n",
       "  'portfolio': 0.46012174315518717,\n",
       "  'battles': 0.46012174315518717},\n",
       " {'@apple': 0.041141519603819544,\n",
       "  'fixed': 0.46509052815946206,\n",
       "  'back': 0.34697389323852923,\n",
       "  'center': 1.1299287451676712,\n",
       "  'gawd': 0.5019509925329315,\n",
       "  '1': 0.3556384550389224,\n",
       "  'app': 0.41865183508982656,\n",
       "  'calendar': 0.5649643725838356,\n",
       "  'love': 0.3880634499424435,\n",
       "  'damn': 0.4389376124820274},\n",
       " {'full': 0.5649643725838356,\n",
       "  '5': 0.3880634499424435,\n",
       "  'storage': 0.5649643725838356,\n",
       "  '@apple': 0.041141519603819544,\n",
       "  'notification': 0.5649643725838356,\n",
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       "  'minutes': 0.5019509925329315,\n",
       "  'chill': 0.5649643725838356},\n",
       " {'iphone': 0.3202670653607764,\n",
       "  '@apple': 0.05028407951577944,\n",
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       "  'keep': 0.5364793041447001,\n",
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       "  '6': 0.36935959339178076,\n",
       "  '#switch': 0.6905120109357991,\n",
       "  'made': 0.5684439788615646},\n",
       " {'@apple': 0.03771305963683458,\n",
       "  'rt': 0.1662583661038404,\n",
       "  'stand': 0.46012174315518717,\n",
       "  'ppl': 0.5178840082018492,\n",
       "  'stickers': 0.5178840082018492,\n",
       "  'bought': 0.4263329841461735,\n",
       "  'shuffle': 0.5178840082018492,\n",
       "  \"can't\": 0.33478196009049765,\n",
       "  '@101baemations': 0.5178840082018492,\n",
       "  'everywhere': 0.5178840082018492,\n",
       "  'prob': 0.5178840082018492,\n",
       "  'ipod': 0.3685707190995114},\n",
       " {'18th': 0.29262507498801826,\n",
       "  'law': 0.29262507498801826,\n",
       "  '@apple': 0.041141519603819544,\n",
       "  'department': 0.29262507498801826,\n",
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       "  'inc': 0.3381394754365976,\n",
       "  '2014': 0.5115995809754083,\n",
       "  '#apple': 0.2364460496712133,\n",
       "  'price': 0.3729701448634192,\n",
       "  '#aapl': 0.10729445419195319,\n",
       "  '02': 0.6214608098422192,\n",
       "  'december': 0.48283137373023016,\n",
       "  'close': 0.6214608098422192},\n",
       " {'@samsung': 0.46509052815946206,\n",
       "  'announcement': 0.5649643725838356,\n",
       "  '2': 0.3022033036841843,\n",
       "  '#aapl': 0.09754041290177562,\n",
       "  'large': 0.5649643725838356,\n",
       "  'screen': 0.5019509925329315,\n",
       "  'criticized': 0.5649643725838356,\n",
       "  'following': 0.5019509925329315,\n",
       "  'samsung': 0.5649643725838356,\n",
       "  'supporters': 0.5649643725838356,\n",
       "  'game': 0.41865183508982656},\n",
       " {'calling': 0.6214608098422192,\n",
       "  '@apple': 0.0452556715642015,\n",
       "  \"we're\": 0.6214608098422192,\n",
       "  'whole': 0.6214608098422192,\n",
       "  'bluetooth': 0.6214608098422192,\n",
       "  '@billgates': 0.6214608098422192,\n",
       "  'taking': 0.5521460917862246,\n",
       "  'new': 0.3218875824868201,\n",
       "  '@microsoft': 0.6214608098422192,\n",
       "  'level': 0.5115995809754083}]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "TFIDF"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For convenience, extract the word_dict and word_list from the TFIDF matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "word_list = list(corpus.vocab().keys())\n",
    "word_dict = dict(zip(word_list, np.arange(len(word_list))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "We have 1939 words in our vocabulary\n"
     ]
    }
   ],
   "source": [
    "vocabulary_size = len(word_dict)\n",
    "print(\"We have\", vocabulary_size, \"words in our vocabulary\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['cat',\n",
       " 'chews',\n",
       " '@apple',\n",
       " 'cords',\n",
       " '#applesnob',\n",
       " 'nobody',\n",
       " 'expects',\n",
       " 'spanish',\n",
       " 'inquisition',\n",
       " '#aapl']"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "word_list[:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now use the TFIDF matrix and our vocabulary to generate the Term Document matrix. This is just a matter of rearranging the values in our (sparse) TFIDF matrix into the full TD matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def term_document_matrix(TFIDF, word_list, word_dict):\n",
    "    vocabulary_size = len(word_dict)\n",
    "    number_documents = len(TFIDF)\n",
    "    \n",
    "    TDM = np.zeros((vocabulary_size, number_documents))\n",
    "    \n",
    "    for doc in range(number_documents):\n",
    "        document = TFIDF[doc]\n",
    "        \n",
    "        for word in document.keys():\n",
    "            pos = word_dict[word]\n",
    "            \n",
    "            TDM[pos, doc] = document[word]\n",
    "            \n",
    "    return TDM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Our dataset has:\n",
      "1939 unique words\n",
      "500 documents\n"
     ]
    }
   ],
   "source": [
    "TDM = term_document_matrix(TFIDF, word_list, word_dict)\n",
    "print(\"Our dataset has:\\n%u unique words\\n%u documents\"%(TDM.shape))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1939, 500)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "TDM.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Explicit Semantic Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In ESA we use the TD matrix of our corpus as a knowledge base that we can use to look up related documents. To demonstrate how this works, let's create a new document:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "new_tweet = ['#macbook', 'mini', 'rocket']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is not an actual sentence since, for clarity, we are not including stopwords.\n",
    "\n",
    "In the TD formulation, the values in the word (row) vector representa how much each document is \"activated\" by that specific word. Naturally, documents in which the word does not appear have weight zero. We can use these word vectors to find a vector representation of our new document where each value is our related it is to every other document in our knowledge base. You can think of this as the set of results one might obtain after a query in a search engine!\n",
    "\n",
    "The **find_related** simply calcuates the vector corresponding to the new \"document\" and returns a list of the corresponding weights sorted in decreasing order:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def find_related_docs(tweet, TDM):\n",
    "    new_vector = np.zeros(TDM.shape[1])\n",
    "    \n",
    "    for word in tweet:\n",
    "        pos = word_dict[word]\n",
    "        new_vector += TDM[pos, :]\n",
    "        \n",
    "    # Now the entries of new_vector tell us which documents are activated by this one.\n",
    "    # Let's extract the list of documents sorted by activation\n",
    "    doc_list = sorted(zip(range(TDM.shape[1]), new_vector), \n",
    "                      key=lambda x:x[1], reverse=True)\n",
    "    \n",
    "    return doc_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "related = find_related_docs(new_tweet, TDM)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's take a look a the top 5 results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6905120109357991 2 #aapl 5 rocket stocks buy december gains apple ...\n",
      "0.59313210196533 167 ipad mini unboxing via @youtube @apple #ipadmini #ipad #macbook #macbookpro #startup #hipster #unboxing\n",
      "0.59313210196533 191 ipad mini unboxing via @youtube @apple #ipadmini #ipad #macbook #macbookpro #startup #hipster #unboxing\n",
      "0.59313210196533 388 ipad mini unboxing via @youtube @apple #ipadmini #ipad #macbook #macbookpro #startup #hipster #unboxing\n",
      "0.5140478217032859 168 ipad mini first time startup via @youtube @apple #ipadmini #ipad #macbook #macbookpro #startup #hipster #unbox\n"
     ]
    }
   ],
   "source": [
    "for tweet, score in related[:5]:\n",
    "    print(score, tweet, \" \".join(tweets[tweet]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With such small documents, the results are easy to interpret. The first two result are due to mentions of **macbook** and **mini**, the third due to the presence of the word **rocket** but the remaining two results don't include any words in common with our original tweet, just words that appear in similar contexts."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "def find_similar_words(tweet, TDM):\n",
    "    new_vector = np.zeros(TDM.shape[1])\n",
    "    \n",
    "    for word in tweet:\n",
    "        pos = word_dict[word]\n",
    "        new_vector += TDM[pos, :]\n",
    "    \n",
    "    sim = [cosine_similarity(new_vector.reshape(1, -1), \n",
    "                             TDM[i, :].reshape(1, -1)).flatten()[0] for i in range(TDM.shape[0])]\n",
    "\n",
    "    sim_words = sorted(zip(range(TDM.shape[0]), sim), \n",
    "                       key=lambda x:x[1], reverse=True)\n",
    "    return sim_words"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "similar = find_similar_words(new_tweet, TDM)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['#macbook', 'mini', 'rocket']"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_tweet"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "#macbook: 0.8216\n",
      "@youtube: 0.805338\n",
      "#startup: 0.805338\n",
      "#hipster: 0.805338\n",
      "mini: 0.787466\n",
      "#ipadmini: 0.765211\n",
      "#macbookpro: 0.680949\n",
      "unboxing: 0.605678\n",
      "#unboxing: 0.605678\n",
      "startup: 0.530861\n",
      "#unbox: 0.50116\n",
      "#ipad: 0.467151\n",
      "via: 0.452331\n",
      "ipad: 0.420346\n",
      "first: 0.401098\n",
      "rocket: 0.388672\n",
      "gains: 0.388672\n",
      "pro: 0.3433\n",
      "13in: 0.290492\n",
      "jh: 0.2691\n"
     ]
    }
   ],
   "source": [
    "for word, score in similar[:20]:\n",
    "    print(\"%s: %g\" % (word_list[word], score))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This approach also returns words that are not included in the document but that are used in a similar context, such as #hipster. One might use this extra words (above some finetuned threshold of similarity) to expand our query and retrieve furhter related documents."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Clustering Documents"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For simplicity we use the AgglomerativeClustering algorithm from sklearn and the visualization code from https://scikit-learn.org/stable/auto_examples/cluster/plot_agglomerative_dendrogram.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_dendrogram(model, **kwargs):\n",
    "    # Create linkage matrix and then plot the dendrogram\n",
    "\n",
    "    # create the counts of samples under each node\n",
    "    counts = np.zeros(model.children_.shape[0])\n",
    "    n_samples = len(model.labels_)\n",
    "    for i, merge in enumerate(model.children_):\n",
    "        current_count = 0\n",
    "        for child_idx in merge:\n",
    "            if child_idx < n_samples:\n",
    "                current_count += 1  # leaf node\n",
    "            else:\n",
    "                current_count += counts[child_idx - n_samples]\n",
    "        counts[i] = current_count\n",
    "\n",
    "    linkage_matrix = np.column_stack([model.children_, model.distances_,\n",
    "                                      counts]).astype(float)\n",
    "\n",
    "    # Plot the corresponding dendrogram\n",
    "    dendrogram(linkage_matrix, **kwargs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define an train the model. For the sake of visualization, we limit ourselves to just 50 documents instead of the whole set. Also note that we must use the transpose of the TDM matrix to ensure that we are clustering documents and not tokens"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "# setting distance_threshold=0 ensures we compute the full tree.\n",
    "model = AgglomerativeClustering(distance_threshold=0, n_clusters=None)\n",
    "model = model.fit(TDM.T[:50])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can confirm that we have the right number of features (tokens)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1939"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.n_features_in_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we plot the dendrogram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 3840x2640 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_dendrogram(model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Latent Semantic Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "LSA analysis, sometimes refered to as Latent Semantic Indexing, relies on the well known Singular Value Decomposition. Singular Values (and Singular Vectors) can be thought of as being a generalization of the more common eigenvalues (and eigenvectors) for the case of non-square matrices. \n",
    "\n",
    "The first step in any LSA analysis is to apply SVD to the Term-Document matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "u, sigma, vt = svd(TDM)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The resulting matrices have the expected shapes, except the singular value matrix, **sigma** that is simply a vector. This is an optimization of the numpy function meant to save memory."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1939, 1939) (500,) (500, 500)\n"
     ]
    }
   ],
   "source": [
    "m, n = TDM.shape\n",
    "print(u.shape, sigma.shape, vt.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1939 500\n"
     ]
    }
   ],
   "source": [
    "print(m, n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now reduce the internal dimension of these matrices to, say, 10. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "k = 20\n",
    "\n",
    "# Convert the vector of singular values into a diagonal matrix\n",
    "sigma_k = sigma[:k]\n",
    "Sk = diag(sigma_k)\n",
    "\n",
    "# Drop the extraneous dimensions in the other two matrices.\n",
    "uk = u[:,:k]\n",
    "vtk = vt[:k, :]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this way, we preserve the most significant (higher sigma values) latent dimensions of the dataset while discarding the rest. The idea is simple, SVD projects the original dataset into an internal space which is a linear combination of the original one. Each dimension in this space can be thought of as an underlying topic in the data. By preserving only the most dominant topics in effect we are simplifying the data and, potentially, removing noise. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1939, 20) (20, 20) (20, 500)\n"
     ]
    }
   ],
   "source": [
    "print(uk.shape, Sk.shape, vtk.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are no easy ways to determine the number of topics to choose, but a good rule of thumb is to identify kinks in the values of sigma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '$\\\\sigma_i$')"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 3840x2640 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(range(500), sigma, '*')\n",
    "plt.xlabel('Component (i)')\n",
    "plt.ylabel(r'$\\sigma_i$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also explore the way in which the topics are defined by considering the words for which they have stronger weights:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Sort the list of words by the weight they have in a specific topic\n",
    "def top_words(vector, word_list):\n",
    "    doc_list = sorted(zip(word_list, vector), key=lambda x:x[1], reverse=True)\n",
    "    \n",
    "    return doc_list"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For example, for topic 1, we have strong mentions of the justice department and a recent federal law decision about unlocking iphones:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "federal 0.2606022427576014\n",
      "law 0.2606022427576013\n",
      "department 0.26060224275760124\n",
      "cites 0.2606022427576012\n",
      "18th 0.2606022427576011\n",
      "century 0.2606022427576009\n",
      "unlock 0.2594558729061549\n",
      "justice 0.25840277676163026\n",
      "iphones 0.25396942955389934\n",
      "@thehill 0.24845399158974746\n"
     ]
    }
   ],
   "source": [
    "topic_words = top_words(uk[:,1], word_list)\n",
    "for word, weight in topic_words[:10]:\n",
    "    print(word, weight)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On the other hand, if we were trying to map a specific sentence or document into the most relevant topic we would simply have to project it into the singular space. First we define the vector in the \"regular\" word space:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "document = ['ipad', 'mini', 'price']\n",
    "\n",
    "doc_vector = np.zeros(vocabulary_size)\n",
    "for word in document:\n",
    "    doc_vector[word_dict[word]] += 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and now we project it into the singular space:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "array([-0.02795687, -0.01210723, -0.00019639,  0.00096848,  0.01986759,\n",
      "        0.00152401, -0.02277111,  0.06085907,  0.0134054 ,  0.03140215,\n",
      "        0.00564585,  0.0869532 ,  0.03682714, -0.00405679,  0.01681271,\n",
      "        0.01352978, -0.0132486 ,  0.02266492, -0.01178019, -0.00777679])\n"
     ]
    }
   ],
   "source": [
    "doc_singular = 1/sigma_k*np.dot(uk.T, doc_vector)\n",
    "pprint(doc_singular)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From where we see that the most relevant topic is topic number 11:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "11\n",
      "thank 0.29774557331500123\n",
      "#macbookpro 0.25909565050446215\n",
      "via 0.24120410802252296\n",
      "@youtube 0.2393559575276826\n",
      "#startup 0.2393559575276826\n",
      "#hipster 0.2393559575276826\n",
      "#macbook 0.23480658188636672\n",
      "yall 0.1720307865112455\n",
      "#unboxing 0.1561683573715782\n",
      "unboxing 0.15616835737157808\n",
      "ipad 0.14586152423301893\n",
      "pro 0.1403175419202523\n",
      "mini 0.13966101518736398\n",
      "#ipadmini 0.13721958345536686\n",
      "update 0.13650380565448705\n",
      "#ipad 0.13097471890592483\n",
      "headphones 0.13031555454628735\n",
      "startup 0.12767076037561614\n",
      "hoes 0.1270331432809359\n",
      "first 0.1242343861347427\n"
     ]
    }
   ],
   "source": [
    "topic = np.argmax(doc_singular)\n",
    "\n",
    "print(topic)\n",
    "\n",
    "topic_words = top_words(uk[:,topic], word_list)\n",
    "for word, weight in topic_words[:20]:\n",
    "    print(word, weight)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Which indeed seems relevant."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Latent Dirichlett Allocation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LatentDirichletAllocation(n_components=15, random_state=42)"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lda = LatentDirichletAllocation(n_components = 15, random_state = 42)\n",
    "lda.fit(TDM.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(15, 1939)"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lda.components_.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Topic 1: digital, claims, long, #tuesday, lol, #passingthetime, #interestingfact, #whoknew, drop, dying\n",
      "Topic 2: customer, companies, hoes, band, brass, @donacamp, #nyc, #winterseve, broadway, #aapl\n",
      "Topic 3: pro, unboxing, #unboxing, #ipad, via, #macbookpro, #hipster, @youtube, #startup, #macbook\n",
      "Topic 4: rt, headphones, new, @ace_kit_uk, apple, macbook, thank, 949.86, £, â\n",
      "Topic 5: contra, juicio, en, clave, aapl, update, intraday, fibonacci, technicals, levels\n",
      "Topic 6: iphones, @thehill, unlock, law, federal, department, cites, 18th, century, get\n",
      "Topic 7: dual, pie, perfome, unlike, @apple, dear, fix, fuck, apps, #ipodtouch5thgen\n",
      "Topic 8: demand, @_iamgambino, lighting, #gorgeous, #grandcentralstation, via, back, boost, strong, thestreet\n",
      "Topic 9: u, #stevejobs, phone, @laurrynk, everything, h8, battery, replace, dear, sucks\n",
      "Topic 10: peanut-butter-sandwich, download, pre-opening, 2, photo, phones, ur, @kcdenton, salut, disgrace\n",
      "Topic 11: screenshot, @timcook, analyst, @jimcramer, take, selling, shares, crest's, reiterates, going\n",
      "Topic 12: popular, besides, #biggerisbetter, mega, launching, rumoured, tab, iphone, shit, pieces\n",
      "Topic 13: love, emails, computers, heads, ..., #aapl, right, trial, steve, jobs\n",
      "Topic 14: raised, peaked, here's, aapl, buy, dropped, genuity, canaccord, #aapl, apple's\n",
      "Topic 15: missed, link, ..., could, much, apple, reasons, yesterday, fallen, 6\n"
     ]
    }
   ],
   "source": [
    "for i, topic in enumerate(lda.components_):\n",
    "        print(\"Topic {}: {}\".format(i + 1, \", \".join([str(x) for x in np.array(word_list)[topic.argsort()[-10:]]])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Non-Negative Matrix Factorization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The idea behind applying NMF to a Term-Document Matrix is similar to the goals behind using SVD to perform Latent Semantic Analysis. NMF is a general matrix factorization algorithm and, as such, the factor matrices it finds can also be thought of as internal or latent dimensions. \n",
    "\n",
    "Similarly to the case of SVD, we can perform a partial reconstruction of the original matrix by reducing the internal dimensions. Naturally, as the number of latent dimensions increases, the reconstruction error decreases since we are removing less and less information"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see how the error changes with the number of components."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2 34.92909306535052\n",
      "3 34.75885149754652\n",
      "4 34.594745843546754\n",
      "5 34.43673790367056\n",
      "6 34.28335461194239\n",
      "7 34.14211219272398\n",
      "8 34.004422279489255\n",
      "9 33.87096916919212\n",
      "10 33.73767706694623\n",
      "11 33.59876549348309\n",
      "12 33.46638007897564\n",
      "13 33.335654064804245\n",
      "14 33.21181477060407\n",
      "15 33.08995476662976\n",
      "16 32.97175762990215\n",
      "17 32.85160117103465\n",
      "18 32.739027138417406\n",
      "19 32.62494477304524\n",
      "20 32.50896281977528\n",
      "21 32.40271172753618\n",
      "22 32.296959006674825\n",
      "23 32.18580481650759\n",
      "24 32.087677811856175\n",
      "25 31.98644594631837\n",
      "26 31.879121444568813\n",
      "27 31.78153990540144\n",
      "28 31.688268724931856\n",
      "29 31.573557724255288\n",
      "30 31.48855381233336\n",
      "31 31.388247546631213\n",
      "32 31.28192483093436\n",
      "33 31.175187230934377\n",
      "34 31.07639810021007\n",
      "35 30.989471674448918\n",
      "36 30.89586796381687\n",
      "37 30.788457558503598\n",
      "38 30.696712827110645\n",
      "39 30.621311283180706\n",
      "40 30.513069648659858\n",
      "41 30.447683850716157\n",
      "42 30.34614116757146\n",
      "43 30.253633729012\n",
      "44 30.172156666616086\n",
      "45 30.074433556389156\n",
      "46 29.97903634466175\n",
      "47 29.908435998514435\n",
      "48 29.823259934637548\n",
      "49 29.714418467338767\n",
      "50 29.647406532536316\n",
      "51 29.5629953857566\n",
      "52 29.483552466530213\n",
      "53 29.379595165639852\n",
      "54 29.31492129580229\n",
      "55 29.25494582545604\n"
     ]
    }
   ],
   "source": [
    "error = []\n",
    "\n",
    "for comps in range(2, 55+1):\n",
    "    nmf = NMF(n_components=comps, init='nndsvd', max_iter=2000).fit(TDM.T)\n",
    "    print(comps, nmf.reconstruction_err_)\n",
    "    error.append(nmf.reconstruction_err_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Any nan values found above are due to numerical instabilities. In practice you should use a well tested numerical library such as sklearn."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Non-Negative Matrix Factorization')"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 3840x2640 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(range(2, 55+1), error)\n",
    "plt.xlabel('Number of Components')\n",
    "plt.ylabel('Reconstruction Error')\n",
    "plt.title('Non-Negative Matrix Factorization')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the remainder of this section, lets fix the number of so that we can use these results to illustrate the power of NMF."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "nmf = NMF(n_components=10, init='nndsvd', max_iter=2000)\n",
    "W = nmf.fit_transform(TDM.T)\n",
    "H = nmf.components_\n",
    "err = nmf.reconstruction_err_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(500, 10)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "W.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When we apply NMF to a Term-Document matrix, as defined above, the resulting factors prove useful for topic detection. In particular, the W matrix provides us with the definition of each topic as a weighted distribution over all the words in the corpus:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at a the top words for each topic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Topic 1: @jpdesloges, last, #aapl, apple, aapl, update, levels, technicals, fibonacci, intraday\n",
      "Topic 2: @thehill, iphones, justice, unlock, federal, law, department, cites, century, 18th\n",
      "Topic 3: @apple, right, imessage, acid, shitty, yo, draining, 3g, @remuuusss, fix\n",
      "Topic 4: comparison, map, drop, ios, requirement, rendition, audio, @apple, apps, #ipodtouch5thgen\n",
      "Topic 5: #hipster, #macbookpro, #macbook, rt, apple, @ace_kit_uk, macbook, â, £, 949.86\n",
      "Topic 6: ur, course, mother, that's, keeps, freezing, shit, hate, faggots, fucking\n",
      "Topic 7: heads, inc, steve, jobs, trial, apple, cnbctv, ..., #apple, #aapl\n",
      "Topic 8: solution, people, thank, rt, @apple, @jodispicer, #passingthetime, #whoknew, #interestingfact, twitter\n",
      "Topic 9: slack, boys, music, breaking, cause, @brwnskin_beauti, lol, dying, hey, fuck\n",
      "Topic 10: please, thank, @apple, @laurrynk, yall, replace, battery, sucks, phone, dear\n"
     ]
    }
   ],
   "source": [
    "for i, topic in enumerate(H):\n",
    "    print(\"Topic {}: {}\".format(i + 1, \", \".join([str(x) for x in np.array(word_list)[topic.argsort()[-10:]]])))"
   ]
  },
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    "     <img src=\"data/D4Sci_logo_full.png\" alt=\"Data For Science, Inc\" align=\"center\" border=\"0\" width=300px> \n",
    "</div>"
   ]
  }
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