2. 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 For Everyone</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 numpy as np\n",
    "from numpy.linalg import svd\n",
    "from numpy import diag\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       : 3.11.7\n",
      "IPython version      : 8.20.0\n",
      "\n",
      "Compiler    : Clang 14.0.6 \n",
      "OS          : Darwin\n",
      "Release     : 23.4.0\n",
      "Machine     : arm64\n",
      "Processor   : arm\n",
      "CPU cores   : 16\n",
      "Architecture: 64bit\n",
      "\n",
      "Git hash: ed7010f27131287f28d990d9846e4ce6cd87e34d\n",
      "\n",
      "numpy     : 1.26.4\n",
      "matplotlib: 3.8.0\n",
      "watermark : 2.4.3\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 = set([word.lower().strip() for word in open(\"data/nltk_stopwords.txt\", \"rt\").readlines()])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[\"should've\",\n",
       " 'weren',\n",
       " 'has',\n",
       " 'him',\n",
       " 'with',\n",
       " 'same',\n",
       " 'between',\n",
       " 'do',\n",
       " 'when',\n",
       " 'other']"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(stopwords)[:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define a function to extract the words from our input file. Here we have to be (slightly) more careful than in the previous lesson since we want to keep #tags and @mentions and remove stopwords."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def extract_words(text, stopwords):\n",
    "    temp = text.split() # Split the text on whitespace\n",
    "    text_words = []\n",
    "\n",
    "    punctuation = set(string.punctuation)\n",
    "    \n",
    "    # Keep #tags and @mentions\n",
    "    punctuation.remove(\"#\")\n",
    "    punctuation.remove(\"@\")\n",
    "    \n",
    "    for word in temp:\n",
    "        # Remove any punctuation characters present in the beginning of the word\n",
    "        while len(word) > 0 and word[0] in punctuation:\n",
    "            word = word[1:]\n",
    "\n",
    "        # Remove any punctuation characters present in the end of the word\n",
    "        while len(word) > 0 and word[-1] in punctuation:\n",
    "            word = word[:-1]\n",
    "\n",
    "        # Simple rule to eliminate (most) URLs \"http://www.google.com\"\n",
    "        if len(word) > 0 and \"/\" not in word:\n",
    "            # If it's not a stopword\n",
    "            if word.lower() not in stopwords:\n",
    "                # Append this word into our list of words.\n",
    "                text_words.append(word.lower())\n",
    "        \n",
    "    return text_words"
   ]
  },
  {
   "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",
    "    tweet = \",\".join(fields[11:])\n",
    "    \n",
    "    if len(tweet) == 0:\n",
    "        continue\n",
    "    \n",
    "    words = extract_words(tweet, stopwords)\n",
    "    \n",
    "    if len(words) > 0:\n",
    "        tweets.append(words)\n",
    "        \n",
    "    if len(tweets) == 200:\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:5', 'rocket', 'stocks', 'buy', 'december', 'gains', 'apple'],\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. These functions were introduced in the previous lesson."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def inv_doc_freq(corpus_words):\n",
    "    number_docs = len(corpus_words)\n",
    "    \n",
    "    document_count = {}\n",
    "\n",
    "    for document in corpus_words:\n",
    "        word_set = set(document)\n",
    "\n",
    "        for word in word_set:\n",
    "            document_count[word] = document_count.get(word, 0) + 1\n",
    "    \n",
    "    IDF = {}\n",
    "    \n",
    "    for word in document_count:\n",
    "        IDF[word] = np.log(number_docs/document_count[word])\n",
    "        \n",
    "    \n",
    "    return IDF\n",
    "\n",
    "def tf_idf(corpus_words):\n",
    "    IDF = inv_doc_freq(corpus_words)\n",
    "    \n",
    "    TFIDF = []\n",
    "    \n",
    "    for document in corpus_words:\n",
    "        TFIDF.append(Counter(document))\n",
    "    \n",
    "    for document in TFIDF:\n",
    "        for word in document:\n",
    "            document[word] = document[word]*IDF[word]\n",
    "            \n",
    "    return TFIDF"
   ]
  },
  {
   "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": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "TFIDF = tf_idf(tweets)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Counter({'cat': 5.298317366548036,\n",
       "          'chews': 5.298317366548036,\n",
       "          'cords': 5.298317366548036,\n",
       "          '#applesnob': 5.298317366548036,\n",
       "          '@apple': 0.2169130015635736}),\n",
       " Counter({'nobody': 5.298317366548036,\n",
       "          'expects': 5.298317366548036,\n",
       "          'spanish': 5.298317366548036,\n",
       "          'inquisition': 5.298317366548036,\n",
       "          '#aapl': 1.9310215365615626}),\n",
       " Counter({'#aapl:5': 5.298317366548036,\n",
       "          'rocket': 5.298317366548036,\n",
       "          'stocks': 5.298317366548036,\n",
       "          'gains': 5.298317366548036,\n",
       "          'december': 4.605170185988092,\n",
       "          'buy': 3.506557897319982,\n",
       "          'apple': 2.5902671654458267}),\n",
       " Counter({'top': 5.298317366548036,\n",
       "          '#tablets': 5.298317366548036,\n",
       "          '3': 4.605170185988092,\n",
       "          'damn': 4.605170185988092,\n",
       "          'right': 3.912023005428146,\n",
       "          '@apple': 0.2169130015635736}),\n",
       " Counter({'know': 4.605170185988092,\n",
       "          'flash': 4.199705077879927,\n",
       "          'crash': 3.912023005428146,\n",
       "          'inc': 3.6888794541139363,\n",
       "          'need': 2.995732273553991,\n",
       "          'apple': 2.5902671654458267,\n",
       "          '#aapl': 1.9310215365615626})]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "TFIDF[:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For convenience, extract the word_dict and word_list from the TFIDF matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def build_vocabulary(TFIDF):\n",
    "    words = set()\n",
    "    \n",
    "    for document in TFIDF:\n",
    "        words |= set(document.keys())\n",
    "    \n",
    "    word_list = list(words)\n",
    "    word_dict = dict(zip(word_list, range(len(word_list))))\n",
    "    \n",
    "    return word_dict, word_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "word_dict, word_list = build_vocabulary(TFIDF)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "We have 927 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": [
       "['jobs',\n",
       " 'dept',\n",
       " 'word',\n",
       " 'night',\n",
       " 'chews',\n",
       " '@timcook',\n",
       " '@applenws',\n",
       " '4',\n",
       " '#worldaidsday',\n",
       " 'needed']"
      ]
     },
     "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",
      "927 unique words\n",
      "200 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": [
       "(927, 200)"
      ]
     },
     "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": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(166, 6.607650686531799),\n",
       " (167, 6.607650686531799),\n",
       " (190, 6.607650686531799),\n",
       " (191, 6.607650686531799),\n",
       " (2, 5.298317366548036)]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "related[:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's take a look a the top 5 results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.607650686531799 166 ipad mini unboxing via @youtube @apple #ipadmini #ipad #macbook #macbookpro #startup #hipster #unboxing\n",
      "6.607650686531799 167 ipad mini first time startup via @youtube @apple #ipadmini #ipad #macbook #macbookpro #startup #hipster #unbox\n",
      "6.607650686531799 190 ipad mini unboxing via @youtube @apple #ipadmini #ipad #macbook #macbookpro #startup #hipster #unboxing\n",
      "6.607650686531799 191 ipad mini first time startup via @youtube @apple #ipadmini #ipad #macbook #macbookpro #startup #hipster #unbox\n",
      "5.298317366548036 2 #aapl:5 rocket stocks buy december gains apple\n"
     ]
    }
   ],
   "source": [
    "for tweet_id, score in related[:5]:\n",
    "    print(score, tweet_id, \" \".join(tweets[tweet_id]))"
   ]
  },
  {
   "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": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cosine_similarity(vec1, vec2):\n",
    "    sim = np.dot(vec1, vec2)\n",
    "    norm1 = np.sqrt(np.dot(vec1, vec1))\n",
    "    norm2 = np.sqrt(np.dot(vec2, vec2))\n",
    "    \n",
    "    return sim/(norm1*norm2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "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, TDM[i, :]) 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",
    "    \n",
    "    return sim_words"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "similar = find_similar_words(new_tweet, TDM)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['#macbook', 'mini', 'rocket']"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_tweet"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "#macbook 0.842346298979266\n",
      "@youtube 0.8273747381258668\n",
      "#hipster 0.8273747381258668\n",
      "#startup 0.8273747381258668\n",
      "mini 0.8227410508913036\n",
      "#ipadmini 0.7963450852368475\n",
      "#macbookpro 0.7800563838816592\n",
      "ipad 0.7617102018231607\n",
      "via 0.7055875474518816\n",
      "#ipad 0.6502130393344844\n"
     ]
    }
   ],
   "source": [
    "for word, score in similar[:10]:\n",
    "    print(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 fine tuned threshold of similarity) to expand our query and retrieve further related documents."
   ]
  },
  {
   "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": 29,
   "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": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(927, 927) (200,) (200, 200)\n"
     ]
    }
   ],
   "source": [
    "m, n = TDM.shape\n",
    "print(u.shape, sigma.shape, vt.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "927 200\n"
     ]
    }
   ],
   "source": [
    "print(m, n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now reduce the internal dimention of these matrices to, say, 10. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "k = 10\n",
    "\n",
    "# Drop the extraneous dimensions in the other two matrices.\n",
    "uk = u[:, :k]\n",
    "vtk = vt[:k, :]\n",
    "\n",
    "# Convert the vector of singular values into a diagonal matrix\n",
    "sigma_k = sigma[:k]\n",
    "Sk = diag(sigma_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": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(927, 10) (10, 10) (10, 200)\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": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '$\\\\sigma_i$')"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 3840x2640 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(range(200), sigma, '*')\n",
    "plt.xlabel(r'$i$')\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": 35,
   "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 3, we have strong mentions of AIDS day and the Produc (RED) iPhone launch:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "day 0.2874648801433019\n",
      "aids 0.2826216409753891\n",
      "world 0.2692253682039415\n",
      "red 0.2647556149261578\n",
      "logo 0.22903406070460522\n",
      "#apple 0.18504347302677887\n",
      "apple 0.13868223906604166\n",
      "dec 0.126388964107643\n",
      "abl 0.1263889641076429\n",
      "launches 0.1263889641076429\n"
     ]
    }
   ],
   "source": [
    "topic_words = top_words(uk[:, 3], 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": 37,
   "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": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "array([-1.62243400e-04,  1.44900491e-02, -1.09973213e-03,  4.30257980e-05,\n",
      "       -9.69106965e-04,  4.54646796e-03, -7.58613138e-04,  2.40772326e-03,\n",
      "       -3.82599561e-03,  1.95924079e-03])\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 1:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "#macbook 0.30723559382139\n",
      "#startup 0.30540145699726695\n",
      "@youtube 0.3054014569972668\n",
      "#hipster 0.30540145699726656\n",
      "#macbookpro 0.29809606289080254\n",
      "via 0.29187957210987736\n",
      "mini 0.20949666233803646\n",
      "ipad 0.20381766001212534\n",
      "#ipadmini 0.1989102566432173\n",
      "startup 0.19327488007614912\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[:10]:\n",
    "    print(word, weight)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Which indeed seems relevant."
   ]
  },
  {
   "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": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "def NMF(V, k):\n",
    "    n, m = V.shape\n",
    "\n",
    "    W = np.random.random((n, k))\n",
    "    H = np.random.random((k, m))\n",
    "\n",
    "    error = 1\n",
    "    err = 1\n",
    "\n",
    "    while err > 1e-3:\n",
    "        old_error = error\n",
    "\n",
    "        hn = np.dot(W.T, V)\n",
    "        hd = np.dot(W.T, np.dot(W, H))\n",
    "\n",
    "        H = H*np.divide(hn, hd)\n",
    "\n",
    "        wn = np.dot(V, H.T)\n",
    "        wd = np.dot(W, np.dot(H, H.T))\n",
    "\n",
    "        W = W*np.divide(wn, wd)\n",
    "\n",
    "        error = np.sum(np.power(V-np.dot(W, H), 2.0))\n",
    "        err = np.abs(old_error-error)\n",
    "\n",
    "    return W, H, error"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see how the error changes with the number of components."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2 32018.631887085055\n",
      "3 31373.95005915488\n",
      "4 30774.179989298864\n",
      "5 30412.75352115216\n",
      "6 29791.57170560251\n",
      "7 29364.28862053748\n",
      "8 28909.80187990415\n",
      "9 28558.76557204411\n",
      "10 28024.99023710909\n",
      "11 27657.906536725688\n",
      "12 27347.876660381447\n",
      "13 26784.260310185968\n",
      "14 26449.62827956901\n",
      "15 26038.484824055056\n",
      "16 25725.22866992439\n",
      "17 25290.938286272245\n",
      "18 24924.853614675354\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/lr/j1bs1q851k15cj5y777nxwph0000gn/T/ipykernel_31018/811614206.py:21: RuntimeWarning: divide by zero encountered in divide\n",
      "  W = W*np.divide(wn, wd)\n",
      "/var/folders/lr/j1bs1q851k15cj5y777nxwph0000gn/T/ipykernel_31018/811614206.py:21: RuntimeWarning: invalid value encountered in divide\n",
      "  W = W*np.divide(wn, wd)\n",
      "/var/folders/lr/j1bs1q851k15cj5y777nxwph0000gn/T/ipykernel_31018/811614206.py:21: RuntimeWarning: invalid value encountered in multiply\n",
      "  W = W*np.divide(wn, wd)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "19 nan\n",
      "20 24155.15231415306\n",
      "21 23803.128544352887\n",
      "22 23459.47919197803\n",
      "23 23151.076689078865\n",
      "24 22829.472584488292\n",
      "25 22516.061653873334\n",
      "CPU times: user 4min 56s, sys: 6.23 s, total: 5min 2s\n",
      "Wall time: 19.7 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "error = []\n",
    "\n",
    "for comps in range(2, 25+1):\n",
    "    W, H, err = NMF(TDM, comps)\n",
    "    print(comps, err)\n",
    "    error.append(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": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Non-Negative Matrix Factorization')"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 3840x2640 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(range(2, 25+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": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "W, H, err = NMF(TDM, 10)"
   ]
  },
  {
   "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 couple of examples:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "search 17.397515780793807\n",
      "wish 16.624991860929047\n",
      "violation 15.775604632491937\n",
      "prosecute 15.062968343990958\n",
      "seizure 14.94066535225985\n",
      "criminal 14.94066535225985\n",
      "privacy 14.940665352259849\n",
      "admin 14.940665352259849\n",
      "could 14.940665352259849\n",
      "@tinfoiltricorn 8.929975215093286\n"
     ]
    }
   ],
   "source": [
    "topic_words = top_words(W[:, 1], word_list)\n",
    "\n",
    "for word, weight in topic_words[:10]:\n",
    "    print(word, weight)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
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     "text": [
      "big 16.61532551006173\n",
      "look 15.541371398947204\n",
      "court 15.480453668433693\n",
      "portfolio 15.480453668433693\n",
      "@samsung 15.480453668433693\n",
      "@robconeybeer 15.480453668433693\n",
      "ip 15.480453668433693\n",
      "battles 15.480453668433693\n",
      "defend 15.480453668433693\n",
      "companies 14.674399458682265\n"
     ]
    }
   ],
   "source": [
    "topic_words = top_words(W[:, 2], word_list)\n",
    "\n",
    "for word, weight in topic_words[:10]:\n",
    "    print(word, weight)"
   ]
  },
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    "<center>\n",
    "     <img src=\"data/D4Sci_logo_full.png\" alt=\"Data For Science, Inc\" align=\"center\" border=\"0\" width=300px> \n",
    "</center>"
   ]
  }
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