explorative-search.ipynb

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    "## Explorative search, graph-based discovery of text documents\n",
    "\n",
    "This notebook introduces Explorative Search. \n",
    "\n",
    "This is a document-word graph-based search technique that leverages NLP and Pagerank, to explore text collections and discover unexpected relations.\n",
    "\n",
    "At the end, you get a way to look for documents that contains a keyword, or that share words similar to documents with this keyword. \n",
    "\n",
    "### Introduction\n",
    "\n",
    "Imagine you have a collection of text documents, and you want to retrieve those which are related to a keyword. A rule of thumb would be : type a keyword, get me all the documents that have this keyword in their text. \n",
    "\n",
    "To rank those results by \"relevance\", classical techniques, such as [Okapi BM25](https://en.wikipedia.org/wiki/Okapi_BM25), are based around Term Frequency (how much the keyword is present in the document) and Inverse Document Frequency (how rare and specific the keyword is). Documents where the keyword is frequent are ranked higher than those where it's not.\n",
    "\n",
    "**This traditional technique works well if you know exactly what you are looking for. But if you don't, it falls appart.**  \n",
    "\n",
    "This is especially the case when dealing with a large knowledge base, where you don't really know what's inside. Instead of looking up for a perticular document, you usually want to just explore the collection, discover interesting relations, or get a better undersanding of the knowledge base. For example, by searching for the keyword \"yoghourt\", you'd actually be interested in learning about \"milk industry\", \"agricultural sector\", \"rural areas\", and other stuff loosely related to yoghourt.\n",
    "\n",
    "The technique I introduce here helps you discover a text-based knowledge base by leveraging a document-word graph representation of the document collection. "
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   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from sklearn.feature_extraction.text import CountVectorizer, TfidfVectorizer\n",
    "from sknetwork.visualization import svg_bigraph\n",
    "from IPython.display import SVG\n",
    "from sknetwork.ranking import BiPageRank, top_k, PageRank\n",
    "\n",
    "# We will not consider those words in processing\n",
    "stop_words = [\"I\", \"the\", \"he\", \"she\", \"it\", \"is\", \"of\", \"to\", \"in\", \"his\", \"her\", \"their\", \"its\", \"a\", \"out\", \"of\", \"on\", \"up\", \"with\", \"for\", \"at\", \"should\", \"not\", \"is\", \"as\", \"no\", \"and\", \"by\", \"be\", \"into\", \"from\"]"
   ]
  },
  {
   "source": [
    "### Data \n",
    "\n",
    "We will be working with a dataset of ABC news headlines (Austalian Broadcasting Corporation). Thanks to Rohit Kulkarni for [sharing this dataset on Kaggle](https://www.kaggle.com/therohk/million-headlines). There are more than a million headlines in this dataset. "
   ],
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   "cell_type": "code",
   "execution_count": 5,
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   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Number of documents: 1155838\n"
     ]
    }
   ],
   "source": [
    "df = pd.read_csv(\"data/abcnews-date-text.csv\")\n",
    "df.drop_duplicates(subset=[\"headline_text\"], ignore_index=True, inplace=True)\n",
    "print(f\"Number of documents: {df.shape[0]}\")"
   ]
  },
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   "execution_count": 6,
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   "outputs": [
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     "text": [
      "Average doc length: 6.56\n"
     ]
    },
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "doc_length = df['headline_text'].apply(lambda x: len(x.split(\" \")))\n",
    "\n",
    "print(f\"Average doc length: {np.mean(doc_length):.2f}\")\n",
    "\n",
    "plt.hist(doc_length, rwidth=0.8)\n",
    "plt.title(\"Distribution of sentence length in documents\")\n",
    "plt.xticks(range(14))\n",
    "plt.xlabel(\"Sentence length\")\n",
    "plt.ylabel(\"# documents\")\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "## Creating a graph out of text\n",
    "\n",
    "A bag-of-word embedding is a vector representation of text, where each row is a document and each column is a word. In its simplest form, if a word is in a document, then there is a 1 in the cell. Otherwise, there is 0. \n",
    "\n",
    "$$x_{\\text{doc}^i} = [0, \\dots, 0, 1, 0, \\dots, 0, 1, 0, 0, 1] \\in \\mathbb{R}^{(\\text{# words})}$$\n",
    "\n",
    "$$X = \\begin{bmatrix} x_{\\text{doc}^1} \\\\ \\dots \\\\ x_{\\text{doc}^{(\\text{# docs})}} \\end{bmatrix} \\in \\mathbb{R}^{(\\text{# docs}) \\times (\\text{# words})}$$\n",
    "\n",
    "For a corpus of text, this representation can be interpretated as a [bigraph](https://en.wikipedia.org/wiki/Bigraph) adjacency matrix. That is, the mathematical encoding of a graph, where documents are linked to each other through shared words. This is called a document-word graph.\n",
    "\n",
    "Below, on the left, you have 30 random article headlines. On the right, they are connected to words. You can jump from an article to another by following their common words. "
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ],
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     },
     "metadata": {},
     "execution_count": 7
    }
   ],
   "source": [
    "nb_sub_samples = 30\n",
    "small_df = df.sample(nb_sub_samples, random_state=10)\n",
    "\n",
    "# Note that min_df is 2 : we only consider words that are present in 2 documents\n",
    "count_2 = CountVectorizer(min_df=2, binary=True, stop_words=stop_words)\n",
    "small_adjacency = count_2.fit_transform(small_df[\"headline_text\"])\n",
    "reverse_vocab = {v: k for k, v in count_2.vocabulary_.items()}\n",
    "names_col = [reverse_vocab[i] for i in range(len(reverse_vocab))]\n",
    "names_row = list(range(nb_sub_samples))\n",
    "\n",
    "image = svg_bigraph(small_adjacency, names_row=names_row, names_col=names_col, width=600)\n",
    "SVG(image)"
   ]
  },
  {
   "source": [
    "Let's now encode as a document-word biadjacency the full dataset. In the following, we'll refer to it loosely as adjacency or graph.\n",
    "\n",
    "Because of the large amount of documents, we won't be showing the graph. \n",
    "\n",
    "Note that this graph only needs to be computed once, and then can be infinitely reused at inference time."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Shape of the full adjacency matrix: (1155838, 62077)\nNumber of non-zero elements: 6471079\nCPU times: user 14 s, sys: 206 ms, total: 14.2 s\nWall time: 14.2 s\n"
     ]
    }
   ],
   "source": [
    "%%time \n",
    "\n",
    "count = CountVectorizer(min_df=2, binary=True, stop_words=stop_words)\n",
    "adjacency = count.fit_transform(df['headline_text'])\n",
    "print(\"Shape of the full adjacency matrix:\", adjacency.shape)\n",
    "print(\"Number of non-zero elements:\", adjacency.nnz)"
   ]
  },
  {
   "source": [
    "We keep only words that appear in at least 2 documents. This is because if a word only in only one document, there is no ranking to do : just return the single document where this word is."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "## Using PageRank to search through documents\n",
    "\n",
    "We are going to use a variant of PageRank algorithm on this adjacency matrix. \n",
    "\n",
    "### The PageRank algorithm\n",
    "\n",
    "[PageRank](https://en.wikipedia.org/wiki/PageRank) is an algorithm developed by Google in the 2000s to find relevant websites based on their URL links. At the time, websites at the top of Google seach were those who were the most linked to, and by websites that were also the most linked to. This ranking of websites is made by averaging several random walks on the website-website graph. \n",
    "\n",
    "Intuitively, imagine robots starting on random webpages, that randomly click on any link they see. These robots keep a record on which websites they end up most often : those would be at the top of the search results. At the end, they create a ranking of all the websites. [Markov chain](https://en.wikipedia.org/wiki/Markov_chain) theory guarantees that the PageRank algorithm converges towards a unique ranking of the websites. \n",
    "\n",
    "BiPageRank is the same idea, but applied to bigraphs. In our case, the algorithm will perform a random walk from an article, to a word, to another article, to a word, and so on. \n",
    "\n",
    "Computationally, this random walk is nothing more than matrix-vector multiplications, something we can easily parallelize and speed up. "
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "bpr = BiPageRank()\n",
    "\n",
    "def disp_results(df, scores, k=10, col='headline_text'):\n",
    "    for rank, (i, row) in enumerate(df.iloc[top_k(scores, k)].iterrows()):\n",
    "        print(f\"{rank+1}: (idx: {i}) {row[col]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "1: (idx: 1077357) what did your 10 year old self think you would be 20 years later\n2: (idx: 954323) nrn spring in nsw has kicked off well but rain needed in 10 days\n3: (idx: 837662) manly sea eagles post 14 12 nrl win over south sydney rabbitohs\n4: (idx: 837969) wests tigers post comfortable 42 12 nrl win over gold coast tit\n5: (idx: 1119404) new hiv cases in wa hit 10 year low thanks to prep pill success\n6: (idx: 1052899) afl scorecentre nmfc crows pies blues port wce gc cats dogs rich\n7: (idx: 1090106) north qld town cut off record flood levels big wet heading west\n8: (idx: 1101349) full time job rate hits new low as casual work takes over report\n9: (idx: 924509) warriors score last gasp 20 16 win over sharks after frantic fi\n10: (idx: 850178) south sydney rabbitohs post 40 18 nrl win over gold coast titan\n"
     ]
    }
   ],
   "source": [
    "scores = bpr.fit_transform(adjacency)\n",
    "\n",
    "disp_results(df, scores)"
   ]
  },
  {
   "source": [
    "Despite most documents being 4-8 words long, the best ranked ones are 10-14 words long. This is to be expected : long documents have more links to other documents, and are thus better ranked. "
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Average doc length in the top-1000: 11.44\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "print(f\"Average doc length in the top-1000: {np.mean(doc_length.iloc[top_k(scores, 1000)]):.2f}\")\n",
    "\n",
    "plt.hist(doc_length.iloc[top_k(scores, 1000)])\n",
    "plt.title(\"Distribution of sentence length in top-1000 best ranked documents\")\n",
    "plt.xticks(range(20))\n",
    "plt.xlabel(\"Sentence length\")\n",
    "plt.ylabel(\"# documents\")\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "### Personalized PageRank\n",
    "\n",
    "PageRank gives us an absolute ranking. Let's see how to adapt this ranking to a search query. \n",
    "\n",
    "The variant we will be using is called Personalized BiPageRank. Basically, instead of starting our random walk anywhere on the graph, we make it start on a specific node of the graph. To get search results relevant to a word, we will be starting our random walk on this word's node. "
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "1: (idx: 487215) tsunami threat overhyped\n2: (idx: 976724) sandery death threat misunderstanding killa nickname\n3: (idx: 194094) tunbridge dam leak threat eases\n4: (idx: 435816) mccrae grassfire no longer a threat\n5: (idx: 435817) mccrae residents face fire threat\n6: (idx: 818197) patient blacklisting threat symptomatic of\n7: (idx: 425455) wanilla fire threat eases\n8: (idx: 957885) kinkuna homes threat of bushfire\n9: (idx: 440708) octuplets grandmother faces foreclosure threat\n10: (idx: 277854) pichi richi marathon under threat\nCPU times: user 3.79 s, sys: 463 ms, total: 4.26 s\nWall time: 4.6 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "scores = bpr.fit_transform(adjacency, seeds_col={count.vocabulary_[\"threat\"]:1})\n",
    "\n",
    "disp_results(df, scores)"
   ]
  },
  {
   "source": [
    "We can also do it by starting on an article's node. This acts as a recommendation of \"similar articles\". The article we look at is \"more women urged to become councillors\". It yields us articles about various urges over councillors."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "1: (idx: 100) more women urged to become councillors\n2: (idx: 181431) push on for more women councillors\n3: (idx: 860260) councillors urged to back more wholistic way to\n4: (idx: 107014) blokes chauvinism dudding potential councillors\n5: (idx: 369155) new councillors urged to quickly grasp issues\n6: (idx: 853565) councillors urged to back old castlemaine gaol\n7: (idx: 647743) lake councillors urged to reject biodiversity offsets policy\n8: (idx: 999085) perth councillors urged not to criticise lord mayor scaffidi\n9: (idx: 43309) councillors urged to consider roles during\n10: (idx: 446823) lake wooloweyah subdivision divides councillors\n"
     ]
    }
   ],
   "source": [
    "scores = bpr.fit_transform(adjacency, seeds_row={100:1})\n",
    "\n",
    "disp_results(df, scores)"
   ]
  },
  {
   "source": [
    "We can also start from several nodes, both articles and words, to perform complex searches. For example, let's look at articles similar to \"more women urged to become councillors\", but also to \"police\" and \"fire\". The third result is about a man charged (i.e. arrested by the *police*) after setting a *fire* in *councillors* office : very relevant to our (bizarre) search query. "
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "1: (idx: 100) more women urged to become councillors\n2: (idx: 126113) councillors under fire over adult entertainment\n3: (idx: 188806) councillors under fire after pay rise\n4: (idx: 749241) man charged over brisbane councillors office fire\n5: (idx: 125191) councillors want no fire ban exemptions\n6: (idx: 626086) no show councillors under fire\n7: (idx: 181431) push on for more women councillors\n8: (idx: 860260) councillors urged to back more wholistic way to\n9: (idx: 277645) police meet councillors over noble park hoons\n10: (idx: 952887) bendigo councillors escorted by police\n11: (idx: 932546) dungog councillors urged to act on storm damage in aged care un\n12: (idx: 107014) blokes chauvinism dudding potential councillors\n13: (idx: 369155) new councillors urged to quickly grasp issues\n14: (idx: 853565) councillors urged to back old castlemaine gaol\n15: (idx: 999085) perth councillors urged not to criticise lord mayor scaffidi\n16: (idx: 914963) councillors urged to approve bendigo hotel pokies\n17: (idx: 647743) lake councillors urged to reject biodiversity offsets policy\n18: (idx: 296972) councillors urged to back nightclubs crackdown\n19: (idx: 852526) councillors urged to reject pretty pool fifo camp\n20: (idx: 43309) councillors urged to consider roles during\nCPU times: user 3.57 s, sys: 304 ms, total: 3.87 s\nWall time: 3.89 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "scores = bpr.fit_transform(adjacency, seeds_row={100:1}, seeds_col={count.vocabulary_[\"police\"]:1, count.vocabulary_[\"fire\"]:1})\n",
    "\n",
    "disp_results(df, scores, 20)"
   ]
  },
  {
   "source": [
    "## Tinkering with the graph\n",
    "\n",
    "Quality and relevancy of search results heavily depends on the quality of the underlying graph. How can we improve it ?"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "### Vary words' importance\n",
    "\n",
    "Not all links should have the same importance. You want links between common words to be weak, and links between rare words to be strong. \n",
    "\n",
    "This is where IDF (Inverse Document Frequency) can come useful. Note that IDF was used in the traditional search algorithm [Okapi BM25](https://en.wikipedia.org/wiki/Okapi_BM25).\n",
    "\n",
    "Let's do a series of comparison, where we search for the keyword \"house\". \n",
    "\n",
    "#### Basic binary count\n",
    "\n",
    "Let's start with the basic \"binary count\" approach we introduced first. \n",
    "\n",
    "Every common word is treated as equally important, which is not the case in practice. This is not the behaviour we want. "
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Binary count\n",
      "1: (idx: 1129765) perth iwan iwanoff designed paganin house restored after fire\n",
      "2: (idx: 974689) perth local treasure lost as iwanoff paganin house burns\n",
      "3: (idx: 859275) mattie furphy house\n",
      "4: (idx: 760275) the upper house ammends the forest peace deal bill\n",
      "5: (idx: 1119631) dance rites sydney opera house winners nunukul yuggera\n",
      "6: (idx: 889750) upper house ammends anti protest laws\n",
      "7: (idx: 692235) blaze destroys torrumbarry house\n",
      "8: (idx: 1017958) tree crashes into house in melbourne kalorama\n",
      "9: (idx: 491128) ratbags in the upper house brumby\n",
      "10: (idx: 670115) barnabas house\n"
     ]
    }
   ],
   "source": [
    "print(\"Binary count\")\n",
    "scores = bpr.fit_transform(adjacency, seeds_col={count.vocabulary_[\"house\"]:1})\n",
    "disp_results(df, scores)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Average : 6.52 tokens long\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def disp_len(df, scores, k=10):\n",
    "    sentences = df.iloc[top_k(scores, k)]['headline_text'].str.split(' ')\n",
    "    sentences = [len(sentence) for sentence in sentences]\n",
    "    print(f\"Average : {np.mean(sentences)} tokens long\") # Global average is 6.56\n",
    "    plt.bar(range(len(sentences)), sentences)\n",
    "    plt.title('Document length by ranking')\n",
    "    plt.xlabel(\"Ranking\")\n",
    "    plt.ylabel(\"Number of tokens in document\")\n",
    "    plt.show()\n",
    "\n",
    "disp_len(df, scores, 100)"
   ]
  },
  {
   "source": [
    "#### TF-IDF\n",
    "\n",
    "Let's encode the adjacency matrix with [TF-IDF](https://en.wikipedia.org/wiki/Tf%E2%80%93idf).\n",
    "\n",
    "$$TFIDF(\\text{word}) = \\frac{\\text{word count}}{\\text{sentence length}} \\log_2(\\frac{\\text{documents count}}{\\text{documents with word count}})$$\n",
    "\n",
    "This rankin favours :\n",
    "- short documents. Indeed, in short documents, the term frequency $\\frac{\\text{word count}}{\\text{sentence length}}$ is the highest since sentence length is small. This means links to short articles are the strongest. \n",
    "- repeating words. Due to the term frequency, query words appearing more than once in the documents are favoured. This can be seen in the ranking below, where every document has \"house\" at least twice. "
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "TF-IDF encoding\n",
      "1: (idx: 1021231) crowded house to reunite for encore opera house gigs\n",
      "2: (idx: 1141783) fatal house fire in guidlford west hydro house in heckenberg\n",
      "3: (idx: 1137501) briggs bad apples house party line up on steps of opera house\n",
      "4: (idx: 1078692) brisbane house detective uncovering house histories\n",
      "5: (idx: 1148698) white house calls house impeachment probe unconstitutional\n",
      "6: (idx: 866466) anglican parish to sell house of worship roberts house\n",
      "7: (idx: 102585) parliament house may house gold coast artworks\n",
      "8: (idx: 760860) police reinforcements conduct house to house\n",
      "9: (idx: 898832) sierra leone to start house to house searches for ebola patients\n",
      "10: (idx: 185546) house to house search begins in new orleans\n"
     ]
    }
   ],
   "source": [
    "tfidf = TfidfVectorizer(min_df=2, stop_words=stop_words, norm=None) # By default tfidf is normalized (divided by the max). We don't want that here. \n",
    "adjacency_tfidf = tfidf.fit_transform(df['headline_text'])\n",
    "\n",
    "print(\"TF-IDF encoding\")\n",
    "scores_tfidf = bpr.fit_transform(adjacency_tfidf, seeds_col={tfidf.vocabulary_[\"house\"]:1})\n",
    "disp_results(df, scores_tfidf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Average : 6.52 tokens long\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "disp_len(df, scores_tfidf, 100)"
   ]
  },
  {
   "source": [
    "#### IDF\n",
    "\n",
    "If you don't want to favour repetition or short documents, we can consider only the IDF. We compute it by dividing the TF-IDF values by the TF (term frequency). \n",
    "\n",
    "$$IDF(\\text{word}) = \\log_2(\\frac{\\text{documents count}}{\\text{documents with word count}})$$\n",
    "\n",
    "Difference is subtle. \n"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "IDF encoding\n",
      "1: (idx: 1021231) crowded house to reunite for encore opera house gigs\n",
      "2: (idx: 1137501) briggs bad apples house party line up on steps of opera house\n",
      "3: (idx: 1078692) brisbane house detective uncovering house histories\n",
      "4: (idx: 1148698) white house calls house impeachment probe unconstitutional\n",
      "5: (idx: 866466) anglican parish to sell house of worship roberts house\n",
      "6: (idx: 898832) sierra leone to start house to house searches for ebola patients\n",
      "7: (idx: 185546) house to house search begins in new orleans\n",
      "8: (idx: 4141) authorities go house to house to fight dengue\n",
      "9: (idx: 1129765) perth iwan iwanoff designed paganin house restored after fire\n",
      "10: (idx: 974689) perth local treasure lost as iwanoff paganin house burns\n"
     ]
    }
   ],
   "source": [
    "freq = TfidfVectorizer(min_df=2, stop_words=stop_words, use_idf=False, vocabulary=tfidf.vocabulary_, norm=None)\n",
    "adjacency_freq = freq.fit_transform(df['headline_text'])\n",
    "\n",
    "adjacency_idf = adjacency_tfidf.copy()\n",
    "adjacency_idf.data = adjacency_idf.data / adjacency_freq.data\n",
    "\n",
    "print(\"IDF encoding\")\n",
    "scores_idf = bpr.fit_transform(adjacency_idf, seeds_col={tfidf.vocabulary_[\"house\"]:1})\n",
    "disp_results(df, scores_idf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Average : 6.47 tokens long\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "disp_len(df, scores_idf, 100)"
   ]
  },
  {
   "source": [
    "#### Thresholded IDF\n",
    "\n",
    "Let's compare the link strenghts distributions of the last 3 techniques. "
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "from sknetwork.linalg.normalization import normalize\n",
    "\n",
    "plt.hist(adjacency.data, alpha=0.5, label='Binary count', density=True, width=1)\n",
    "plt.hist(adjacency_tfidf.data, bins=50, alpha=0.5, label='TF-IDF', density=True)\n",
    "plt.hist(adjacency_idf.data, bins=50, alpha=0.5, label='IDF', density=True)\n",
    "plt.xlim(xmax=15)\n",
    "plt.ylim(ymax=0.25)\n",
    "plt.title(\"Comparison of link strengths distributions\\nfor various adjacency encoding\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "TF-IDF max link strenght: 47.85841908641853\nIDF max link strenght: 47.85841908641853\n"
     ]
    }
   ],
   "source": [
    "print(\"TF-IDF max link strenght:\", adjacency_tfidf.data.max())\n",
    "print(\"IDF max link strenght:\", adjacency_idf.data.max())"
   ]
  },
  {
   "source": [
    "For the IDF and DF distributions of link strengths, there is a long tail. This means that a few keywords have a very disproportionally large value. Those will pull any search results toward them. These are probably words that appeared in only 2 or 3 documents (we've kept only words that appeared at least twice). \n",
    "\n",
    "To prevent this issue, we **threshold** the IDF values."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "# You can chose it using quantiles\n",
    "threshold = np.quantile(adjacency_idf.data, 0.999)\n",
    "\n",
    "adjacency_idf_thresh = adjacency_idf.copy()\n",
    "adjacency_idf_thresh.data[adjacency_idf.data > threshold] = threshold\n",
    "\n",
    "plt.hist(adjacency_idf_thresh.data, bins=50)\n",
    "plt.title('Thresholded IDF distribution of link strengths')\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "In our case, it doesn't change the search result, but it's safer for exotic queries or datasets. You can similarly do a lower threshold to remove weak links, assuming they are not important, and this way sparsify more the document-word graph. "
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Thresholded IDF encoding\n",
      "1: (idx: 1021231) crowded house to reunite for encore opera house gigs\n",
      "2: (idx: 1137501) briggs bad apples house party line up on steps of opera house\n",
      "3: (idx: 1078692) brisbane house detective uncovering house histories\n",
      "4: (idx: 1148698) white house calls house impeachment probe unconstitutional\n",
      "5: (idx: 866466) anglican parish to sell house of worship roberts house\n",
      "6: (idx: 898832) sierra leone to start house to house searches for ebola patients\n",
      "7: (idx: 185546) house to house search begins in new orleans\n",
      "8: (idx: 4141) authorities go house to house to fight dengue\n",
      "9: (idx: 1129765) perth iwan iwanoff designed paganin house restored after fire\n",
      "10: (idx: 974689) perth local treasure lost as iwanoff paganin house burns\n"
     ]
    }
   ],
   "source": [
    "print(\"Thresholded IDF encoding\")\n",
    "scores_idf = bpr.fit_transform(adjacency_idf_thresh, seeds_col={tfidf.vocabulary_[\"house\"]:1})\n",
    "disp_results(df, scores_idf)"
   ]
  },
  {
   "source": [
    "\n",
    "#### Using IDF for parsing the search query\n",
    "\n",
    "Notice how we can assign weights to words in the search query. Just like words in a document are not all important, words in a query are not all important.\n",
    "\n",
    "The idea is to assign weights to keywords based on their IDF encoding (or any other previous encoding). "
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "ceo IDF: 7.6059747147371475\nping IDF: 12.321279715543366\n"
     ]
    }
   ],
   "source": [
    "ceo_idf = tfidf.idf_[tfidf.vocabulary_[\"ceo\"]] \n",
    "ping_idf = tfidf.idf_[tfidf.vocabulary_[\"ping\"]]\n",
    "\n",
    "print(\"ceo IDF:\", house_idf)\n",
    "print(\"ping IDF:\", ping_idf)"
   ]
  },
  {
   "source": [
    "If we look for \"ceo ping\", you can see how \"ceo\" is kind of ignored by the search engine to favour results related to \"ping\". "
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "1: (idx: 116274) ping ping leaves coast for china olympics role\n2: (idx: 794097) shang ping xie speaks to pacific beat\n3: (idx: 802705) xi jing ping has 'the floor to himself' at apec after o\n4: (idx: 874609) cameras to ping drivers of unregistered uninsured cars\n5: (idx: 762557) ping pong bum features at the lucy creek olympics\n6: (idx: 713861) malaysian senator gan ping sieu talks to radio\n7: (idx: 1118157) ping pong playing robot on display at china import expo\n8: (idx: 385962) aussie team takes aim at chinas ping pong royalty\n9: (idx: 51511) outrage at prisoners ping pong payout\n10: (idx: 749443) ceo of kini tv yong kai ping speaks to asia\n11: (idx: 1119196) ah ping ban sentence for body in suitcase murder annabelle chen\n12: (idx: 786699) extended interview with ping fu\n13: (idx: 1024184) ping pongathon aims to stop human trafficking\n14: (idx: 845302) pliskova; shang impres at malaysian open\n15: (idx: 887213) extended interview with jing ulrich\n16: (idx: 1091011) sa liberal candidate jing lee pushing for upper house election\n17: (idx: 25736) group seeks to stop big gan gan development\n18: (idx: 250196) camera snaps unregistered uninsured drivers\n19: (idx: 798799) uninsured ambulance patients in regional victoria being billed\n20: (idx: 580402) uninsured shouldnt be covered for floods\n"
     ]
    }
   ],
   "source": [
    "scores_idf = bpr.fit_transform(adjacency_idf, seeds_col={\n",
    "    tfidf.vocabulary_[\"ceo\"]: ceo_idf,\n",
    "    tfidf.vocabulary_[\"ping\"]: ping_idf\n",
    "    })\n",
    "disp_results(df, scores_idf, 20)"
   ]
  },
  {
   "source": [
    "### Lower the word quantity\n",
    "\n",
    "According to my experience, this search technique works best with short documents that have all roughly the same size:\n",
    "\n",
    "- Signal-to-noise ratio is high: with too many parasit words, you'll have less relevant results. \n",
    "- The algorithm is much faster with a sparse and small graph. In that sense, rare and meaningful links are great. \n",
    "- If a document has too many words, it has more chance to show up in search results, regardless of its content. Think of an article that contains all the others articles: it will always come up on top. \n",
    "\n",
    "Let's see how you can lower documents' length. "
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "#### Stemming and lemmatization\n",
    "\n",
    "These are two NLP techniques that clean up the text before building the graph. \n",
    "- **[Stemming](https://www.geeksforgeeks.org/python-stemming-words-with-nltk/)** : remove the varying end of words. Ex: liking, likely, liked, likes => like \n",
    "- **[Lemmatization](https://www.geeksforgeeks.org/python-lemmatization-with-nltk/)** : get back to the root of the word. Ex: better => good, rocks => rock, maxima => maximum\n",
    "\n",
    "This way, singular and plurals become the same tokens (words).\n",
    "\n",
    "Even though you only need to do it once for each document, lemmatization is costly. It needs to understand the role of each word in a sentence (noun, verb, adjective, etc.). In this notebook, we will perform it only on a susbsample of 30,000 documents. "
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "CPU times: user 3min 3s, sys: 1.18 s, total: 3min 4s\nWall time: 3min 8s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "import spacy\n",
    "\n",
    "# Initialize spacy 'en' model, keeping only tagger component needed for lemmatization\n",
    "nlp = spacy.load('en_core_web_sm', disable=['parser', 'ner'])\n",
    "\n",
    "# Lemmatization takes a long time, because it needs to guess the role of each word in a sentence\n",
    "# We will do it on a subsample of our dataset\n",
    "\n",
    "df_small = df.sample(30000, random_state=10)\n",
    "\n",
    "def lemmatize(sentence):\n",
    "    # Apply lemmatization to each word in a sentence\n",
    "    return [token.lemma_ for token in nlp(sentence)]\n",
    "\n",
    "df_small['cleaned_text'] = df_small[\"headline_text\"].map(lambda x: lemmatize(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We already tokenized our text in the previous step, so we change the preprocessor and tokenizer to a dummy function\n",
    "def dummy(x):\n",
    "    return x\n",
    "\n",
    "count_lem = CountVectorizer(min_df=2, binary=True, stop_words=stop_words, preprocessor=dummy, tokenizer=dummy, token_pattern=None)\n",
    "adjacency_small_lem = count_lem.fit_transform(df_small[\"cleaned_text\"].to_list())\n",
    "\n",
    "# We will also compare the results to the method without lemmatization\n",
    "count_small = CountVectorizer(min_df=2, binary=True, stop_words=stop_words)\n",
    "adjacency_small = count_small.fit_transform(df_small[\"headline_text\"])"
   ]
  },
  {
   "source": [
    "With lemmatization, we have ~20% less tokens. Since PageRank works by doing matrix multiplication, at scale, this could be a huge improvement in inference time. "
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Without lemmatization: 11767 tokens.\nWith lemmatization: 9472 tokens.\n"
     ]
    }
   ],
   "source": [
    "print(f\"Without lemmatization: {len(count_small.vocabulary_)} tokens.\")\n",
    "print(f\"With lemmatization: {len(count_lem.vocabulary_)} tokens.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "['accidents',\n",
       " 'riders',\n",
       " 'documents',\n",
       " 'wearing',\n",
       " 'lyons',\n",
       " 'voices',\n",
       " 'undermining',\n",
       " 'fired',\n",
       " 'bucks',\n",
       " 'dumps']"
      ]
     },
     "metadata": {},
     "execution_count": 84
    }
   ],
   "source": [
    "# Some of the removed tokens : mostly composed words. \n",
    "list(set(count_small.vocabulary_.keys()) - set(count_lem.vocabulary_.keys()))[:10]"
   ]
  },
  {
   "source": [
    "We run the algorithm on a query example, the article 1000. "
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "1: (idx: 1000) assault rate battered by tougher pub laws\n",
      "2: (idx: 11934) power outages as darwin battered by severe storm\n",
      "3: (idx: 18875) battered reds desperate for turnaround\n",
      "4: (idx: 3429) storm battered sunshine coast cleans up\n",
      "5: (idx: 23571) pacific island nations battered by heavy rains and strong winds\n",
      "6: (idx: 16117) homes flooded as england battered by more rain\n",
      "7: (idx: 17796) call for tougher pollution laws as hunter tops list of hotspots\n",
      "8: (idx: 19821) tougher laws planned against repeat drink drivers\n",
      "9: (idx: 5114) texting and driving deserves tougher penalty\n",
      "10: (idx: 2727) arsonists to face tougher penalties\n",
      "CPU times: user 170 ms, sys: 12.1 ms, total: 182 ms\n",
      "Wall time: 194 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# Without lemmatization\n",
    "scores = bpr.fit_transform(adjacency_small, seeds_row={1000:1})\n",
    "\n",
    "disp_results(df_small.reset_index(), scores)"
   ]
  },
  {
   "source": [
    "With lemmatization, the explorative search algorithm ranks higher articles which have any form of the verb \"shed\", such as \"sheds\". Every variation of \"shed light\" is better ranked. "
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "1: (idx: 1000) assault rate battered by tougher pub laws\n2: (idx: 29934) 43 dead as storm batters caribbean\n3: (idx: 29855) irene batters bahamas; heads for us\n4: (idx: 13702) rockin research shows head banging batters brains\n5: (idx: 18875) battered reds desperate for turnaround\n6: (idx: 1750) bulls buck the trend to batter blues\n7: (idx: 11934) power outages as darwin battered by severe storm\n8: (idx: 4788) typhoon soudelor batters chinas south east\n9: (idx: 21782) extreme weather batters parts of nsw\n10: (idx: 23571) pacific island nations battered by heavy rains and strong winds\nCPU times: user 108 ms, sys: 74 µs, total: 108 ms\nWall time: 110 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# With lemmatization\n",
    "scores = bpr.fit_transform(adjacency_small_lem, seeds_row={1000:1})\n",
    "\n",
    "disp_results(df_small.reset_index(), scores)"
   ]
  },
  {
   "source": [
    "Note that you'll have to do some query processing : the user usually isn't looking for lemmatized words, or considered lemmatized words as equivalent. \n",
    "\n",
    "If a user looks for a word, a trick is to put as seed every article containing _exactly_ this word. This way, PageRank takes care of ranking pages based on loose links, but starting from a more specific query. Let's take an example with the word \"fired\". "
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "False\n"
     ]
    }
   ],
   "source": [
    "print(\"fired\" in count_lem.vocabulary_) # fired is not in the vocabulary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "1: (idx: 16269) utah police officer who dragged screaming nurse is fired\n2: (idx: 11044) shots fired in airport van heist\n3: (idx: 24876) shot fired mcdonalds para hills\n4: (idx: 7133) claims mortar from gaza fired into israel\n5: (idx: 509) cctv of queanbeyan hotel ram raid shows shot fired near employee\n6: (idx: 17726) anthony scaramucci on being fired from the white\n7: (idx: 3018) rockets fired into kabul on day two of jirga\n8: (idx: 28766) shots fired outside hotel\n9: (idx: 9786) qassam rockets fired at southern israel no injuries\n10: (idx: 8205) man arrested after shots fired in northern tasmania\n"
     ]
    }
   ],
   "source": [
    "# Due to sampling, we reindex articles between 0 and 30 000\n",
    "articles_with_fired = np.arange(0, df_small.shape[0])[df_small[\"headline_text\"].map(lambda headline: \"fired\" in headline)]\n",
    "# Otherwise we could just do\n",
    "# df_small[df_small[\"headline_text\"].map(lambda headline: \"fired\" in headline)].index\n",
    "\n",
    "# We set as seeds all the articles with \"fired\" in them. \n",
    "scores = bpr.fit_transform(adjacency_small_lem, seeds_row={article_id:1 for article_id in articles_with_fired})\n",
    "\n",
    "disp_results(df_small.reset_index(), scores) # We see that articles with fired are on top, but still ranked"
   ]
  },
  {
   "source": [
    "#### Keywords summary\n",
    "\n",
    "Long documents have an unfair advantage over short ones: they are connected to more documents, and thus show up more often in search results, even if they are not relevant to the search query. For the extreme pathological case, think of a document containing the text of every other document.  \n",
    "\n",
    "Thus, to shorten these documents, we can \n",
    "\n",
    "- Troncate them (consider only the first 10 words for example). A common baseline for NLP text summarization algorithms is to compare them to just keeping the first 3 sentences of a text. \n",
    "- Summarize them to their most important keywords, tags, topics... \n",
    "- Do both: summarize them to their keywords, and only keep the 10 most important keywords. \n",
    "\n",
    "I'll show you a graph-based technique to detect keywords. \n",
    "\n",
    "##### For mid-sized text documents\n",
    "\n",
    "First, we build the co-occurence matrix, that contains how many times a word follows another. Then, we run PageRank over it. "
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_small = df.sample(30000, random_state=10) # Only consider a subsample \n",
    "\n",
    "count_small = CountVectorizer(min_df=2, binary=True, stop_words=stop_words)\n",
    "adjacency_small = count_small.fit_transform(df_small[\"headline_text\"])\n",
    "\n",
    "cooccurence = (adjacency_small.T * adjacency_small)\n",
    "cooccurence.setdiag(0)\n",
    "cooccurence = cooccurence.astype(np.int).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "pr = PageRank()\n",
    "words_scores = pr.fit_transform(cooccurence)"
   ]
  },
  {
   "source": [
    "We now have a ranked list of all the words of our documents, from most central to less central ones. Note that, by inspecting the most central words, you can spot stop words. "
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Top 20 keywords: ['over', 'after', 'police', 'new', 'man', 'says', 'us', 'court', 'more', 'govt', 'council', 'australia', 'fire', 'nsw', 'australian', 'water', 'plan', 'off', 'sydney', 'wa']\nBottom 20 keywords: ['gx', 'bovine', 'fleming', 'gardner', 'canberras', 'staggers', 'leeton', 'milking', 'nc', 'florence', 'almond', 'cw', 'triabunna', 'pkg', 'pigeons', 'zach', 'nimmie', 'oberon', 'cansdell', 'coonawarra']\n"
     ]
    }
   ],
   "source": [
    "reverse_vocab_small = {idx: word for word, idx in count_small.vocabulary_.items()}\n",
    "ordered_keywords = [reverse_vocab_small[idx] for idx in np.argsort(-words_scores)]\n",
    "reverse_ordered_keywords = [reverse_vocab_small[idx] for idx in np.argsort(words_scores)]\n",
    "\n",
    "print(\"Top 20 keywords:\", ordered_keywords[:20])\n",
    "print(\"Bottom 20 keywords:\", ordered_keywords[-20:])"
   ]
  },
  {
   "source": [
    "To summarize an article to its keyword, we keep only its 10 most rare (least central) keywords. This way, articles that have a lengthy description with keyword stuffing (putting loads of popular keywords) won't be advantaged by Pagerank. "
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "CPU times: user 1min 3s, sys: 15.4 ms, total: 1min 3s\nWall time: 1min 3s\n"
     ]
    }
   ],
   "source": [
    "%%time \n",
    "# Just like lemmatization, this is the lengthiest part\n",
    "\n",
    "def keep_only_k_keywords(txt, k=5):\n",
    "    tokens = txt.split(\" \") # You may want to do more fancy tokenization here\n",
    "    keyword_summary = []\n",
    "    for keyword in reverse_ordered_keywords:\n",
    "        if keyword in tokens:\n",
    "            keyword_summary.append(keyword)\n",
    "        if len(keyword_summary) >= k:\n",
    "            break\n",
    "    return keyword_summary\n",
    "\n",
    "df_small['keyword_text'] = df_small[\"headline_text\"].map(keep_only_k_keywords)"
   ]
  },
  {
   "source": [
    "Compare results. Note how the number of connexions (edges) in the graph is lowered much more than the amount of keywords. "
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Before keyword summarization: 11767 tokens, 158597 edges\nAfter keyword summarization: 11726 tokens, 136182 edges\n"
     ]
    }
   ],
   "source": [
    "count_small_kw = CountVectorizer(min_df=2, binary=True, stop_words=stop_words, tokenizer=dummy, preprocessor=dummy)\n",
    "adjacency_small_kw = count_small_kw.fit_transform(df_small[\"keyword_text\"])\n",
    "\n",
    "print(f\"Before keyword summarization: {len(count_small.vocabulary_)} tokens, {adjacency_small.sum()} edges\")\n",
    "print(f\"After keyword summarization: {len(count_small_kw.vocabulary_)} tokens, {adjacency_small_kw.sum()} edges\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Before keyword summarization\n1: (idx: 913322) victorian upper house considers sanction westgate distributor\n2: (idx: 1080744) ssm introduced in the house of representatives\n3: (idx: 361600) fire damages vacant house in moe\n4: (idx: 493499) upper house hearings on track\n5: (idx: 384766) kim landers traces obamas quest for the white house\n6: (idx: 1018904) man dies in sydney house fire started by heater\n7: (idx: 963499) le corbusier tapestry on display at parliament house\n8: (idx: 930914) verrender who's the real culprit behind soaring house prices\n9: (idx: 584603) suspicious house fire in coconut grove\n10: (idx: 344089) gm bill introduced into upper house\n"
     ]
    }
   ],
   "source": [
    "print(\"Before keyword summarization\")\n",
    "scores = bpr.fit_transform(adjacency_small, seeds_col={count_small.vocabulary_[\"house\"]:1})\n",
    "disp_results(df_small, scores)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "After keyword summarization\n1: (idx: 1080744) ssm introduced in the house of representatives\n2: (idx: 361600) fire damages vacant house in moe\n3: (idx: 584603) suspicious house fire in coconut grove\n4: (idx: 963499) le corbusier tapestry on display at parliament house\n5: (idx: 493499) upper house hearings on track\n6: (idx: 531052) candles may have sparked brisbane house fire\n7: (idx: 684038) candles blamed for house fire\n8: (idx: 1155051) article one and two of impeachment passes house of reps\n9: (idx: 178573) more mercury removed from hamilton boarding house\n10: (idx: 344089) gm bill introduced into upper house\n"
     ]
    }
   ],
   "source": [
    "print(\"After keyword summarization\")\n",
    "scores = bpr.fit_transform(adjacency_small_kw, seeds_col={count_small_kw.vocabulary_[\"house\"]:1})\n",
    "disp_results(df_small, scores)"
   ]
  },
  {
   "source": [
    "##### For longer documents\n",
    "\n",
    "- [Textrank](https://cran.r-project.org/web/packages/textrank/vignettes/textrank.html): similar to what we did above using PageRank, but on a single document instead of the whole corpus. \n",
    "- [Rake](https://pypi.org/project/rake-nltk/): also for a single Document like Textrank, but rank keywords using co-occurence and frequency instead of PageRank."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "## Using other metadata to link documents\n",
    "\n",
    "We are building a graph linking document to each other. But links don't have to only be words. Typically, you'd want to use metadata : tags, categories, dates (shared month+year), shared followers or subscribers... \n",
    "\n",
    "In our case we don't have metadatas, so let's make them up. "
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "df[\"fake_date\"] = pd.date_range(\"01-01-2001\", \"01-01-2010\", periods=df.shape[0])\n",
    "df[\"month\"] = df[\"fake_date\"].dt.month\n",
    "df[\"year\"] = df[\"fake_date\"].dt.year"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import OneHotEncoder\n",
    "\n",
    "oh_month = OneHotEncoder()\n",
    "month_adj = oh_month.fit_transform(df[\"month\"].to_numpy().reshape(-1,1))\n",
    "oh_year = OneHotEncoder()\n",
    "year_adj = oh_month.fit_transform(df[\"year\"].to_numpy().reshape(-1,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.sparse import hstack, csr_matrix\n",
    "\n",
    "# We assign massive weights to month and year so that the link is very visible\n",
    "adjacency_metadata = hstack([adjacency_idf, month_adj*20, year_adj*40])\n",
    "adjacency_metadata = csr_matrix(adjacency_metadata)"
   ]
  },
  {
   "source": [
    "Plotting the distributions, we see that year distribution of top results is heavily skewed after we introduced metadata. "
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "scores_idf = bpr.fit_transform(adjacency_metadata, seeds_col={tfidf.vocabulary_[\"house\"]:1})\n",
    "\n",
    "plt.hist(df['year'], density=True, label=\"Overall distribution\", alpha=0.5)\n",
    "plt.hist(df.iloc[top_k(scores_idf, 100)]['year'], density=True, label=\"Top 100\", alpha=0.5)\n",
    "plt.legend()\n",
    "plt.title(\"Comparison of year distribution in top-100 results and dataset\")\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "Instead of relying on BiPageRank, you could use PageRank but with an adjacency $A$ equivalent to the document-word biadjacency $B$. You need for that to stack the biadjacency.\n",
    "\n",
    "$$A = \\begin{bmatrix} 0 & B \\\\ B^T & 0  \\end{bmatrix}$$\n",
    "\n",
    "This way you can introduce some word-word similarity in square matrix $W$. For example, using [word2vec](https://en.wikipedia.org/wiki/Word2vec) embeddings. \n",
    "\n",
    "$$A = \\begin{bmatrix} 0 & B \\\\ B^T & W \\end{bmatrix}$$\n",
    "\n",
    "And this can be done for any metadata matrix $V$ added, like the one with years added before. For example, we could say that 2 consecutive years are linked. Or, if our metadata $V$ represents country, $V_{sim}$ could link country from the same continent. \n",
    "\n",
    "$$A = \\begin{bmatrix} 0 & B & V\\\\ B^T & W & 0 \\\\ V^T & 0 & V_{sim} \\end{bmatrix}$$"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "## Evaluation\n",
    "\n",
    "In this whole notebook, despite many plots and example, I didn't give any performance metric. \n",
    "\n",
    "This is because evaluating search results is usually done through user studies : you ask several people to subjectively assess the ranking. This is hard to do with ad hoc datasets and outside of any concrete use case. \n",
    "\n",
    "In Google's case, with PageRank, they managed to do so by counting clicks and dwell time : if people clicked on the first links and stayed long on the page, this was a good ranking. I'd suggest you do something similar in your use case.\n",
    "\n",
    "On this topic, I refer you to the Felix Engelmann and Elias Zevudakis bachelor's thesis : [Using Combined Document-Word Graphsfor Wikipedia Search](https://west.uni-koblenz.de/assets/theses/bachelorsthesis_elias_zervudakis_and_felix_engelmann.pdf). They basically used a similar document-word graph approach, put actually put in the work to assess the search systems. They found out that, for searching in Wikipedia, this new technique was not better than traditional algorithms. But again, that maybe was because people were looking for one thing in perticular, and didn't want to explore the documents. \n",
    "\n",
    "In a nutshell, evaluating Explorative search is still an open question."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "\n",
    "\n",
    "### Special thanks \n",
    "\n",
    "Thanks to Thomas Bonald, my teacher at Télécom Paris, for developing the amazing [scikit-network library](https://scikit-network.readthedocs.io/en/latest/index.html) to handle graphs and for opening me to the world of graphs.\n",
    "\n",
    "Thanks to [Foundamental](https://foundamental.com/), the company where I did an internship, and gave me the opportunity to experiment these ideas freely."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ]
}