{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "toc": true
   },
   "source": [
    "<h1>Table of Contents<span class=\"tocSkip\"></span></h1>\n",
    "<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#PageRank\" data-toc-modified-id=\"PageRank-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>PageRank</a></span><ul class=\"toc-item\"><li><span><a href=\"#Taxation\" data-toc-modified-id=\"Taxation-1.1\"><span class=\"toc-item-num\">1.1&nbsp;&nbsp;</span>Taxation</a></span></li></ul></li><li><span><a href=\"#Reference\" data-toc-modified-id=\"Reference-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>Reference</a></span></li></ul></div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
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     "execution_count": 1,
     "metadata": {},
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    }
   ],
   "source": [
    "# code for loading the format for the notebook\n",
    "import os\n",
    "\n",
    "# path : store the current path to convert back to it later\n",
    "path = os.getcwd()\n",
    "os.chdir(os.path.join('..', 'notebook_format'))\n",
    "\n",
    "from formats import load_style\n",
    "load_style(plot_style=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ethen 2019-03-02 10:24:46 \n",
      "\n",
      "CPython 3.6.4\n",
      "IPython 6.4.0\n",
      "\n",
      "numpy 1.14.2\n",
      "networkx 2.2\n",
      "matplotlib 2.2.3\n"
     ]
    }
   ],
   "source": [
    "os.chdir(path)\n",
    "\n",
    "# 1. magic for inline plot\n",
    "# 2. magic to print version\n",
    "# 3. magic so that the notebook will reload external python modules\n",
    "# 4. magic to enable retina (high resolution) plots\n",
    "# https://gist.github.com/minrk/3301035\n",
    "%matplotlib inline\n",
    "%load_ext watermark\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "%config InlineBackend.figure_format='retina'\n",
    "\n",
    "import numpy as np\n",
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%watermark -a 'Ethen' -d -t -v -p numpy,networkx,matplotlib"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PageRank"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "PageRank is a function that assigns a number weighting each page in the Web, the intent is that the higher the PageRank of a page, the more important the page is. We can think of the Web as a directed graph, where the pages are the nodes and if there exists a link that connects page1 to page2 then there would be an edge connecting the two nodes.\n",
    "\n",
    "Imagine an toy example where there are only 4 pages/nodes, ${A, B, C, D}$:\n",
    "\n",
    "- $A$ has links connecting itself to each of ther other three pages.\n",
    "- $B$ has links to $A$ and $D$.\n",
    "- $D$ has links to $B$ and $C$.\n",
    "- $C$ has links only to $A$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<networkx.classes.digraph.DiGraph at 0x10e7b0208>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nodes = ['A', 'B', 'C', 'D']\n",
    "edges = [\n",
    "    ('A', 'B'),\n",
    "    ('A', 'C'),\n",
    "    ('A', 'D'),\n",
    "    ('B', 'A'),\n",
    "    ('B', 'D'),\n",
    "    ('D', 'B'),\n",
    "    ('D', 'C'),\n",
    "    ('C', 'A')\n",
    "]\n",
    "\n",
    "graph = nx.DiGraph()\n",
    "graph.add_nodes_from(nodes)\n",
    "graph.add_edges_from(edges)\n",
    "graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 467,
       "width": 628
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# change default style figure and font size\n",
    "plt.rcParams['figure.figsize'] = 8, 6\n",
    "plt.rcParams['font.size'] = 12\n",
    "\n",
    "# quick and dirty visualization of the graph we've defined above\n",
    "nx.draw(graph, with_labels=True, node_color='skyblue', alpha=0.7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given this graph, we can build a transition matrix to depict what is the probability of landing on a given page after 1 step. If we look at an example below, the matrix has:\n",
    "\n",
    "- $n$ rows and columns if there are $n$ pages\n",
    "- Each element in the matrix, $m_{ij}$ takes on the value of $1 / k$ if page $i$ has $k$ edges and one of them is $j$. Otherwise $m_{ij}$ is 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.        , 0.33333333, 0.33333333, 0.33333333],\n",
       "       [0.5       , 0.        , 0.        , 0.5       ],\n",
       "       [1.        , 0.        , 0.        , 0.        ],\n",
       "       [0.        , 0.5       , 0.5       , 0.        ]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trans_matrix = nx.to_numpy_array(graph)\n",
    "trans_matrix /= trans_matrix.sum(axis=1, keepdims=True)\n",
    "trans_matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now suppose we start at any of the $n$ pages of the Web with equal probability. Then the initial vector $v_0$ will have $1/n$ for each page. If $M$ is the transition matrix of the Web, then after one step, the distribution\n",
    "of us landing on each of the page can be computed by a matrix vector multiplication. $v_0 M$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.375     , 0.20833333, 0.20833333, 0.20833333])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_nodes = trans_matrix.shape[0]\n",
    "init_vector = np.repeat(1 / n_nodes, n_nodes)\n",
    "init_vector @ trans_matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see after 1 step, the probability of landing on the first page, page $A$, is higher than the probability of landing on other pages. We can repeat this matrix vector multiplication for multiple times and our results will eventually converge. Giving us an estimated probability of landing on each page, which in term is PageRank's estimate of how important a given page is when compared to all the other page in the Web."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.33333333, 0.22222222, 0.22222222, 0.22222222])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# we can tweak the number of iterations parameter\n",
    "# and see that the resulting probability remains\n",
    "# the same even if we increased the number to 50\n",
    "n_iters = 30\n",
    "result = init_vector\n",
    "for _ in range(n_iters):\n",
    "    result = result @ trans_matrix\n",
    "\n",
    "result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This sort of convergence behavior is an example of the Markov Chain processes. It is known that the distribution of $v = Mv$ converges, provided two conditions are met:\n",
    "\n",
    "- The graph is strongly connected; that is, it is possible to get from any\n",
    "node to any other node.\n",
    "- There are no dead ends: nodes that have no edges out.\n",
    "\n",
    "If we stare at the formula $v = Mv$ long enough, we can observe that our final result vector $v$ is an eigenvector of the matrix $M$ (recall an eigenvector of a matrix $M$ is a vector $v$ that satisfies $v = \\lambda Mv$ for some constant eigenvalue $\\lambda$)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Taxation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The vanilla PageRank that we've introduced above needs some tweaks to handle data that can appear in real world scenarios. The two problems that we need to avoid is what's called **spider traps** and **dead end**.\n",
    "\n",
    "**spider trap** is a set of nodes with edges, but these edges all links within the page itself. This causes the PageRank calculation to place all the PageRank score within the spider traps."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 467,
       "width": 636
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# we replaced C's out-link, ('C', 'A'),\n",
    "# from the list of edges with a link within\n",
    "# the page itself ('C', 'C'), note that\n",
    "# we can also avoid this problem by note\n",
    "# including self-loops in the edges\n",
    "nodes = ['A', 'B', 'C', 'D']\n",
    "edges = [\n",
    "    ('A', 'B'),\n",
    "    ('A', 'C'),\n",
    "    ('A', 'D'),\n",
    "    ('B', 'A'),\n",
    "    ('B', 'D'),\n",
    "    ('D', 'B'),\n",
    "    ('D', 'C'),\n",
    "    ('C', 'C')\n",
    "]\n",
    "\n",
    "graph = nx.DiGraph()\n",
    "graph.add_nodes_from(nodes)\n",
    "graph.add_edges_from(edges)\n",
    "\n",
    "# not showing the self-loop edge for node C\n",
    "nx.draw(graph, with_labels=True, node_color='skyblue', alpha=0.7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.        , 0.33333333, 0.33333333, 0.33333333],\n",
       "       [0.5       , 0.        , 0.        , 0.5       ],\n",
       "       [0.        , 0.        , 1.        , 0.        ],\n",
       "       [0.        , 0.5       , 0.5       , 0.        ]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# notice in the transition probability matrix, the third row, node C\n",
    "# contains 1 for a single entry\n",
    "trans_matrix = nx.to_numpy_array(graph)\n",
    "trans_matrix /= trans_matrix.sum(axis=1, keepdims=True)\n",
    "trans_matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6.04874159e-07, 8.81559995e-07, 9.99997632e-01, 8.81559995e-07])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_iters = 40\n",
    "result = init_vector\n",
    "for _ in range(n_iters):\n",
    "    result = result @ trans_matrix\n",
    "\n",
    "result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As predicted, all the PageRank is at node $C$, since once we land there, there's no way for us to leave.\n",
    "\n",
    "The other problem **dead end** describes pages that have no out-links, as a result pages that reaches these dead ends will not have any PageRank."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 467,
       "width": 628
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# we remove C's out-link, ('C', 'A'),\n",
    "# from the list of edges\n",
    "nodes = ['A', 'B', 'C', 'D']\n",
    "edges = [\n",
    "    ('A', 'B'),\n",
    "    ('A', 'C'),\n",
    "    ('A', 'D'),\n",
    "    ('B', 'A'),\n",
    "    ('B', 'D'),\n",
    "    ('D', 'B'),\n",
    "    ('D', 'C')\n",
    "]\n",
    "\n",
    "graph = nx.DiGraph()\n",
    "graph.add_nodes_from(nodes)\n",
    "graph.add_edges_from(edges)\n",
    "nx.draw(graph, with_labels=True, node_color='skyblue', alpha=0.7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.        , 0.33333333, 0.33333333, 0.33333333],\n",
       "       [0.5       , 0.        , 0.        , 0.5       ],\n",
       "       [0.        , 0.        , 0.        , 0.        ],\n",
       "       [0.        , 0.5       , 0.5       , 0.        ]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# trick for numpy for dealing with zero division\n",
    "# https://stackoverflow.com/questions/26248654/numpy-return-0-with-divide-by-zero\n",
    "trans_matrix = nx.to_numpy_array(graph)\n",
    "summed = trans_matrix.sum(axis=1, keepdims=True)\n",
    "trans_matrix = np.divide(trans_matrix, summed,\n",
    "                         out=np.zeros_like(trans_matrix), where=summed!=0)\n",
    "\n",
    "# notice in the transition probability matrix, the third row, node C\n",
    "# consists of all 0\n",
    "trans_matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6.04874159e-07, 8.81559995e-07, 8.81559995e-07, 8.81559995e-07])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_iters = 40\n",
    "result = init_vector\n",
    "for _ in range(n_iters):\n",
    "    result = result @ trans_matrix\n",
    "\n",
    "result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we see, the result tells us the probability of us being anywhere goes to 0, as the number of steps increase.\n",
    "\n",
    "To avoid the two problems mentioned above, we will modify the calculation of PageRank. At each step, we will give it a small probability of \"teleporting\" to a random page, rather than following an out-link from their current page. The notation form for the description above would be:\n",
    "\n",
    "\\begin{align}\n",
    "v^\\prime = \\beta M v + (1 - \\beta) e / n\n",
    "\\end{align}\n",
    "\n",
    "where:\n",
    "\n",
    "- $\\beta$ is a chosen constant, usually in the range of 0.8 to 0.9.\n",
    "- $e$ is a vector of all 1s with the appropriate number of elements so that the matrix addition adds up.\n",
    "- $n$ is the number of pages/nodes in the Web graph.\n",
    "- The term, $\\beta M v$ denotes that at this step, there is a probability $\\beta$ that we will follow an out-link from their present page.\n",
    "- Notice the term $(1 - \\beta) e / n$ does not depend on $v$, thus if there are some dead ends in the graph, there will always be some fraction of opportunity to jump out of that rabbit hole.\n",
    "- This idea of adding $\\beta$ is referred to as taxation (`networkx` package calls this damping factor)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.025, 0.325, 0.325, 0.325],\n",
       "       [0.475, 0.025, 0.025, 0.475],\n",
       "       [0.25 , 0.25 , 0.25 , 0.25 ],\n",
       "       [0.025, 0.475, 0.475, 0.025]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def build_trans_matrix(graph: nx.DiGraph, beta: float=0.9) -> np.ndarray:\n",
    "    n_nodes = len(graph)\n",
    "    trans_matrix = nx.to_numpy_array(graph)\n",
    "\n",
    "    # assign uniform probability to dangling nodes (nodes without out links)\n",
    "    const_vector = np.repeat(1.0 / n_nodes, n_nodes)\n",
    "    row_sum = trans_matrix.sum(axis=1)\n",
    "    dangling_nodes = np.where(row_sum == 0)[0]\n",
    "    if len(dangling_nodes):\n",
    "        for node in dangling_nodes:\n",
    "            trans_matrix[node] = const_vector\n",
    "            row_sum[node] = 1\n",
    "\n",
    "    trans_matrix /= row_sum.reshape(-1, 1)\n",
    "    return beta * trans_matrix + (1 - beta) * const_vector\n",
    "\n",
    "\n",
    "trans_matrix = build_trans_matrix(graph)\n",
    "trans_matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.20408163, 0.26530612, 0.26530612, 0.26530612])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_iters = 20\n",
    "result = init_vector\n",
    "for _ in range(n_iters):\n",
    "    result = result @ trans_matrix\n",
    "\n",
    "result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result looks much more reasonable after introducing the taxation. We can also compare the it with the `pagerank` function from `networkx`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'A': 0.204081934263649,\n",
       " 'B': 0.265306021912117,\n",
       " 'C': 0.265306021912117,\n",
       " 'D': 0.265306021912117}"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pagerank_score = nx.pagerank(graph, alpha=0.9)\n",
    "pagerank_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Having seen how to calculate the PageRank vector, we should examine how this information is being used. Of course each search engine has its own secret formula that decides the ordering of pages in response to users search query. But we can guess that first, in order to be considered for the ranking at all, a page has to have at least one of the search terms in the query. Then amongst the qualified pages, a score is computed for each, and an important component of this score is the PageRank of the page (we can think of component as a feature to a machine learning ranker). Other components might include the presence or absence of search terms in prominent places, such as headers or the links to\n",
    "the page itself."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Reference"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- [Networkx Documentation: PageRank](https://networkx.github.io/documentation/networkx-1.10/reference/generated/networkx.algorithms.link_analysis.pagerank_alg.pagerank.html)\n",
    "- [Online Book: Mining Massive Dataset - Chapter 5 Link Analysis](http://infolab.stanford.edu/~ullman/mmds/book.pdf)"
   ]
  }
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