PageRank.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "N_G0XNqCw3sl"
   },
   "source": [
    "# Page Rank: How important a web page is\n",
    "Search engine mechanism\n",
    "1. Tour the web page in advance to collect information\n",
    "2. List web pages that contain / relevant text entered by the user\n",
    "3. **Arrange web pages in order of importance and return them to the user**\n",
    "\n",
    "Arrange web pages in order of importance←today's topic"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "5ld1BFbkw3sm"
   },
   "source": [
    "## Create graph (web pages)\n",
    "\n",
    "node: web page\n",
    "edge: link"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 255
    },
    "colab_type": "code",
    "id": "fMg7ju_Uw3sm",
    "outputId": "9b86c613-8c4c-49d8-8644-4bbf5a50d278"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# -*- coding: utf-8 -*-\n",
    "import networkx as nx\n",
    "import numpy as np\n",
    "# Directed Graph\n",
    "g = nx.DiGraph()\n",
    "\n",
    "# Add node = web page\n",
    "g.add_node(1)\n",
    "g.add_node(2)\n",
    "g.add_node(3)                                                                                                                     \n",
    "g.add_node(4)\n",
    "g.add_node(5)\n",
    "g.add_node(6)\n",
    "\n",
    "\n",
    "#Add edge (\"link\")\n",
    "g.add_edge(1,2)\n",
    "g.add_edge(1,4)\n",
    "g.add_edge(1,5)\n",
    "g.add_edge(2,3)\n",
    "g.add_edge(3,1)\n",
    "g.add_edge(3,4)\n",
    "g.add_edge(3,5)\n",
    "g.add_edge(4,5)\n",
    "g.add_edge(2,6)\n",
    "g.add_edge(5,6)\n",
    "g.add_edge(1,6)\n",
    "g.add_edge(6,3)\n",
    "\n",
    "nx.draw_networkx(g)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "dt_VtYjCw3sr"
   },
   "source": [
    "# PageRank \n",
    "PageRank is a google's algorithm to evaluate the imprtance of a webpage.\n",
    "\n",
    "Page rank is based on the fact that　**\"Important websites\" are linked from many sites**.\n",
    "\n",
    "**Larry Page** and **Sergey Brin** assumed the behavior of Internet users as a **random surfer** as follows.\n",
    "1. Initial states: Everyone starts by randomly selecting the first page \n",
    "2. The person staying on one page transits to another page at the next time slice.\n",
    "    The transition destination page is selected with equal probability from the linked pages from the currently staying page (**link transition**).\n",
    "    Surfers occasionally(〜15%) fly to pages without links (does not have anything to do with sites you've been browsing) (**teleport**)\n",
    "3. Rank a page with a **high probability of staying** as a useful page.\n",
    "\n",
    "PageRank of a website A \n",
    "$$PR(A) = (1-\\alpha)(teleport) + \\alpha(link transition)$$\n",
    "$$= (1-\\alpha)(teleport) + \\alpha (\\sum_{i=1}^{n} \\frac{PR(T_i)}{d(T_i)})$$\n",
    "\n",
    "$\\alpha$ : constant(mainly 0.85)\n",
    "\n",
    "$n$ : number of web pages (nodes)\n",
    "\n",
    "$PR(T_i)$ : PageRank of a page($Ti$) which has link to the website A\n",
    "\n",
    "$d(T_i)$ : The number of the link from the page $Ti$  (equals to \"outdegree\")\n",
    "\n",
    "By using networkX(nx), you can get the pagerank of the pages easily."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "id": "fX_Hng40w3ss",
    "outputId": "da08b732-22c3-4454-a986-a7b0b8a1b478"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-----pagerank-----\n",
      "{1: 0.09874162030309819, 2: 0.04598264175871525, 3: 0.2602674715555196, 4: 0.11972426206181344, 5: 0.22149035859853752, 6: 0.2537936457223158}\n"
     ]
    }
   ],
   "source": [
    "#pagerank\n",
    "pr=nx.pagerank(g,alpha=0.85)\n",
    "print(\"-----pagerank-----\")\n",
    "print(pr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 421
    },
    "colab_type": "code",
    "id": "RFL2ON1Nw3su",
    "outputId": "823edd20-a80d-4e1f-9575-3d02922511ca"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1: Text(0,7,'1'),\n",
       " 2: Text(4,14,'2'),\n",
       " 3: Text(10,14,'3'),\n",
       " 4: Text(14,7,'4'),\n",
       " 5: Text(10,0,'5'),\n",
       " 6: Text(4,0,'6')}"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "node_size = []\n",
    "for i in range(1,7):\n",
    "    node_size.append(pr[i] * 8000)\n",
    "\n",
    "pos={}\n",
    "pos[1]=(0,7)\n",
    "pos[2]=(4,14)\n",
    "pos[3]=(10,14)\n",
    "pos[4]=(14,7)\n",
    "pos[5]=(10,0)\n",
    "pos[6]=(4,0)\n",
    "nx.draw(g, pos, arrowsize=30, node_size = node_size)\n",
    "nx.draw_networkx_labels(g, pos, font_size=18, font_color=\"w\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "DEgLoo_Aw3sx"
   },
   "source": [
    "Q. How can we calculate the PR?\n",
    "## A. **Use LINEAR ALGEBRA!!**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "BdHCu8fXw3sx"
   },
   "source": [
    "You can make the **transition matrix** .\n",
    "1. Link transition matrix \n",
    "2. Teleportation matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "mRJpIJOgw3sy"
   },
   "source": [
    "## 1. Link transition\n",
    "\n",
    "$$L_{ij}=\\frac{A_{ij}}{d(i)}$$\n",
    "$d(i)$ is the outdegree of the node i. $$d(i) = \\sum_{j=0}^{n} A_{ij}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 119
    },
    "colab_type": "code",
    "id": "DzW4d46Cw3sy",
    "outputId": "10c88df6-6600-4588-adc0-3339813a0c99"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0. 1. 0. 1. 1. 1.]\n",
      " [0. 0. 1. 0. 0. 1.]\n",
      " [1. 0. 0. 1. 1. 0.]\n",
      " [0. 0. 0. 0. 1. 0.]\n",
      " [0. 0. 0. 0. 0. 1.]\n",
      " [0. 0. 1. 0. 0. 0.]]\n"
     ]
    }
   ],
   "source": [
    "A = nx.to_numpy_matrix(g)\n",
    "print(A)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "SJHT7eTGw3s1"
   },
   "source": [
    "For example, d(1) is 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 119
    },
    "colab_type": "code",
    "id": "ws11kZM3w3s1",
    "outputId": "e2b660eb-f798-4f44-bfeb-9ae7a66aa302"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[4.]\n",
      " [2.]\n",
      " [3.]\n",
      " [1.]\n",
      " [1.]\n",
      " [1.]]\n"
     ]
    }
   ],
   "source": [
    "D = np.sum(A, axis=1)\n",
    "print(D)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.25       0.5        0.33333333 1.         1.         1.        ]\n"
     ]
    }
   ],
   "source": [
    "D_inv = np.zeros(6)\n",
    "\n",
    "for j in range(6):\n",
    "    D_inv[j] = np.reciprocal(D[j,0])\n",
    "print(D_inv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.         0.25       0.         0.25       0.25       0.25      ]\n",
      " [0.         0.         0.5        0.         0.         0.5       ]\n",
      " [0.33333333 0.         0.         0.33333333 0.33333333 0.        ]\n",
      " [0.         0.         0.         0.         1.         0.        ]\n",
      " [0.         0.         0.         0.         0.         1.        ]\n",
      " [0.         0.         1.         0.         0.         0.        ]]\n"
     ]
    }
   ],
   "source": [
    "L = np.zeros((6,6))\n",
    "for i in range(0,6):\n",
    "    for j in range(0,6):\n",
    "        L[i,j] = A[i,j] * D_inv[i]\n",
    "print(L)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "WOQD0X2fw3s9"
   },
   "source": [
    "## 2. Teleportation matrix (=Initial states)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "UfoqPQtOw3s9",
    "outputId": "1d64f991-a35c-46e6-fef2-8d0a4773af62"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.16666667 0.16666667 0.16666667 0.16666667 0.16666667 0.16666667]]\n"
     ]
    }
   ],
   "source": [
    "T = np.full((1,6), 1/6)\n",
    "print(T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "uKXpzE2Tw3s_"
   },
   "source": [
    "$$PR(time) = 0.15 * T + 0.85 * PR(time - 1) * L$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "feASasK1w3tA",
    "outputId": "537afbbc-16f1-4abd-b1bc-3b62cf167323"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.07222222 0.06041667 0.2375     0.10763889 0.24930556 0.27291667]]\n"
     ]
    }
   ],
   "source": [
    "PR1 = 0.15* T + 0.85 * np.dot(T, L)\n",
    "print(PR1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "GI8e6Dcgw3tC"
   },
   "outputs": [],
   "source": [
    "def PR(t, T, L):\n",
    "    if t == 1:\n",
    "        return 0.15* T + 0.85 * np.dot(T, L)\n",
    "    else:\n",
    "        return 0.15 * T + 0.85 * np.dot(PR(t-1, T, L), L)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "Hfl7kDVfw3tD",
    "outputId": "f50b50c6-37a2-4250-bbec-f4f3e784ee80"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.07222222 0.06041667 0.2375     0.10763889 0.24930556 0.27291667]]\n"
     ]
    }
   ],
   "source": [
    "print(PR(1, T, L))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "LdDku5cjw3tF",
    "outputId": "f016b504-15ff-481b-8c44-68427402df86"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.0991236  0.0456917  0.26234495 0.1198153  0.22039447 0.25262998]]\n"
     ]
    }
   ],
   "source": [
    "print(PR(10, T, L))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "x1-aZ3Xpxz5F",
    "outputId": "d013d320-fd4c-45da-ba21-71d6a3d7ae83"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.09871457 0.04598071 0.26030431 0.11969528 0.22146421 0.25384093]]\n"
     ]
    }
   ],
   "source": [
    "pagerank20 = PR(20, T, L)\n",
    "print(pagerank20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 421
    },
    "colab_type": "code",
    "id": "vKDRoTgHw3tI",
    "outputId": "e377144d-2332-4cce-8b40-a03fc849011e"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1: Text(0,7,'1'),\n",
       " 2: Text(4,14,'2'),\n",
       " 3: Text(10,14,'3'),\n",
       " 4: Text(14,7,'4'),\n",
       " 5: Text(10,0,'5'),\n",
       " 6: Text(4,0,'6')}"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "node_size = []\n",
    "for i in range(0,6):\n",
    "    node_size.append(pagerank20[0,i] * 8000)\n",
    "\n",
    "pos={}\n",
    "pos[1]=(0,7)\n",
    "pos[2]=(4,14)\n",
    "pos[3]=(10,14)\n",
    "pos[4]=(14,7)\n",
    "pos[5]=(10,0)\n",
    "pos[6]=(4,0)\n",
    "nx.draw(g, pos, arrowsize=30, node_size = node_size)\n",
    "nx.draw_networkx_labels(g, pos, font_size=18, font_color=\"w\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "lnwmZqbGyInS"
   },
   "source": [
    "**The calculation result is approaching the result of networkX!**\n",
    "In reality, even t = 10 is considered sufficient."
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "name": "pageRank-Copy1.ipynb",
   "provenance": [],
   "version": "0.3.2"
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}