Add PageRank file

Author: Harold-Ran

Page_Rank/Page_Rank.ipynb

@@ -0,0 +1,170 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### PageRank算法\n",
+    "以下图所示的有向图为例，计算每个结点的PR：\n",
+    "<img style=\"float: center;\" src=\"directed_graph.png\" width=\"20%\">"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "\n",
+    "\n",
+    "n = 7  #有向图中一共有7个节点\n",
+    "d = 0.85  #阻尼因子根据经验值确定，这里我们随意给一个值\n",
+    "M = np.array([[0, 1/4, 1/3, 0, 0, 1/2, 0],\n",
+    "              [1/4, 0, 0, 1/5, 0, 0, 0],\n",
+    "              [0, 1/4, 0, 1/5, 1/4, 0, 0],\n",
+    "              [0, 0, 1/3, 0, 1/4, 0, 0],\n",
+    "              [1/4, 0, 0, 1/5, 0, 0, 0],\n",
+    "              [1/4, 1/4, 0, 1/5, 1/4, 0, 0],\n",
+    "              [1/4, 1/4, 1/3, 1/5, 1/4, 1/2, 0]])  #根据有向图中各节点的连接情况写出转移矩阵\n",
+    "R0 = np.full((7, 1), 1/7)  #设置初始向量R0，R0是一个7*1的列向量，因为有7个节点，我们把R0的每一个值都设为1/7\n",
+    "eps = 0.000001  #设置计算精度"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### 1. PageRank的迭代算法"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "t = 0  #用来累计迭代次数\n",
+    "R = R0  #对R向量进行初始化\n",
+    "judge = False  #用来判断是否继续迭代\n",
+    "while not judge:\n",
+    "    next_R = d * np.matmul(M, R) + (1 - d) / n * np.ones((7, 1))  #计算新的R向量\n",
+    "    diff = np.linalg.norm(R - next_R)  #计算新的R向量与之前的R向量之间的距离，这里采用的是欧氏距离\n",
+    "    if diff < eps:  #若两向量之间的距离足够小\n",
+    "        judge = True  #则停止迭代\n",
+    "    R = next_R  #更新R向量\n",
+    "    t += 1  #迭代次数加一\n",
+    "R = R / np.sum(R)  #对R向量进行规范化，保证其总和为1，表示各节点的概率分布"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "迭代次数： 24\n",
+      "PageRank: \n",
+      " [[0.17030305]\n",
+      " [0.10568394]\n",
+      " [0.11441021]\n",
+      " [0.10629792]\n",
+      " [0.10568394]\n",
+      " [0.15059975]\n",
+      " [0.24702119]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "print('迭代次数：', t)\n",
+    "print('PageRank: \\n', R)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### 1. PageRank的幂法"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "t = 0  #用来累计迭代次数\n",
+    "x = R0  #对x向量进行初始化\n",
+    "judge = False  #用来判断是否继续迭代\n",
+    "A = d * M + (1 - d) / n * np.eye(n)  #计算A矩阵，其中np.eye(n)用来创建n阶单位阵E\n",
+    "while not judge:\n",
+    "    next_y = np.matmul(A, x)  #计算新的y向量\n",
+    "    next_x = next_y / np.linalg.norm(next_y)  #对新的y向量规范化得到新的x向量\n",
+    "    diff = np.linalg.norm(x - next_x)  #计算新的x向量与之前的x向量之间的距离，这里采用的是欧氏距离\n",
+    "    if diff < eps:  #若两向量之间的距离足够小\n",
+    "        judge = True  #则停止迭代\n",
+    "        R = x  #得到R向量\n",
+    "    x = next_x  #更新x向量\n",
+    "    t += 1  #迭代次数加一\n",
+    "R = R / np.sum(R)  #对R向量进行规范化，保证其总和为1，表示各节点的概率分布"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "迭代次数： 25\n",
+      "PageRank: \n",
+      " [[0.18860772]\n",
+      " [0.09038084]\n",
+      " [0.0875305 ]\n",
+      " [0.07523049]\n",
+      " [0.09038084]\n",
+      " [0.15604764]\n",
+      " [0.31182196]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "print('迭代次数：', t)\n",
+    "print('PageRank: \\n', R)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "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": "3.7.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}