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Commit 394ee38

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Add PageRank file
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‎Page_Rank/Page_Rank.ipynb‎

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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### PageRank算法\n",
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"以下图所示的有向图为例,计算每个结点的PR:\n",
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"<img style=\"float: center;\" src=\"directed_graph.png\" width=\"20%\">"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 26,
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"\n",
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"\n",
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"n = 7 #有向图中一共有7个节点\n",
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"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",
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"M = np.array([[0, 1/4, 1/3, 0, 0, 1/2, 0],\n",
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" [1/4, 0, 0, 1/5, 0, 0, 0],\n",
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" [0, 1/4, 0, 1/5, 1/4, 0, 0],\n",
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" [0, 0, 1/3, 0, 1/4, 0, 0],\n",
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" [1/4, 0, 0, 1/5, 0, 0, 0],\n",
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" [1/4, 1/4, 0, 1/5, 1/4, 0, 0],\n",
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" [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",
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"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",
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"eps = 0.000001 #设置计算精度"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### 1. PageRank的迭代算法"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 27,
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"metadata": {},
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"outputs": [],
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"source": [
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"t = 0 #用来累计迭代次数\n",
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"R = R0 #对R向量进行初始化\n",
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"judge = False #用来判断是否继续迭代\n",
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"while not judge:\n",
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" next_R = d * np.matmul(M, R) + (1 - d) / n * np.ones((7, 1)) #计算新的R向量\n",
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" 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",
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" if diff < eps: #若两向量之间的距离足够小\n",
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" judge = True #则停止迭代\n",
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" R = next_R #更新R向量\n",
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" t += 1 #迭代次数加一\n",
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"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"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 28,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"迭代次数: 24\n",
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"PageRank: \n",
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" [[0.17030305]\n",
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" [0.10568394]\n",
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" [0.11441021]\n",
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" [0.10629792]\n",
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" [0.10568394]\n",
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" [0.15059975]\n",
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" [0.24702119]]\n"
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]
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}
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],
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"source": [
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"print('迭代次数:', t)\n",
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"print('PageRank: \\n', R)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### 1. PageRank的幂法"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 29,
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"metadata": {},
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"outputs": [],
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"source": [
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"t = 0 #用来累计迭代次数\n",
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"x = R0 #对x向量进行初始化\n",
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"judge = False #用来判断是否继续迭代\n",
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"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",
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"while not judge:\n",
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" next_y = np.matmul(A, x) #计算新的y向量\n",
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" 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",
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" 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",
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" if diff < eps: #若两向量之间的距离足够小\n",
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" judge = True #则停止迭代\n",
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" R = x #得到R向量\n",
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" x = next_x #更新x向量\n",
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" t += 1 #迭代次数加一\n",
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"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"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 30,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"迭代次数: 25\n",
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"PageRank: \n",
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" [[0.18860772]\n",
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" [0.09038084]\n",
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" [0.0875305 ]\n",
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" [0.07523049]\n",
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" [0.09038084]\n",
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" [0.15604764]\n",
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" [0.31182196]]\n"
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]
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}
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],
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"source": [
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"print('迭代次数:', t)\n",
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"print('PageRank: \\n', R)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.7.3"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}

‎Page_Rank/directed_graph.png‎

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