PageRank算法并行实现

算法为王系列文章，涵盖了计算机算法，数据挖掘(机器学习)算法，统计算法，金融算法等的多种跨学科算法组合。在大数据时代的背景下，算法已经成为了金字塔顶的明星。一个好的算法可以创造一个伟大帝国，就像Google。

算法为王的时代正式到来….

关于作者：

张丹(Conan), 程序员Java,R,PHP,Javascript
weibo：@Conan_Z
blog: http://blog.fens.me
email: bsspirit@gmail.com

转载请注明出处：
http://blog.fens.me/algorithm-pagerank-mapreduce/

前言

Google通过PageRank算法模型，实现了对全互联网网页的打分。但对于海量数据的处理，在单机下是不可能实现，所以如何将PageRank并行计算，将是本文的重点。

本文将继续上一篇文章 PageRank算法R语言实现，把PageRank单机实现，改成并行实现，利用MapReduce计算框架，在集群中跑起来。

PageRank算法并行化原理
MapReduce分步式编程

1. PageRank算法分步式原理

单机算法原理请参考文章：PageRank算法R语言实现

PageRank的分步式算法原理，简单来讲，就是通过矩阵计算实现并行化。

1). 把邻接矩阵的列，按数据行存储

邻接矩阵

[,1]   [,2]   [,3]   [,4]
[1,] 0.0375000 0.0375 0.0375 0.0375
[2,] 0.3208333 0.0375 0.0375 0.8875
[3,] 0.3208333 0.4625 0.0375 0.0375
[4,] 0.3208333 0.4625 0.8875 0.0375

按行存储HDFS


1       0.037499994,0.32083333,0.32083333,0.32083333
2       0.037499994,0.037499994,0.4625,0.4625
3       0.037499994,0.037499994,0.037499994,0.88750005
4       0.037499994,0.88750005,0.037499994,0.037499994

2). 迭代：求矩阵特征值

map过程：

input: 邻接矩阵, pr值
output: key为pr的行号，value为邻接矩阵和pr值的乘法求和公式

reduce过程：

input: key为pr的行号，value为邻接矩阵和pr值的乘法求和公式
output: key为pr的行号, value为计算的结果，即pr值

第1次迭代


0.0375000 0.0375 0.0375 0.0375     1     0.150000
0.3208333 0.0375 0.0375 0.8875  *  1  =  1.283333
0.3208333 0.4625 0.0375 0.0375     1     0.858333
0.3208333 0.4625 0.8875 0.0375     1     1.708333

第2次迭代


0.0375000 0.0375 0.0375 0.0375     0.150000      0.150000
0.3208333 0.0375 0.0375 0.8875  *  1.283333  =   1.6445833
0.3208333 0.4625 0.0375 0.0375     0.858333      0.7379167
0.3208333 0.4625 0.8875 0.0375     1.708333      1.4675000

… 10次迭代

特征值

3). 标准化PR值


0.150000                                              0.0375000
1.4955721  / (0.15+1.4955721+0.8255034+1.5289245) =   0.3738930
0.8255034                                             0.2063759
1.5289245                                             0.3822311

2. MapReduce分步式编程

MapReduce流程分解

HDFS目录

input(/user/hdfs/pagerank): HDFS的根目录
input_pr(/user/hdfs/pagerank/pr): 临时目录，存储中间结果PR值
tmp1(/user/hdfs/pagerank/tmp1):临时目录，存储邻接矩阵
tmp2(/user/hdfs/pagerank/tmp2):临时目录，迭代计算PR值，然后保存到input_pr
result(/user/hdfs/pagerank/result): PR值输出结果

开发步骤:

网页链接关系数据: page.csv
出始的PR数据:pr.csv
邻接矩阵: AdjacencyMatrix.java
PageRank计算: PageRank.java
PR标准化: Normal.java
启动程序: PageRankJob.java

1). 网页链接关系数据: page.csv

新建文件:page.csv


1,2
1,3
1,4
2,3
2,4
3,4
4,2

2). 出始的PR数据:pr.csv

设置网页的初始值都是1

新建文件：pr.csv


1,1
2,1
3,1
4,1

3). 邻接矩阵: AdjacencyMatrix.java

矩阵解释：

阻尼系数为0.85
页面数为4
reduce以行输出矩阵的列，输出列主要用于分步式存储，下一步需要转成行

新建程序:AdjacencyMatrix.java


package org.conan.myhadoop.pagerank;import java.io.IOException;
import java.util.Arrays;
import java.util.Map;import org.apache.hadoop.fs.Path;
import org.apache.hadoop.io.LongWritable;
import org.apache.hadoop.io.Text;
import org.apache.hadoop.mapred.JobConf;
import org.apache.hadoop.mapreduce.Job;
import org.apache.hadoop.mapreduce.Mapper;
import org.apache.hadoop.mapreduce.Reducer;
import org.apache.hadoop.mapreduce.lib.input.FileInputFormat;
import org.apache.hadoop.mapreduce.lib.input.TextInputFormat;
import org.apache.hadoop.mapreduce.lib.output.FileOutputFormat;
import org.apache.hadoop.mapreduce.lib.output.TextOutputFormat;
import org.conan.myhadoop.hdfs.HdfsDAO;public class AdjacencyMatrix {private static int nums = 4;// 页面数private static float d = 0.85f;// 阻尼系数public static class AdjacencyMatrixMapper extends Mapper<LongWritable, Text, Text, Text> {@Overridepublic void map(LongWritable key, Text values, Context context) throws IOException, InterruptedException {System.out.println(values.toString());String[] tokens = PageRankJob.DELIMITER.split(values.toString());Text k = new Text(tokens[0]);Text v = new Text(tokens[1]);context.write(k, v);}}public static class AdjacencyMatrixReducer extends Reducer<Text, Text, Text, Text> {@Overridepublic void reduce(Text key, Iterable values, Context context) throws IOException, InterruptedException {float[] G = new float[nums];// 概率矩阵列Arrays.fill(G, (float) (1 - d) / G.length);float[] A = new float[nums];// 近邻矩阵列int sum = 0;// 链出数量for (Text val : values) {int idx = Integer.parseInt(val.toString());A[idx - 1] = 1;sum++;}if (sum == 0) {// 分母不能为0sum = 1;}StringBuilder sb = new StringBuilder();for (int i = 0; i < A.length; i++) {sb.append("," + (float) (G[i] + d * A[i] / sum));}Text v = new Text(sb.toString().substring(1));System.out.println(key + ":" + v.toString());context.write(key, v);}}public static void run(Map<String, String> path) throws IOException, InterruptedException, ClassNotFoundException {JobConf conf = PageRankJob.config();String input = path.get("input");String input_pr = path.get("input_pr");String output = path.get("tmp1");String page = path.get("page");String pr = path.get("pr");HdfsDAO hdfs = new HdfsDAO(PageRankJob.HDFS, conf);hdfs.rmr(input);hdfs.mkdirs(input);hdfs.mkdirs(input_pr);hdfs.copyFile(page, input);hdfs.copyFile(pr, input_pr);Job job = new Job(conf);job.setJarByClass(AdjacencyMatrix.class);job.setOutputKeyClass(Text.class);job.setOutputValueClass(Text.class);job.setMapperClass(AdjacencyMatrixMapper.class);job.setReducerClass(AdjacencyMatrixReducer.class);job.setInputFormatClass(TextInputFormat.class);job.setOutputFormatClass(TextOutputFormat.class);FileInputFormat.setInputPaths(job, new Path(page));FileOutputFormat.setOutputPath(job, new Path(output));job.waitForCompletion(true);}
}

4). PageRank计算: PageRank.java

矩阵解释:

实现邻接与PR矩阵的乘法
map以邻接矩阵的行号为key，由于上一步是输出的是列，所以这里需要转成行
reduce计算得到未标准化的特征值

新建文件: PageRank.java


package org.conan.myhadoop.pagerank;import java.io.IOException;
import java.util.HashMap;
import java.util.Iterator;
import java.util.Map;import org.apache.hadoop.fs.Path;
import org.apache.hadoop.io.LongWritable;
import org.apache.hadoop.io.Text;
import org.apache.hadoop.mapred.JobConf;
import org.apache.hadoop.mapreduce.Job;
import org.apache.hadoop.mapreduce.Mapper;
import org.apache.hadoop.mapreduce.Reducer;
import org.apache.hadoop.mapreduce.lib.input.FileInputFormat;
import org.apache.hadoop.mapreduce.lib.input.FileSplit;
import org.apache.hadoop.mapreduce.lib.input.TextInputFormat;
import org.apache.hadoop.mapreduce.lib.output.FileOutputFormat;
import org.apache.hadoop.mapreduce.lib.output.TextOutputFormat;
import org.conan.myhadoop.hdfs.HdfsDAO;public class PageRank {public static class PageRankMapper extends Mapper<LongWritable, Text, Text, Text> {private String flag;// tmp1 or resultprivate static int nums = 4;// 页面数@Overrideprotected void setup(Context context) throws IOException, InterruptedException {FileSplit split = (FileSplit) context.getInputSplit();flag = split.getPath().getParent().getName();// 判断读的数据集}@Overridepublic void map(LongWritable key, Text values, Context context) throws IOException, InterruptedException {System.out.println(values.toString());String[] tokens = PageRankJob.DELIMITER.split(values.toString());if (flag.equals("tmp1")) {String row = values.toString().substring(0,1);String[] vals = PageRankJob.DELIMITER.split(values.toString().substring(2));// 矩阵转置for (int i = 0; i < vals.length; i++) {Text k = new Text(String.valueOf(i + 1));Text v = new Text(String.valueOf("A:" + (row) + "," + vals[i]));context.write(k, v);}} else if (flag.equals("pr")) {for (int i = 1; i <= nums; i++) {Text k = new Text(String.valueOf(i));Text v = new Text("B:" + tokens[0] + "," + tokens[1]);context.write(k, v);}}}}public static class PageRankReducer extends Reducer<Text, Text, Text, Text> {@Overridepublic void reduce(Text key, Iterable values, Context context) throws IOException, InterruptedException {Map<Integer, Float> mapA = new HashMap<Integer, Float>();Map<Integer, Float> mapB = new HashMap<Integer, Float>();float pr = 0f;for (Text line : values) {System.out.println(line);String vals = line.toString();if (vals.startsWith("A:")) {String[] tokenA = PageRankJob.DELIMITER.split(vals.substring(2));mapA.put(Integer.parseInt(tokenA[0]), Float.parseFloat(tokenA[1]));}if (vals.startsWith("B:")) {String[] tokenB = PageRankJob.DELIMITER.split(vals.substring(2));mapB.put(Integer.parseInt(tokenB[0]), Float.parseFloat(tokenB[1]));}}Iterator iterA = mapA.keySet().iterator();while(iterA.hasNext()){int idx = iterA.next();float A = mapA.get(idx);float B = mapB.get(idx);pr += A * B;}context.write(key, new Text(PageRankJob.scaleFloat(pr)));// System.out.println(key + ":" + PageRankJob.scaleFloat(pr));}}public static void run(Map<String, String> path) throws IOException, InterruptedException, ClassNotFoundException {JobConf conf = PageRankJob.config();String input = path.get("tmp1");String output = path.get("tmp2");String pr = path.get("input_pr");HdfsDAO hdfs = new HdfsDAO(PageRankJob.HDFS, conf);hdfs.rmr(output);Job job = new Job(conf);job.setJarByClass(PageRank.class);job.setOutputKeyClass(Text.class);job.setOutputValueClass(Text.class);job.setMapperClass(PageRankMapper.class);job.setReducerClass(PageRankReducer.class);job.setInputFormatClass(TextInputFormat.class);job.setOutputFormatClass(TextOutputFormat.class);FileInputFormat.setInputPaths(job, new Path(input), new Path(pr));FileOutputFormat.setOutputPath(job, new Path(output));job.waitForCompletion(true);hdfs.rmr(pr);hdfs.rename(output, pr);}
}

5). PR标准化: Normal.java

矩阵解释:

对PR的计算结果标准化，让所以PR值落在(0,1)区间

新建文件：Normal.java


package org.conan.myhadoop.pagerank;import java.io.IOException;
import java.util.ArrayList;
import java.util.List;
import java.util.Map;import org.apache.hadoop.fs.Path;
import org.apache.hadoop.io.LongWritable;
import org.apache.hadoop.io.Text;
import org.apache.hadoop.mapred.JobConf;
import org.apache.hadoop.mapreduce.Job;
import org.apache.hadoop.mapreduce.Mapper;
import org.apache.hadoop.mapreduce.Reducer;
import org.apache.hadoop.mapreduce.lib.input.FileInputFormat;
import org.apache.hadoop.mapreduce.lib.input.TextInputFormat;
import org.apache.hadoop.mapreduce.lib.output.FileOutputFormat;
import org.apache.hadoop.mapreduce.lib.output.TextOutputFormat;
import org.conan.myhadoop.hdfs.HdfsDAO;public class Normal {public static class NormalMapper extends Mapper<LongWritable, Text, Text, Text> {Text k = new Text("1");@Overridepublic void map(LongWritable key, Text values, Context context) throws IOException, InterruptedException {System.out.println(values.toString());context.write(k, values);}}public static class NormalReducer extends Reducer<Text, Text, Text, Text> {@Overridepublic void reduce(Text key, Iterable values, Context context) throws IOException, InterruptedException {List vList = new ArrayList();float sum = 0f;for (Text line : values) {vList.add(line.toString());String[] vals = PageRankJob.DELIMITER.split(line.toString());float f = Float.parseFloat(vals[1]);sum += f;}for (String line : vList) {String[] vals = PageRankJob.DELIMITER.split(line.toString());Text k = new Text(vals[0]);float f = Float.parseFloat(vals[1]);Text v = new Text(PageRankJob.scaleFloat((float) (f / sum)));context.write(k, v);System.out.println(k + ":" + v);}}}public static void run(Map<String, String> path) throws IOException, InterruptedException, ClassNotFoundException {JobConf conf = PageRankJob.config();String input = path.get("input_pr");String output = path.get("result");HdfsDAO hdfs = new HdfsDAO(PageRankJob.HDFS, conf);hdfs.rmr(output);Job job = new Job(conf);job.setJarByClass(Normal.class);job.setOutputKeyClass(Text.class);job.setOutputValueClass(Text.class);job.setMapperClass(NormalMapper.class);job.setReducerClass(NormalReducer.class);job.setInputFormatClass(TextInputFormat.class);job.setOutputFormatClass(TextOutputFormat.class);FileInputFormat.setInputPaths(job, new Path(input));FileOutputFormat.setOutputPath(job, new Path(output));job.waitForCompletion(true);}
}

6). 启动程序: PageRankJob.java

新建文件：PageRankJob.java


package org.conan.myhadoop.pagerank;import java.text.DecimalFormat;
import java.util.HashMap;
import java.util.Map;
import java.util.regex.Pattern;import org.apache.hadoop.mapred.JobConf;public class PageRankJob {public static final String HDFS = "hdfs://192.168.1.210:9000";public static final Pattern DELIMITER = Pattern.compile("[\t,]");public static void main(String[] args) {Map<String, String> path = new HashMap<String, String>();path.put("page", "logfile/pagerank/page.csv");// 本地的数据文件path.put("pr", "logfile/pagerank/pr.csv");// 本地的数据文件path.put("input", HDFS + "/user/hdfs/pagerank");// HDFS的目录path.put("input_pr", HDFS + "/user/hdfs/pagerank/pr");// pr存储目path.put("tmp1", HDFS + "/user/hdfs/pagerank/tmp1");// 临时目录,存放邻接矩阵path.put("tmp2", HDFS + "/user/hdfs/pagerank/tmp2");// 临时目录,计算到得PR,覆盖input_prpath.put("result", HDFS + "/user/hdfs/pagerank/result");// 计算结果的PRtry {AdjacencyMatrix.run(path);int iter = 3;for (int i = 0; i < iter; i++) {// 迭代执行PageRank.run(path);}Normal.run(path);} catch (Exception e) {e.printStackTrace();}System.exit(0);}public static JobConf config() {// Hadoop集群的远程配置信息JobConf conf = new JobConf(PageRankJob.class);conf.setJobName("PageRank");conf.addResource("classpath:/hadoop/core-site.xml");conf.addResource("classpath:/hadoop/hdfs-site.xml");conf.addResource("classpath:/hadoop/mapred-site.xml");return conf;}public static String scaleFloat(float f) {// 保留6位小数DecimalFormat df = new DecimalFormat("##0.000000");return df.format(f);}
}

程序代码已上传到github:

https://github.com/bsspirit/maven_hadoop_template/tree/master/src/main/java/org/conan/myhadoop/pagerank

这样就实现了，PageRank的并行吧！接下来，我们就可以用PageRank做一些有意思的应用了。

转载请注明出处：
http://blog.fens.me/algorithm-pagerank-mapreduce/