概率语言模型及其变形系列(5)-LDA Gibbs Sampling 的JAVA实现

本系列博文介绍常见概率语言模型及其变形模型，主要总结PLSA、LDA及LDA的变形模型及参数Inference方法。初步计划内容如下

第一篇：PLSA及EM算法

第二篇：LDA及Gibbs Samping

第三篇：LDA变形模型-Twitter LDA，TimeUserLDA，ATM，Labeled-LDA，MaxEnt-LDA等

第四篇：基于变形LDA的paper分类总结（bibliography）

第五篇：LDA Gibbs Sampling 的JAVA实现

第五篇 LDA Gibbs Sampling的JAVA 实现

在本系列博文的前两篇，我们系统介绍了PLSA, LDA以及它们的参数Inference 方法，重点分析了模型表示和公式推导部分。曾有位学者说，“做研究要顶天立地”，意思是说做研究空有模型和理论还不够，我们还得有扎实的程序code和真实数据的实验结果来作为支撑。本文就重点分析 LDA Gibbs Sampling的JAVA 实现，并给出apply到newsgroup18828新闻文档集上得出的Topic建模结果。

本项目Github地址 https://github.com/yangliuy/LDAGibbsSampling

1、文档集预处理

要用LDA对文本进行topic建模，首先要对文本进行预处理，包括token，去停用词，stem，去noise词，去掉低频词等等。当语料库比较大时，我们也可以不进行stem。然后将文本转换成term的index表示形式，因为后面实现LDA的过程中经常需要在term和index之间进行映射。Documents类的实现如下，里面定义了Document内部类，用于描述文本集合中的文档。

 package liuyang.nlp.lda.main;

 import java.io.File;
 import java.util.ArrayList;
 import java.util.HashMap;
 import java.util.Map;
 import java.util.regex.Matcher;
 import java.util.regex.Pattern;

 import liuyang.nlp.lda.com.FileUtil;
 import liuyang.nlp.lda.com.Stopwords;

 /**Class for corpus which consists of M documents
  * @author yangliu
  * @blog http://blog.csdn.net/yangliuy
  * @mail [email protected]
  */

 public class Documents {

     ArrayList<Document> docs;
     Map<String, Integer> termToIndexMap;
     ArrayList<String> indexToTermMap;
     Map<String,Integer> termCountMap;

     public Documents(){
         docs = new ArrayList<Document>();
         termToIndexMap = new HashMap<String, Integer>();
         indexToTermMap = new ArrayList<String>();
         termCountMap = new HashMap<String, Integer>();
     }

     public void readDocs(String docsPath){
         for(File docFile : new File(docsPath).listFiles()){
             Document doc = new Document(docFile.getAbsolutePath(), termToIndexMap, indexToTermMap, termCountMap);
             docs.add(doc);
         }
     }

     public static class Document {
         private String docName;
         int[] docWords;

         public Document(String docName, Map<String, Integer> termToIndexMap, ArrayList<String> indexToTermMap, Map<String, Integer> termCountMap){
             this.docName = docName;
             //Read file and initialize word index array
             ArrayList<String> docLines = new ArrayList<String>();
             ArrayList<String> words = new ArrayList<String>();
             FileUtil.readLines(docName, docLines);
             for(String line : docLines){
                 FileUtil.tokenizeAndLowerCase(line, words);
             }
             //Remove stop words and noise words
             for(int i = 0; i < words.size(); i++){
                 if(Stopwords.isStopword(words.get(i)) || isNoiseWord(words.get(i))){
                     words.remove(i);
                     i--;
                 }
             }
             //Transfer word to index
             this.docWords = new int[words.size()];
             for(int i = 0; i < words.size(); i++){
                 String word = words.get(i);
                 if(!termToIndexMap.containsKey(word)){
                     int newIndex = termToIndexMap.size();
                     termToIndexMap.put(word, newIndex);
                     indexToTermMap.add(word);
                     termCountMap.put(word, new Integer(1));
                     docWords[i] = newIndex;
                 } else {
                     docWords[i] = termToIndexMap.get(word);
                     termCountMap.put(word, termCountMap.get(word) + 1);
                 }
             }
             words.clear();
         }

         public boolean isNoiseWord(String string) {
             // TODO Auto-generated method stub
             string = string.toLowerCase().trim();
             Pattern MY_PATTERN = Pattern.compile(".*[a-zA-Z]+.*");
             Matcher m = MY_PATTERN.matcher(string);
             // filter @xxx and URL
             if(string.matches(".*www\\..*") || string.matches(".*\\.com.*") ||
                     string.matches(".*http:.*") )
                 return true;
             if (!m.matches()) {
                 return true;
             } else
                 return false;
         }

     }
 }

2 LDA Gibbs Sampling

文本预处理完毕后我们就可以实现LDA Gibbs Sampling。 首先我们要定义需要的参数，我的实现中在程序中给出了参数默认值，同时也支持配置文件覆盖，程序默认优先选用配置文件的参数设置。整个算法流程包括模型初始化，迭代Inference，不断更新主题和待估计参数，最后输出收敛时的参数估计结果。

包含主函数的配置参数解析类如下：

 package liuyang.nlp.lda.main;

 import java.io.File;
 import java.io.IOException;
 import java.util.ArrayList;

 import liuyang.nlp.lda.com.FileUtil;
 import liuyang.nlp.lda.conf.ConstantConfig;
 import liuyang.nlp.lda.conf.PathConfig;

 /**Liu Yang's implementation of Gibbs Sampling of LDA
  * @author yangliu
  * @blog http://blog.csdn.net/yangliuy
  * @mail [email protected]
  */

 public class LdaGibbsSampling {

     public static class modelparameters {
         float alpha = 0.5f; //usual value is 50 / K
         float beta = 0.1f;//usual value is 0.1
         int topicNum = 100;
         int iteration = 100;
         int saveStep = 10;
         int beginSaveIters = 50;
     }

     /**Get parameters from configuring file. If the
      * configuring file has value in it, use the value.
      * Else the default value in program will be used
      * @param ldaparameters
      * @param parameterFile
      * @return void
      */
     private static void getParametersFromFile(modelparameters ldaparameters,
             String parameterFile) {
         // TODO Auto-generated method stub
         ArrayList<String> paramLines = new ArrayList<String>();
         FileUtil.readLines(parameterFile, paramLines);
         for(String line : paramLines){
             String[] lineParts = line.split("\t");
             switch(parameters.valueOf(lineParts[0])){
             case alpha:
                 ldaparameters.alpha = Float.valueOf(lineParts[1]);
                 break;
             case beta:
                 ldaparameters.beta = Float.valueOf(lineParts[1]);
                 break;
             case topicNum:
                 ldaparameters.topicNum = Integer.valueOf(lineParts[1]);
                 break;
             case iteration:
                 ldaparameters.iteration = Integer.valueOf(lineParts[1]);
                 break;
             case saveStep:
                 ldaparameters.saveStep = Integer.valueOf(lineParts[1]);
                 break;
             case beginSaveIters:
                 ldaparameters.beginSaveIters = Integer.valueOf(lineParts[1]);
                 break;
             }
         }
     }

     public enum parameters{
         alpha, beta, topicNum, iteration, saveStep, beginSaveIters;
     }

     /**
      * @param args
      * @throws IOException
      */
     public static void main(String[] args) throws IOException {
         // TODO Auto-generated method stub
         String originalDocsPath = PathConfig.ldaDocsPath;
         String resultPath = PathConfig.LdaResultsPath;
         String parameterFile= ConstantConfig.LDAPARAMETERFILE;

         modelparameters ldaparameters = new modelparameters();
         getParametersFromFile(ldaparameters, parameterFile);
         Documents docSet = new Documents();
         docSet.readDocs(originalDocsPath);
         System.out.println("wordMap size " + docSet.termToIndexMap.size());
         FileUtil.mkdir(new File(resultPath));
         LdaModel model = new LdaModel(ldaparameters);
         System.out.println("1 Initialize the model ...");
         model.initializeModel(docSet);
         System.out.println("2 Learning and Saving the model ...");
         model.inferenceModel(docSet);
         System.out.println("3 Output the final model ...");
         model.saveIteratedModel(ldaparameters.iteration, docSet);
         System.out.println("Done!");
     }
 }

LDA 模型实现类如下

 package liuyang.nlp.lda.main;

 /**Class for Lda model
  * @author yangliu
  * @blog http://blog.csdn.net/yangliuy
  * @mail [email protected]
  */
 import java.io.BufferedWriter;
 import java.io.FileWriter;
 import java.io.IOException;
 import java.util.ArrayList;
 import java.util.Collections;
 import java.util.Comparator;
 import java.util.List;

 import liuyang.nlp.lda.com.FileUtil;
 import liuyang.nlp.lda.conf.PathConfig;

 public class LdaModel {

     int [][] doc;//word index array
     int V, K, M;//vocabulary size, topic number, document number
     int [][] z;//topic label array
     float alpha; //doc-topic dirichlet prior parameter
     float beta; //topic-word dirichlet prior parameter
     int [][] nmk;//given document m, count times of topic k. M*K
     int [][] nkt;//given topic k, count times of term t. K*V
     int [] nmkSum;//Sum for each row in nmk
     int [] nktSum;//Sum for each row in nkt
     double [][] phi;//Parameters for topic-word distribution K*V
     double [][] theta;//Parameters for doc-topic distribution M*K
     int iterations;//Times of iterations
     int saveStep;//The number of iterations between two saving
     int beginSaveIters;//Begin save model at this iteration

     public LdaModel(LdaGibbsSampling.modelparameters modelparam) {
         // TODO Auto-generated constructor stub
         alpha = modelparam.alpha;
         beta = modelparam.beta;
         iterations = modelparam.iteration;
         K = modelparam.topicNum;
         saveStep = modelparam.saveStep;
         beginSaveIters = modelparam.beginSaveIters;
     }

     public void initializeModel(Documents docSet) {
         // TODO Auto-generated method stub
         M = docSet.docs.size();
         V = docSet.termToIndexMap.size();
         nmk = new int [M][K];
         nkt = new int[K][V];
         nmkSum = new int[M];
         nktSum = new int[K];
         phi = new double[K][V];
         theta = new double[M][K];

         //initialize documents index array
         doc = new int[M][];
         for(int m = 0; m < M; m++){
             //Notice the limit of memory
             int N = docSet.docs.get(m).docWords.length;
             doc[m] = new int[N];
             for(int n = 0; n < N; n++){
                 doc[m][n] = docSet.docs.get(m).docWords[n];
             }
         }

         //initialize topic lable z for each word
         z = new int[M][];
         for(int m = 0; m < M; m++){
             int N = docSet.docs.get(m).docWords.length;
             z[m] = new int[N];
             for(int n = 0; n < N; n++){
                 int initTopic = (int)(Math.random() * K);// From 0 to K - 1
                 z[m][n] = initTopic;
                 //number of words in doc m assigned to topic initTopic add 1
                 nmk[m][initTopic]++;
                 //number of terms doc[m][n] assigned to topic initTopic add 1
                 nkt[initTopic][doc[m][n]]++;
                 // total number of words assigned to topic initTopic add 1
                 nktSum[initTopic]++;
             }
              // total number of words in document m is N
             nmkSum[m] = N;
         }
     }

     public void inferenceModel(Documents docSet) throws IOException {
         // TODO Auto-generated method stub
         if(iterations < saveStep + beginSaveIters){
             System.err.println("Error: the number of iterations should be larger than " + (saveStep + beginSaveIters));
             System.exit(0);
         }
         for(int i = 0; i < iterations; i++){
             System.out.println("Iteration " + i);
             if((i >= beginSaveIters) && (((i - beginSaveIters) % saveStep) == 0)){
                 //Saving the model
                 System.out.println("Saving model at iteration " + i +" ... ");
                 //Firstly update parameters
                 updateEstimatedParameters();
                 //Secondly print model variables
                 saveIteratedModel(i, docSet);
             }

             //Use Gibbs Sampling to update z[][]
             for(int m = 0; m < M; m++){
                 int N = docSet.docs.get(m).docWords.length;
                 for(int n = 0; n < N; n++){
                     // Sample from p(z_i|z_-i, w)
                     int newTopic = sampleTopicZ(m, n);
                     z[m][n] = newTopic;
                 }
             }
         }
     }

     private void updateEstimatedParameters() {
         // TODO Auto-generated method stub
         for(int k = 0; k < K; k++){
             for(int t = 0; t < V; t++){
                 phi[k][t] = (nkt[k][t] + beta) / (nktSum[k] + V * beta);
             }
         }

         for(int m = 0; m < M; m++){
             for(int k = 0; k < K; k++){
                 theta[m][k] = (nmk[m][k] + alpha) / (nmkSum[m] + K * alpha);
             }
         }
     }

     private int sampleTopicZ(int m, int n) {
         // TODO Auto-generated method stub
         // Sample from p(z_i|z_-i, w) using Gibbs upde rule

         //Remove topic label for w_{m,n}
         int oldTopic = z[m][n];
         nmk[m][oldTopic]--;
         nkt[oldTopic][doc[m][n]]--;
         nmkSum[m]--;
         nktSum[oldTopic]--;

         //Compute p(z_i = k|z_-i, w)
         double [] p = new double[K];
         for(int k = 0; k < K; k++){
             p[k] = (nkt[k][doc[m][n]] + beta) / (nktSum[k] + V * beta) * (nmk[m][k] + alpha) / (nmkSum[m] + K * alpha);
         }

         //Sample a new topic label for w_{m, n} like roulette
         //Compute cumulated probability for p
         for(int k = 1; k < K; k++){
             p[k] += p[k - 1];
         }
         double u = Math.random() * p[K - 1]; //p[] is unnormalised
         int newTopic;
         for(newTopic = 0; newTopic < K; newTopic++){
             if(u < p[newTopic]){
                 break;
             }
         }

         //Add new topic label for w_{m, n}
         nmk[m][newTopic]++;
         nkt[newTopic][doc[m][n]]++;
         nmkSum[m]++;
         nktSum[newTopic]++;
         return newTopic;
     }

     public void saveIteratedModel(int iters, Documents docSet) throws IOException {
         // TODO Auto-generated method stub
         //lda.params lda.phi lda.theta lda.tassign lda.twords
         //lda.params
         String resPath = PathConfig.LdaResultsPath;
         String modelName = "lda_" + iters;
         ArrayList<String> lines = new ArrayList<String>();
         lines.add("alpha = " + alpha);
         lines.add("beta = " + beta);
         lines.add("topicNum = " + K);
         lines.add("docNum = " + M);
         lines.add("termNum = " + V);
         lines.add("iterations = " + iterations);
         lines.add("saveStep = " + saveStep);
         lines.add("beginSaveIters = " + beginSaveIters);
         FileUtil.writeLines(resPath + modelName + ".params", lines);

         //lda.phi K*V
         BufferedWriter writer = new BufferedWriter(new FileWriter(resPath + modelName + ".phi"));
         for (int i = 0; i < K; i++){
             for (int j = 0; j < V; j++){
                 writer.write(phi[i][j] + "\t");
             }
             writer.write("\n");
         }
         writer.close();

         //lda.theta M*K
         writer = new BufferedWriter(new FileWriter(resPath + modelName + ".theta"));
         for(int i = 0; i < M; i++){
             for(int j = 0; j < K; j++){
                 writer.write(theta[i][j] + "\t");
             }
             writer.write("\n");
         }
         writer.close();

         //lda.tassign
         writer = new BufferedWriter(new FileWriter(resPath + modelName + ".tassign"));
         for(int m = 0; m < M; m++){
             for(int n = 0; n < doc[m].length; n++){
                 writer.write(doc[m][n] + ":" + z[m][n] + "\t");
             }
             writer.write("\n");
         }
         writer.close();

         //lda.twords phi[][] K*V
         writer = new BufferedWriter(new FileWriter(resPath + modelName + ".twords"));
         int topNum = 20; //Find the top 20 topic words in each topic
         for(int i = 0; i < K; i++){
             List<Integer> tWordsIndexArray = new ArrayList<Integer>();
             for(int j = 0; j < V; j++){
                 tWordsIndexArray.add(new Integer(j));
             }
             Collections.sort(tWordsIndexArray, new LdaModel.TwordsComparable(phi[i]));
             writer.write("topic " + i + "\t:\t");
             for(int t = 0; t < topNum; t++){
                 writer.write(docSet.indexToTermMap.get(tWordsIndexArray.get(t)) + " " + phi[i][tWordsIndexArray.get(t)] + "\t");
             }
             writer.write("\n");
         }
         writer.close();
     }

     public class TwordsComparable implements Comparator<Integer> {

         public double [] sortProb; // Store probability of each word in topic k

         public TwordsComparable (double[] sortProb){
             this.sortProb = sortProb;
         }

         @Override
         public int compare(Integer o1, Integer o2) {
             // TODO Auto-generated method stub
             //Sort topic word index according to the probability of each word in topic k
             if(sortProb[o1] > sortProb[o2]) return -1;
             else if(sortProb[o1] < sortProb[o2]) return 1;
             else return 0;
         }
     }
 }

程序的实现细节可以参考我在程序中给出的注释，如果理解LDA Gibbs Sampling的算法流程，上面的代码很好理解。其实排除输入输出和参数解析的代码，标准LDA 的Gibbs sampling只需要不到200行程序就可以搞定。当然，里面有很多可以考虑优化和变形的地方。

还有com和conf目录下的源文件分别放置常用函数和配置类，完整的JAVA工程见Github https://github.com/yangliuy/LDAGibbsSampling

3 用LDA Gibbs Sampling对Newsgroup 18828文档集进行主题分析

下面我们给出将上面的LDA Gibbs Sampling的实现Apply到Newsgroup 18828文档集进行主题分析的结果。 我实验时用到的数据已经上传到Github中，感兴趣的朋友可以直接从Github中下载工程运行。 我在Newsgroup 18828文档集随机选择了9个目录，每个目录下选择一个文档，将它们放置在data\LdaOriginalDocs目录下，我设定的模型参数如下

 alpha   0.5
 beta    0.1
 topicNum    10
 iteration   100
 saveStep    10
 beginSaveIters  80

即设定alpha和beta的值为0.5和0.1， Topic数目为10，迭代100次，从第80次开始保存模型结果，每10次保存一次。

经过100次Gibbs Sampling迭代后，程序输出10个Topic下top的topic words以及对应的概率值如下

我们可以看到虽然是unsupervised learning, LDA分析出来的Topic words还是非常make sense的。比如第5个topic是宗教类的，第6个topic是天文类的，第7个topic是计算机类的。程序的输出还包括模型参数.param文件，topic-word分布phi向量.phi文件，doc-topic分布theta向量.theta文件以及每个文档中每个单词分配到的主题label的.tassign文件。感兴趣的朋友可以从Github https://github.com/yangliuy/LDAGibbsSampling 下载完整工程自己换用其他数据集进行主题分析实验。 本程序是初步实现版本，如果大家发现任何问题或者bug欢迎交流，我第一时间在Github修复bug更新版本。

4 参考文献

[1] Christopher M. Bishop. Pattern Recognition and Machine Learning (Information Science and Statistics). Springer-Verlag New York, Inc., Secaucus, NJ, USA, 2006.
[2] Gregor Heinrich. Parameter estimation for text analysis. Technical report, 2004.
[3] Wang Yi. Distributed Gibbs Sampling of Latent Topic Models: The Gritty Details Technical report, 2005.

[4] Wayne Xin Zhao, Note for pLSA and LDA, Technical report, 2011.

[5] Freddy Chong Tat Chua. Dimensionality reduction and clustering of text documents.Technical report, 2009.

[6] Jgibblda, http://jgibblda.sourceforge.net/

[7]David M. Blei, Andrew Y. Ng, and Michael I. Jordan. 2003. Latent dirichlet allocation. J. Mach. Learn. Res. 3 (March 2003), 993-1022.