[置顶] 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.