隐马尔科夫模型的解码算法和前向算法



隐马尔科夫模型的解码算法和前向算法

隐马尔科夫模型算是语音识别的支柱了，观察序列是语音信号的MFCC编码，得到的隐藏序列就是音素了。音素加上神经网络就可以构建一个语音识别系统。最近也在学习这个方面，所以试着先把解码算法（维特比算法）和计算观察序列出现概率的前向算法实现了一下。用的语言是Java，感觉IDEA比eclipse舒心。其中前行算法的代码是在解码算法的基础上简单改的，在时间和空间上还有很多可以优化的地方，但是并没有这个需求啊关于HMM模型的资料，找到了这两篇很好的文章，真是非常感谢作者啊贝叶斯网络简介 ： http://blog.csdn.net/memory513773348/article/details/16973807HMM学习最佳范例： http://www.52nlp.cn/hmm-learn-best-practices-seven-forward-backward-algorithm-5 HMM和贝叶斯网络属于概率图模型，相关的教材有Koller的经典著作《Porbabilistic Graphical Models》，1200多页的巨著public class HMM {public static void main(String[] args) {double[][] trans = {{0.01,0.5,0.49},{0.18,0.01,0.81},{0.7,0.29,0.01}};double[][] mis = {{0.1,0.8,0.1},{0.3,0.3,0.4},{0.2,0.1,0.7}};double[] init = {0.1,0.5,0.4};int[] view = {2,1,2,0,2,1,2,1,0,0,0,1};int[] res = HMM.decode(view,trans,mis,init);for(int i: res){System.out.print(i+" ");}System.out.println("");double r = HMM.forward(view,trans,mis,init);System.out.println(r);}public static int argmax(double[] input ){double local_max = -100000000.0;int index = 0;for(int i=0;i<input.length;++i){if(input[i]>local_max){local_max = input[i];index = i;}}return index;}public static int[] decode(int[] view, double[][] trans, double[][] mis, double[] init) {int stats_num = trans.length;int view_num = view.length;int loop_head = 0;int[] result = new int[view.length];double[] tmp = new double[stats_num];node[] net = new node[stats_num*view_num];// initfor(int i=0;i<stats_num;++i){net[i] = new node(i, Math.log(init[i])+Math.log(mis[i][view[0]]), null);}// build the netfor(int i=1;i<view_num;++i){for(int j=0;j<stats_num;++j){for(int k=0;k<stats_num;++k){tmp[k] = net[loop_head+k].log_p + Math.log(trans[net[loop_head+k].name][k]) + Math.log(mis[j][view[i]]);}int index = HMM.argmax(tmp);net[loop_head+stats_num+j] = new node(j,tmp[index],net[loop_head+index]);}loop_head += stats_num;}// find the best endint index = loop_head;double local_max = -10000000.0;for(int i = loop_head;i<loop_head+stats_num;++i){if(net[i].log_p>local_max){local_max = net[i].log_p;index = i;}}// fill the result along the linenode end = net[index];for(int i=view.length-1;i>=0;--i){result[i] = end.name;//System.out.println(end.log_p);end = end.back;}// return the resultreturn result;}public static double forward(int[] view, double[][] trans, double[][] mis, double[] init) {int stats_num = trans.length;int view_num = view.length;int loop_head = 0;double tmp = 0;node[] net = new node[stats_num*view_num];for(int i=0;i<stats_num;++i){net[i] = new node(i, Math.log(init[i])+Math.log(mis[i][view[0]]), null);}for(int i=1;i<view_num;++i){for(int j=0;j<stats_num;++j){tmp = 0;for(int k=0;k<stats_num;++k){tmp += Math.exp(net[loop_head+k].log_p + Math.log(trans[net[loop_head+k].name][k]) + Math.log(mis[j][view[i]]));}tmp = Math.log(tmp);net[loop_head+stats_num+j] = new node(j,tmp,null);}loop_head += stats_num;}tmp = 0;for(int i = loop_head;i<loop_head+stats_num;++i){tmp += Math.exp(net[i].log_p);}return tmp;}}class node {public node(int name, double log_p, node back) {this.name = name;this.log_p = log_p;this.back = back;}int name;node back;double log_p ;}