隐马尔可夫模型的前向算法(java实现)，今天奉上

隐马尔可夫模型的前向算法(手动实现)，今天奉上，由于研究生期间，实现的时候没有多加注释，这里为了让更好的人进入自然语言处理领域，特此，将前向算法奉上，具体公式可参考52nlp的HMN系列博客。

参考了大部分网站公式和借鉴。在此表示感谢。

后向算法和维特比算法，后续更新。

HMM类：

                                                                                        }
                                           }
                      }
     }
     
                     System.out.println("转移矩阵：");
                                       System.out.print(HMMHelper.fmtlog(logA[i][j]));
             }
             System.out.println();
         }
     }
 
                     System.out.println("发射矩阵：");
                                       System.out.print(HMMHelper.fmtlog(logB[i][j]));
             }
             System.out.println();
         }
     }
     
     
 }

Forward类：

          
          
                            }
     
                                alpha =                        alpha[ 0 ][ i ] = logPI[ i ] + logB[ i ][ O[ 0 ] ];
         }
                                                                                      sum = TCMMath.logplus( sum, alpha[t - 1][ j ] + logA[ j ][ i ]);
                 }
                 alpha[ t ][ i ] = logB[ i ][ O[ t ] ] + sum;             }
         }
     }
     
                                                                sum = TCMMath.logplus(sum, alpha[ T-1 ][ i ]);         }
              }
     
                                                   System.out.print(HMMHelper.fmtlog(alpha[ i ][ j ]));
             }
             System.out.println();
         }
     }
 }

测试类：

         test();
     }
 
                                        { 0.500, 0.375, 0.125 }, 
                 { 0.250, 0.125, 0.625 }, 
                 { 0.250, 0.375, 0.375 } };
                                   { 0.60, 0.20, 0.15, 0.05 }, 
                 { 0.25, 0.25, 0.25, 0.25 }, 
                 { 0.05, 0.10, 0.35, 0.50 } };
         
                               
                           System.out.println("初始概率向量：{"+PI[0]+" "+PI[1]+" "+PI[2]+"}");
         System.out.println("隐藏状态序列：{"+Box.one+" "+Box.two+" "+Box.three+"}");
         System.out.println("观测序列：{"+Color.yellow+" "+Color.red+" "+Color.blue+" "+Color.yellow+" "+Color.green+"}");
         
                    Forward foreward=         foreward.CalculateForeMatrix();         System.out.println( HMMHelper.fmtlog( foreward.logProb() ) );         
                   * 后向算法测试
    }
 }