谁做过 EM算法 java实现
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发布时间：2022-04-22 09:11
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时间：2023-09-21 13:07
参考：
package nlp;/**
* @author Orisun
* date 2011-10-22
*/
import java.util.ArrayList;
public class BaumWelch {
int M; // 隐藏状态的种数
int N; // 输出活动的种数
double[] PI; // 初始状态概率矩阵
double[][] A; // 状态转移矩阵
double[][] B; // 混淆矩阵
ArrayList<Integer> observation = new ArrayList<Integer>(); // 观察到的集合
ArrayList<Integer> state = new ArrayList<Integer>(); // 中间状态集合
int[] out_seq = { 2, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1,
1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 2, 1 }; // 测试用的观察序列
int[] hidden_seq = { 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1,
1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1 }; // 测试用的隐藏状态序列
int T = 32; // 序列长度为32
double[][] alpha = new double[T][]; // 向前变量
double PO;
double[][] beta = new double[T][]; // 向后变量
double[][] gamma = new double[T][];
double[][][] xi = new double[T - 1][][];
// 初始化参数。Baum-Welch得到的是局部最优解，所以初始参数直接影响解的好坏
public void initParameters() {
M = 2;
N = 2;
PI = new double[M];
PI[0] = 0.5;
PI[1] = 0.5;
A = new double[M][];
B = new double[M][];
for (int i = 0; i < M; i++) {
A[i] = new double[M];
B[i] = new double[N];
}
A[0][0] = 0.8125;
A[0][1] = 0.1875;
A[1][0] = 0.2;
A[1][1] = 0.8;
B[0][0] = 0.875;
B[0][1] = 0.125;
B[1][0] = 0.25;
B[1][1] = 0.75;
observation.add(1);
observation.add(2);
state.add(1);
state.add(2);
for (int t = 0; t < T; t++) {
alpha[t] = new double[M];
beta[t] = new double[M];
gamma[t] = new double[M];
}
for (int t = 0; t < T - 1; t++) {
xi[t] = new double[M][];
for (int i = 0; i < M; i++)
xi[t][i] = new double[M];
}
}
// 更新向前变量
public void updateAlpha() {
for (int i = 0; i < M; i++) {
alpha[0][i] = PI[i] * B[i][observation.indexOf(out_seq[0])];
}
for (int t = 1; t < T; t++) {
for (int i = 0; i < M; i++) {
alpha[t][i] = 0;
for (int j = 0; j < M; j++) {
alpha[t][i] += alpha[t - 1][j] * A[j][i];
}
alpha[t][i] *= B[i][observation.indexOf(out_seq[t])];
}
}
}
// 更新观察序列出现的概率，它在一些公式中当分母
public void updatePO() {
for (int i = 0; i < M; i++)
PO += alpha[T - 1][i];
}
// 更新向后变量
public void updateBeta() {
for (int i = 0; i < M; i++) {
beta[T - 1][i] = 1;
}
for (int t = T - 2; t >= 0; t--) {
for (int i = 0; i < M; i++) {
for (int j = 0; j < M; j++) {
beta[t][i] += A[i][j]
* B[j][observation.indexOf(out_seq[t + 1])]
* beta[t + 1][j];
}
}
}
}
// 更新xi
public void updateXi() {
for (int t = 0; t < T - 1; t++) {
double frac = 0.0;
for (int i = 0; i < M; i++) {
for (int j = 0; j < M; j++) {
frac += alpha[t][i] * A[i][j]
* B[j][observation.indexOf(out_seq[t + 1])]
* beta[t + 1][j];
}
}
for (int i = 0; i < M; i++) {
for (int j = 0; j < M; j++) {
xi[t][i][j] = alpha[t][i] * A[i][j]
* B[j][observation.indexOf(out_seq[t + 1])]
* beta[t + 1][j] / frac;
}
}
}
}
// 更新gamma
public void updateGamma() {
for (int t = 0; t < T - 1; t++) {
double frac = 0.0;
for (int i = 0; i < M; i++) {
frac += alpha[t][i] * beta[t][i];
}
// double frac = PO;
for (int i = 0; i < M; i++) {
gamma[t][i] = alpha[t][i] * beta[t][i] / frac;
}
// for(int i=0;i<M;i++){
// gamma[t][i]=0;
// for(int j=0;j<M;j++)
// gamma[t][i]+=xi[t][i][j];
// }
}
}
// 更新状态概率矩阵
public void updatePI() {
for (int i = 0; i < M; i++)
PI[i] = gamma[0][i];
}
// 更新状态转移矩阵
public void updateA() {
for (int i = 0; i < M; i++) {
double frac = 0.0;
for (int t = 0; t < T - 1; t++) {
frac += gamma[t][i];
}
for (int j = 0; j < M; j++) {
double dem = 0.0;
// for (int t = 0; t < T - 1; t++) {
// dem += xi[t][i][j];
// for (int k = 0; k < M; k++)
// frac += xi[t][i][k];
// }
for (int t = 0; t < T - 1; t++) {
dem += xi[t][i][j];
}
A[i][j] = dem / frac;
}
}
}
// 更新混淆矩阵
public void updateB() {
for (int i = 0; i < M; i++) {
double frac = 0.0;
for (int t = 0; t < T; t++)
frac += gamma[t][i];
for (int j = 0; j < N; j++) {
double dem = 0.0;
for (int t = 0; t < T; t++) {
if (out_seq[t] == observation.get(j))
dem += gamma[t][i];
}
B[i][j] = dem / frac;
}
}
}
// 运行Baum-Welch算法
public void run() {
initParameters();
int iter = 22; // 迭代次数
while (iter-- > 0) {
// E-Step
updateAlpha();
// updatePO();
updateBeta();
updateGamma();
updatePI();
updateXi();
// M-Step
updateA();
updateB();
}
}
public static void main(String[] args) {
BaumWelch bw = new BaumWelch();
bw.run();
System.out.println("训练后的初始状态概率矩阵：");
for (int i = 0; i < bw.M; i++)
System.out.print(bw.PI[i] + "\t");
System.out.println();
System.out.println("训练后的状态转移矩阵：");
for (int i = 0; i < bw.M; i++) {
for (int j = 0; j < bw.M; j++) {
System.out.print(bw.A[i][j] + "\t");
}
System.out.println();
}
System.out.println("训练后的混淆矩阵：");
for (int i = 0; i < bw.M; i++) {
for (int j = 0; j < bw.N; j++) {
System.out.print(bw.B[i][j] + "\t");
}
System.out.println();
}
}
}
