void BaumWelch(HMM *phmm, int T, int *O, double **alpha, double **beta,
double **gamma)
{
int i, j, k;
int t, l = 0;
double probf, probb, val, threshold;
double numeratorA, denominatorA;
double numeratorB, denominatorB;
double ***xi, *scale;
double delta, deltaprev, probprev;
double ratio;
deltaprev = 10e-70;
xi = AllocXi(T, phmm->N);
scale = dvector(1, T);
ForwardWithScale(phmm, T, O, alpha, scale, &probf);
BackwardWithScale(phmm, T, O, beta, scale, &probb);
ComputeGamma(phmm, T, alpha, beta, gamma);
ComputeXi(phmm, T, O, alpha, beta, xi);
probprev = probf;
do {
/* reestimate frequency of state i in time t=1 */
for (i = 1; i <= phmm->N; i++)
phmm->pi[i] = .001 + .999*gamma[1][i];
/* reestimate transition matrix and symbol prob in
each state */
for (i = 1; i <= phmm->N; i++) {
denominatorA = 0.0;
for (t = 1; t <= T - 1; t++)
denominatorA += gamma[t][i];
for (j = 1; j <= phmm->N; j++) {
numeratorA = 0.0;
for (t = 1; t <= T - 1; t++)
numeratorA += xi[t][i][j];
phmm->A[i][j] = .001 +
.999*numeratorA/denominatorA;
}
denominatorB = denominatorA + gamma[T][i];
for (k = 1; k <= phmm->M; k++) {
numeratorB = 0.0;
for (t = 1; t <= T; t++) {
if (O[t] == k)
numeratorB += gamma[t][i];
}
phmm->B[i][k] = .001 +
.999*numeratorB/denominatorB;
}
}
ForwardWithScale(phmm, T, O, alpha, scale, &probf);
BackwardWithScale(phmm, T, O, beta, scale, &probb);
ComputeGamma(phmm, T, alpha, beta, gamma);
ComputeXi(phmm, T, O, alpha, beta, xi);
delta = probf - probprev;
ratio = delta/deltaprev;
probprev = probf;
deltaprev = delta;
l++;
}
while (ratio > DELTA);
printf("num iterations: %d\n", l);
FreeXi(xi, T, phmm->N);
free_dvector(scale, 1, T);
}
void BaumWelch(HMM *phmm, int T, int *O, double **alpha, double **beta,
double **gamma, int *pniter,
double *plogprobinit, double *plogprobfinal)
{
int i, j, k;
int t, l = 0;
double logprobf, logprobb, threshold;
double numeratorA, denominatorA;
double numeratorB, denominatorB;
double ***xi, *scale;
double delta, deltaprev, logprobprev;
deltaprev = 10e-70;
xi = AllocXi(T, phmm->N);
scale = dvector(1, T);
ForwardWithScale(phmm, T, O, alpha, scale, &logprobf);
*plogprobinit = logprobf; /* log P(O |intial model) */
BackwardWithScale(phmm, T, O, beta, scale, &logprobb);
ComputeGamma(phmm, T, alpha, beta, gamma);
ComputeXi(phmm, T, O, alpha, beta, xi);
logprobprev = logprobf;
do {
/* reestimate frequency of state i in time t=1 */
for (i = 1; i <= phmm->N; i++)
phmm->pi[i] = .001 + .999*gamma[1][i];
/* reestimate transition matrix and symbol prob in
each state */
for (i = 1; i <= phmm->N; i++) {
denominatorA = 0.0;
for (t = 1; t <= T - 1; t++)
denominatorA += gamma[t][i];
for (j = 1; j <= phmm->N; j++) {
numeratorA = 0.0;
for (t = 1; t <= T - 1; t++)
numeratorA += xi[t][i][j];
phmm->A[i][j] = .001 +
.999*numeratorA/denominatorA;
}
denominatorB = denominatorA + gamma[T][i];
for (k = 1; k <= phmm->M; k++) {
numeratorB = 0.0;
for (t = 1; t <= T; t++) {
if (O[t] == k)
numeratorB += gamma[t][i];
}
phmm->B[i][k] = .001 +
.999*numeratorB/denominatorB;
}
}
ForwardWithScale(phmm, T, O, alpha, scale, &logprobf);
BackwardWithScale(phmm, T, O, beta, scale, &logprobb);
ComputeGamma(phmm, T, alpha, beta, gamma);
ComputeXi(phmm, T, O, alpha, beta, xi);
/* compute difference between log probability of
two iterations */
delta = logprobf - logprobprev;
logprobprev = logprobf;
l++;
}
while (delta > DELTA); /* if log probability does not
change much, exit */
*pniter = l;
*plogprobfinal = logprobf; /* log P(O|estimated model) */
FreeXi(xi, T, phmm->N);
free_dvector(scale, 1, T);
}
/******************************************************************************
**函数名称：BaumWelch
**功能：BaumWelch算法
**参数：phmm：HMM模型指针
** T：观察序列长度
** O：观察序列
** alpha，beta，gamma，pniter均为中间变量
** plogprobinit：初始概率
** plogprobfinal: 最终概率
**/
void BaumWelch(HMM *phmm, int T, int *O, double **alpha, double **beta,
double **gamma, int *pniter,
double *plogprobinit, double *plogprobfinal)
{
int i, j, k;
int t, l = 0;
double logprobf, logprobb;
double numeratorA, denominatorA;
double numeratorB, denominatorB;
double ***xi, *scale;
double delta, deltaprev, logprobprev;
deltaprev = 10e-70;
xi = AllocXi(T, phmm->N);
scale = dvector(1, T);
ForwardWithScale(phmm, T, O, alpha, scale, &logprobf);
*plogprobinit = logprobf; /* log P(O |初始状态) */
BackwardWithScale(phmm, T, O, beta, scale, &logprobb);
ComputeGamma(phmm, T, alpha, beta, gamma);
ComputeXi(phmm, T, O, alpha, beta, xi);
logprobprev = logprobf;
do {
/* 重新估计 t=1 时，状态为i 的频率 */
for (i = 1; i <= phmm->N; i++)
phmm->pi[i] = .001 + .999*gamma[1][i];
/* 重新估计转移矩阵和观察矩阵 */
for (i = 1; i <= phmm->N; i++)
{
denominatorA = 0.0;
for (t = 1; t <= T - 1; t++)
denominatorA += gamma[t][i];
for (j = 1; j <= phmm->N; j++)
{
numeratorA = 0.0;
for (t = 1; t <= T - 1; t++)
numeratorA += xi[t][i][j];
phmm->A[i][j] = .001 +
.999*numeratorA/denominatorA;
}
denominatorB = denominatorA + gamma[T][i];
for (k = 1; k <= phmm->M; k++)
{
numeratorB = 0.0;
for (t = 1; t <= T; t++)
{
if (O[t] == k)
numeratorB += gamma[t][i];
}
phmm->B[i][k] = .001 +
.999*numeratorB/denominatorB;
}
}
ForwardWithScale(phmm, T, O, alpha, scale, &logprobf);
BackwardWithScale(phmm, T, O, beta, scale, &logprobb);
ComputeGamma(phmm, T, alpha, beta, gamma);
ComputeXi(phmm, T, O, alpha, beta, xi);
/* 计算两次直接的概率差 */
delta = logprobf - logprobprev;
logprobprev = logprobf;
l++;
}
while (delta > DELTA); /* 如果差的不太大，表明收敛，退出 */
*pniter = l;
*plogprobfinal = logprobf; /* log P(O|estimated model) */
FreeXi(xi, T, phmm->N);
free_dvector(scale, 1, T);
}