Ergodic HMM

When the number of categories $N$ is known and segmentation boundaries are unknown, it is possible to apply the Ergodic HMM. In this case, one can consider that 'category' corresponds to 'state' and the signal sequence corresponds to the symbol generated from the state. The problem divides into the following two problems.

1. The problem of estimating the HMM parameter $\mbox{\boldmath$X$}$ that maximizes the likelihood of the signal sequence. Parameter $\mbox{\boldmath$X$}$ consists of the initial state probability $\mbox{\boldmath$\pi$}= (\pi_i)$ , the state transition probability $\mbox{\boldmath$A$}= (a_{ij})$ and the symbol output probability $\mbox{\boldmath$B$}= ( b_j(l) )$ .

2. The problem of estimating the state transition sequence that generate the highest probability of outputting the signal sequence $\mbox{\boldmath$X$}$ for the HMM parameter $\mbox{\boldmath$M$}$ (estimate of optimal state sequence).

Fig.2 outlines our solution.

図 2: Flow chart that includes an Ergodic HMM for the $N$-signal source problem