Initial HMM parameters

In this study, we used the Moore type discrete Ergodic HMM. The number of states (categories) of the Ergodic HMM was set at 4, the same as the number of speakers.

It is well known that the Baum-Welch algorithm runs toward local maxima, Therefore, the speaker classification rate seems greatly depends on the initial parameters. Accordingly, the initial parameters were calculated in the following three ways.

1. Experiment 1 : (true values are given to all parameters)

   As the initial HMM parameters $\mbox{\boldmath$M$}$, true values were given to the initial state probability $\mbox{\boldmath$\pi$}^{(0)}$, the state transition probability $\mbox{\boldmath$A$}^{(0)}$ and the symbol output probability $\mbox{\boldmath$B$}^{(0)}$.

2. Experiment 2 : (true value is given only to the symbol output probability)

   Symbol output probability $\mbox{\boldmath$B$}^{(0)}$ was given its true value. Initial state probability $\mbox{\boldmath$\pi$}^{(0)}$ and the state transition probability $\mbox{\boldmath$A$}^{(0)}$ were given uniform probabilities.

3. Experiment 3 : (random values)

   The initial state probability $\mbox{\boldmath$\pi$}^{(0)}$ and the state transition probability $\mbox{\boldmath$A$}^{(0)}$ were given uniform probabilities. The symbol output probability $\mbox{\boldmath$B$}^{(0)}$ was assigned random probabilities. Note that the Baum-Welch learning algorithm does not work if a uniform probability is given to $\mbox{\boldmath$B$}^{(0)}$.