Motivation

  

Figure 3: The main phases of HMM training based on the Viterbi segmentation.

The main phases of HMM training are shown in Figure 3. Conventionally the HMMs are initialized by using either manual segmentation of the training samples or a segmentation provided by another previously trained HMM. Equal duration of the states is normally assumed for the initial segmentation into states inside each phoneme. The parameters of each state are then obtained by finding a model that maximizes the likelihood of the associated data. The actual training loop (Figure 3) consists of alternating segmentation and likelihood maximization phases [Rabiner, 1989]. When the HMMs are ready their performance can be tuned by corrective training [Bahl et al., 1988].

The investigations to apply SOM for the training of MDHMMs were motivated mainly by the following three ideas and needs:

1.

A suitable algorithm is needed to initialize the centroids of the Gaussian mixtures used for the modeling of the output density functions of the HMM states. If the number of mixtures is large, the traditional approaches seem sometimes to fail in providing a good basis for convergence to high quality solutions, e.g. see Publication 6.

2.

A smooth probability density representation is desired for dealing with the finite amount of training data to simultaneously maintain a high level of generalization and modeling accuracy for the independent test data.

3.

For mixture densities with a large number of mixture components it is not reasonable to compute and sum the contributions of all components, to get an approximation for the density function. If the set of components, where the majority of the best matches are expected to occur, can be quickly separated, significant savings in the recognition speed are to be expected without a notable increase in the error rate.