Elimination of trajectory folding phenomenon: HMM, trajectory mixture HMM and mixture stochastic trajectory model

In this paper, a study of topology of Hidden Markov Model (HMM) used in speech recognition is addressed. Our main contribution is the introduction of the notion of trajectory folding phenomenon of HMM. In complex phonetic contexts and in speaker-variability, this phenomenon degrades the discriminability of HMM. The goal of this paper is to give some explanation and experimental evidence suggesting the existence of this phenomenon. The systems eliminating (partially or entirely) the trajectory folding are HMM with a special topology, called Trajectory Mixture HMM (TMHMM), and a Mixture Stochastic Trajectory Model (MSTM), proposed recently. HMM, TMHMM and MSTM have been tested on a 1011 words vocabulary, speaker dependent and multi-speaker continuous French speech recognition task. With similar number of model parameters, TMHMM and MSTM cuts down the error rate produced by the HMM, which confirms our hypothesis.