Maximum Likelihood Successive State Splitting Algorithm for Tied-Mixture HMnet

This paper shows how a divisive state clustering algorithm that generates acoustic Hidden Markov models(HMM)can benefit from a tied-mixture representation of the probability density function(pdf)of a state and increase the recognition performance. Popular decision tree based clustering algorthms, like for example the Successive State Splitting algorithm(SSS)make use of a simplification when clustering data. They represent a state using a single Gaussian pdf. We show that this approximation of the true pdf by a single Gaussian is too coarse, for example a single Gaussian cannot represent the differences in the symmetric parts of the pdf's of the new hypothetical states generated when evaluating the state split gain(which will determine the state split). The use of more sophisticated representations would lead to intractable computational problems that we solve by using a tied-mixture pdf representation. Additionally, we constrain the codebook to be immutable during the split. Between state spilits, this constraint is relaxed and the codebook is updated. In this paper, we thus propose an extension to the SSS algorithm, the so-called Tied-mixture Successive State Splitting algorithm(TM-SSS). TM-SSS shows up to about 31% error reduction in comparison with Maximum-Likelihood Successive State Split algorithm(ML-SSS)for a word recognition experiment