Maximum likelihood successive state splitting algorithm for tied-mixture HMnet

This paper shows how a divisive state clustering algorithm that generates a coustic Hidden Markov models (HMM) can benefit from a tied-mixture represen tation of the probability density function (pdf) of a state and increase th e recognition performance. Popular decision tree based clustering algorithm s, like for example the Successive State Splitting algorithm (SSS) make use of a simplification when clustering data. They represent a state using a s ingle Gaussian pdf. We show that this approximation of the true pdf by a si ngle Gaussian is too coarse, for example a single Gaussian cannot represent the differences in the symmetric parts of the pdf's of the new hypothetica l states generated when evaluating the state split gain (which will determi ne the state split). The use of more sophisticated representations would le ad to intractable computational problems that we solve by using a tied-mixt ure pdf representation. Additionally, we constrain the codebook to be immut able during the split. Between state splits, this constraint is relaxed and the codebook is updated. In this paper, we thus propose an extension to th e SSS algorithm, the so-called Tied-mixture Successive State Splitting algo rithm (TM-SSS). TM-SSS shows up to about 31% error reduction in comparison with Maximum-Likelihood Successive State Split algorithm (ML-SSS) for a wor d recognition experiment.