STATE-DEPENDENT TIME WARPING IN THE TRENDED HIDDEN MARKOV MODEL

In this paper we present an algorithm for estimating state-dependent p olynomial coefficients in the nonstationary-state hidden Markov model (or the trended HMM) which allows for the flexibility of linear time w arping or scaling in individual model states. The need for the state-d ependent time warping arises from the consideration that due to speaki ng rate variation and other temporal factors in speech, multiple state -segmented speech data sequences used for training a single set of pol ynomial coefficients often vary appreciably in their sequence lengths. The algorithm is developed based on a general framework with use of a uxiliary parameters, which, of no interests in themselves, nevertheles s provide an intermediate tool for achieving maximal accuracy for esti mating the polynomial coefficients in the trended HMM. It is proved th at the proposed estimation algorithm converges to a solution equivalen t to the state-optimized maximum likelihood estimate. Effectiveness of the algorithm is demonstrated in experiments designed to fit a single trended HMM simultaneously to multiple sequences of speech data which are different renditions of the same word yet vary over a wide range in the sequence length. Speech recognition experiments have been perfo rmed based on the standard acoustic-phonetic TIMIT database. The speec h recognition results demonstrate the advantages of the time-warping t rended HMMs over the regular trended HMMs measured about 10 to 15% imp rovement in terms of the recognition rate.