The Training Algorithm of Fuzzy Coupled Hidden Markov Models

Abstract

A variety of coupled hidden Markov models (CHMMs) have recently been proposed as extensions of HMM to better characterize multiple interdependent sequences. The resulting models have multiple state variables that are temporally coupled via matrices of conditional probabilities. A generalised fuzzy approach to statistical modelling techniques is proposed in this paper. Fuzzy C-means (FCM) and fuzzy entropy (FE) techniques are combined into a generalised fuzzy technique and applied to coupled hidden Markov models. The CHMM based on the fuzzy c-means (FCM) and fuzzy entropy (FE) is referred to as FCM-FE-CHMM in this paper. By building up a generalised fuzzy objective function, several new formulae solving Training algorithms are theoretically derived for FCM-FE-CHMM. The fuzzy modelling techniques are very flexible since the degree of fuzziness, the degree of fuzzy entropy.