Parameters Training Problem On Some Special HMMS

There are three problems needed to be solved by using Hidden Markov models, which are recognizing, decoding and learning. Learning problem, namely parameter estimation problem, is the core problem of HMM. This paper mainly discusses learning problem. It discusses the algorithms of discrete HMM and continuous HMM parameters estimation respectively and analyzes large sample properties of HMM maximum likelihood estimation(MLE). On the other hand, combined with fuzzy information techniques, algorithms of HMM estimation based on fuzzy clustering are proposed, which solves some HMM parameters training problems.The innovation of this article:1 MLE of discrete HMM and continuous HMM are presented respectively. We also discuss large sample properties of MLE using the properties of entropy. It shows that the MLE is consistent estimation and is also asymptotically normal.2 Fuzzy information techniques including fuzzy clustering and maximum fuzzy entropy are introduced to the HMM parameters training. Algorithm of discrete HMM parameters training based on fuzzy clustering is proposed. It shows that the algorithm has excellent convergence. It ensures that the initial parameters will converge to a local optimized value under conditions.3 Fuzzy techniques are further applied to continuous HMM of one state(Gaussian Mixture Models, GMM). Two algorithms of GMM parameters training, including FCM-GMM algorithm and FE-GMM algorithm, are proposed based on further analysis of conventional estimation algorithm(EM algorithm). It comes to a conclusion that the EM algorithm is special instance of the two algorithms.