Tsallis Entropy-Regularized Yang-Type Fuzzy <i>c</i> -Hidden Markov Models

This study proposes Tsallis entropy-regularized Yang-type fuzzy c -hidden Markov models (TYFCHMMs), a fuzzy clustering algorithm based on hidden Markov model (HMM), for series data. First, the relationship between a Gaussian mixture model with identity covariances, which is a conventional probabilistic clustering algorithm for vectorial data, and Yang-type fuzzy c -means, which is a conventional fuzzy clustering algorithm for vectorial data, is determined. Second, the relationship between Bezdek-type fuzzy c -means and Tsallis entropy-regularized fuzzy c -means, which are two conventional fuzzy clustering algorithms for vectorial data, is determined. Based on these relationships, TYFCHMMs are constructed from mixtures of HMMs (MoHMMs), which are conventional probabilistic clustering algorithms based on HMM for series data, using Yang-type fuzzification and Tsallis entropy regularization. Through numerical tests using an artificial dataset, the effects of parameters on the clustering results of TYFCHMMs and the close relationship between TYFCHMMs and MoHMMs are identified. Furthermore, numerical tests using ten real datasets confirmed that TYFCHMMs outperform MoHMMs in terms of clustering accuracy.