Second-order hidden Markov models based on the fuzzy c-means and fuzzy entropy

Second-order hidden Markov models (HMM2) have been widely used in pattern recognition, especially in speech recognition. Their main advantages are their capabilities to model noisy temporal signals of variable length. This paper presents an extension of HMM2 based on the fuzzy c-means (FCM) and fuzzy entropy (FE) referred to as FCM-FE-HMM2. By building up a generalised fuzzy objective function, several new formulae solving model training problem are theoretically derived for FCM-FE-HMM2.