Training fuzzy third-order hidden Markov models for matrix data

A generalised fuzzy approach to statistical modelling techniques for pattern recognition is proposed in this paper. Fuzzy C-means (FCM) and fuzzy entropy (FE) techniques are combined into a generalised fuzzy technique and applied to third-order two-dimensional hidden Markov mode(2-D HMM). 2-D HMM is an extension of 1-D HMM to 2-D, it provides a reasonable statistical method to model matrix data. By using the ideal that the sequences of states on columns or rows of a third-order 2-D HMM can be seen as states of a 1-D HMM and building up a generalised fuzzy objective function, several new formulae solving model training problem problem are theoretically derived.