Brief Paper: Augmentation of Hidden Markov Chain for Complex Sequential Data in Context

Abstract

The classical HMM is defined by a parameter triple <italic>λ</italic> = (<italic>π</italic>, <italic>A</italic>, <italic>B</italic>), where each parameter represents a collection of probability distributions: initial state, state transition and output distributions in order. This paper proposes a new stationary parameter <italic>e</italic> =(<italic>e</italic>₁,<italic>e</italic>₂,…,<italic>e_N</italic>) where <italic>N</italic> is the number of states and <italic>e_t</italic> = <italic>P</italic>(|<italic>x_t</italic> = <italic>i</italic>,<italic>y</italic>) for describing how an input pattern <italic>y</italic> ends in state <italic>x_t</italic> = <italic>i</italic> at time <italic>t</italic> followed by nothing. It is often said that all is well that ends well. We argue here that all should end well. The paper sets the framework for the theory and presents an efficient inference and training algorithms based on dynamic programming and expectation-maximization. The proposed model is applicable to analyzing any sequential data with two or more finite segmental patterns are concatenated, each forming a context to its neighbors. Experiments on online Hangul handwriting characters have proven the effect of the proposed augmentation in terms of highly intuitive segmentation as well as recognition performance and 13.2% error rate reduction.