A Novel Method for Decoding Any High-Order Hidden Markov Model

Fei Ye,Yifei Wang

doi:10.1155/2014/231704

Abstract

This paper proposes a novel method for decoding any high-order hidden Markov model. First, the high-order hidden Markov model is transformed into an equivalent first-order hidden Markov model by Hadar’s transformation. Next, the optimal state sequence of the equivalent first-order hidden Markov model is recognized by the existing Viterbi algorithm of the first-order hidden Markov model. Finally, the optimal state sequence of the high-order hidden Markov model is inferred from the optimal state sequence of the equivalent first-order hidden Markov model. This method provides a unified algorithm framework for decoding hidden Markov models including the first-order hidden Markov model and any high-order hidden Markov model.

Highlights

Hidden Markov models are powerful tools for modeling and analyzing sequential data
Hidden Markov models have been used in many fields including handwriting recognition [1,2,3], speech recognition [4, 5], computational biology [6, 7], and longitudinal data analysis [8, 9]
We propose a novel method for decoding any high-order hidden Markov model

Summary

Introduction

Hidden Markov models are powerful tools for modeling and analyzing sequential data. For several decades, hidden Markov models have been used in many fields including handwriting recognition [1,2,3], speech recognition [4, 5], computational biology [6, 7], and longitudinal data analysis [8, 9]. In the traditional first-order hidden Markov model, the Viterbi algorithm is utilized to recognize the optimal state sequence [13]. The first one is called the extended approach, which is to extend directly the existing algorithms of the first-order hidden Markov model to highorder hidden Markov models [14,15,16]. The high-order hidden Markov model is transformed into an equivalent first-order hidden Markov model by Hadar’s transformation. The optimal state sequence of the equivalent first-order hidden Markov model is recognized by the existing Viterbi algorithm of the first-order hidden Markov model. The optimal state sequence of the high-order hidden Markov model is inferred from the optimal state sequence of the equivalent first-order hidden Markov model

High-Order Hidden Markov Model and Hadar’s Transformation

Methodology

Conclusions