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Basic problems solving for two-dimensional discrete 3 × 4 order hidden markov model

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  • Wang, Guo-gang
  • Gan, Zong-liang
  • Tang, Gui-jin
  • Cui, Zi-guan
  • Zhu, Xiu-chang

Abstract

A novel model is proposed to overcome the shortages of the classical hypothesis of the two-dimensional discrete hidden Markov model. In the proposed model, the state transition probability depends on not only immediate horizontal and vertical states but also on immediate diagonal state, and the observation symbol probability depends on not only current state but also on immediate horizontal, vertical and diagonal states. This paper defines the structure of the model, and studies the three basic problems of the model, including probability calculation, path backtracking and parameters estimation. By exploiting the idea that the sequences of states on rows or columns of the model can be seen as states of a one-dimensional discrete 1 × 2 order hidden Markov model, several algorithms solving the three questions are theoretically derived. Simulation results further demonstrate the performance of the algorithms. Compared with the two-dimensional discrete hidden Markov model, there are more statistical characteristics in the structure of the proposed model, therefore the proposed model theoretically can more accurately describe some practical problems.

Suggested Citation

  • Wang, Guo-gang & Gan, Zong-liang & Tang, Gui-jin & Cui, Zi-guan & Zhu, Xiu-chang, 2016. "Basic problems solving for two-dimensional discrete 3 × 4 order hidden markov model," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 73-82.
    • Handle: RePEc:eee:chsofr:v:89:y:2016:i:c:p:73-82
    DOI: 10.1016/j.chaos.2015.09.025
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    References listed on IDEAS

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    1. Fei Ye & Yifei Wang, 2014. "A Novel Method for Decoding Any High-Order Hidden Markov Model," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-6, November.
    2. Michael Seifert & Khalil Abou-El-Ardat & Betty Friedrich & Barbara Klink & Andreas Deutsch, 2014. "Autoregressive Higher-Order Hidden Markov Models: Exploiting Local Chromosomal Dependencies in the Analysis of Tumor Expression Profiles," PLOS ONE, Public Library of Science, vol. 9(6), pages 1-16, June.
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    1. Wang, Guo-gang & Tang, Gui-jin & Gan, Zong-liang & Cui, Zi-guan & Zhu, Xiu-chang, 2016. "Basic problems and solution methods for two-dimensional continuous 3 × 3 order hidden Markov model," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 435-446.

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