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Pairwise Markov Chains
May 2003 (vol. 25 no. 5)
pp. 634-639

Abstract—We propose a new model called a Pairwise Markov Chain (PMC), which generalizes the classical Hidden Markov Chain (HMC) model. The generalization, which allows one to model more complex situations, in particular implies that in PMC the hidden process is not necessarily a Markov process. However, PMC allows one to use the classical Bayesian restoration methods like Maximum APosteriori (MAP), or Maximal Posterior Mode (MPM). So, akin to HMC, PMC allows one to restore hidden stochastic processes, with numerous applications to signal and image processing, such as speech recognition, image segmentation, and symbol detection or classification, among others. Furthermore, we propose an original method of parameter estimation, which generalizes the classical Iterative Conditional Estimation (ICE) valid for of classical hidden Markov chain model, and whose extension to possibly non-Gaussian and correlated noise is briefly treated. Some preliminary experiments validate the interest of the new model.

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Index Terms:
Bayesian restoration, hidden data, image segmentation, iterative conditional estimation, hidden Markov chain, pairwise Markov chain, unsupervised classification.
Citation:
Wojciech Pieczynski, "Pairwise Markov Chains," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 25, no. 5, pp. 634-639, May 2003, doi:10.1109/TPAMI.2003.1195998
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