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Unsupervised data classification using pairwise Markov chains with automatic copulas selection

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  • Derrode, Stéphane
  • Pieczynski, Wojciech

Abstract

The Pairwise Markov Chain (PMC) model assumes the couple of observations and states processes to be a Markov chain. To extend the modeling capability of class-conditional densities involved in the PMC model, copulas are introduced and the influence of their shape on classification error rates is studied. In particular, systematic experiments show that the use of wrong copulas can degrade significantly classification performances. Then an algorithm is presented to identify automatically the right copulas from a finite set of admissible copulas, by extending the general “Iterative Conditional Estimation” (ICE) parameters estimation method to the context considered. The unsupervised segmentation of a radar image illustrates the nice behavior of the algorithm.

Suggested Citation

  • Derrode, Stéphane & Pieczynski, Wojciech, 2013. "Unsupervised data classification using pairwise Markov chains with automatic copulas selection," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 81-98.
    • Handle: RePEc:eee:csdana:v:63:y:2013:i:c:p:81-98
    DOI: 10.1016/j.csda.2013.01.027
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    References listed on IDEAS

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    1. Genest, Christian & Rémillard, Bruno & Beaudoin, David, 2009. "Goodness-of-fit tests for copulas: A review and a power study," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 199-213, April.
    2. Qu, Xiaomei & Zhou, Jie & Shen, Xiaojing, 2010. "Archimedean copula estimation and model selection via l1-norm symmetric distribution," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 406-414, April.
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    4. Christos Ntantamis, 2010. "Detecting Structural Breaks using Hidden Markov Models," CREATES Research Papers 2010-52, Department of Economics and Business Economics, Aarhus University.
    5. Nikoloulopoulos, Aristidis K. & Karlis, Dimitris, 2008. "Copula model evaluation based on parametric bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3342-3353, March.
    6. Huard, David & Evin, Guillaume & Favre, Anne-Catherine, 2006. "Bayesian copula selection," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 809-822, November.
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    1. Jüri Lember & Joonas Sova, 2021. "Regenerativity of Viterbi Process for Pairwise Markov Models," Journal of Theoretical Probability, Springer, vol. 34(1), pages 1-33, March.
    2. Lember, Jüri & Matzinger, Heinrich & Sova, Joonas & Zucca, Fabio, 2018. "Lower bounds for moments of global scores of pairwise Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 128(5), pages 1678-1710.
    3. Kristi Kuljus & Jüri Lember, 2023. "Pairwise Markov Models and Hybrid Segmentation Approach," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-32, June.
    4. Agboton, Damien Joseph, 2024. "Prévision des Cycles Budgétaires dans les Etats membres de l'Union Economique et Monétaire Ouest Africaine (UEMOA) :Une approche basée sur les Chaînes de Markov [Forecasting Budgetary Cycles in the," MPRA Paper 121821, University Library of Munich, Germany.
    5. Lember, Jüri & Sova, Joonas, 2020. "Existence of infinite Viterbi path for pairwise Markov models," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1388-1425.
    6. Gorynin, Ivan & Derrode, Stéphane & Monfrini, Emmanuel & Pieczynski, Wojciech, 2017. "Fast smoothing in switching approximations of non-linear and non-Gaussian models," Computational Statistics & Data Analysis, Elsevier, vol. 114(C), pages 38-46.
    7. Gangloff, Hugo & Morales, Katherine & Petetin, Yohan, 2023. "Deep parameterizations of pairwise and triplet Markov models for unsupervised classification of sequential data," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    8. Agboton, Damien Joseph, 2024. "Prévision des Cycles Budgétaires dans les Etats membres de l'Union Economique et Monétaire Ouest Africaine (UEMOA) :Une approche basée sur les Chaînes de Markov [Voici la traduction en anglais : Fo," MPRA Paper 121820, University Library of Munich, Germany.

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