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Clustering Multivariate Time Series Using Hidden Markov Models

Author

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  • Shima Ghassempour

    (School of Computing, Engineering and Mathematics, University of Western Sydney, Campbelltown, NSW 2751 , Australia
    Centre for Health Research, University of Western Sydney, Campbelltown, NSW 2751 , Australia)

  • Federico Girosi

    (Centre for Health Research, University of Western Sydney, Campbelltown, NSW 2751 , Australia)

  • Anthony Maeder

    (School of Computing, Engineering and Mathematics, University of Western Sydney, Campbelltown, NSW 2751 , Australia
    Centre for Health Research, University of Western Sydney, Campbelltown, NSW 2751 , Australia)

Abstract

In this paper we describe an algorithm for clustering multivariate time series with variables taking both categorical and continuous values. Time series of this type are frequent in health care, where they represent the health trajectories of individuals. The problem is challenging because categorical variables make it difficult to define a meaningful distance between trajectories. We propose an approach based on Hidden Markov Models (HMMs), where we first map each trajectory into an HMM, then define a suitable distance between HMMs and finally proceed to cluster the HMMs with a method based on a distance matrix. We test our approach on a simulated, but realistic, data set of 1,255 trajectories of individuals of age 45 and over, on a synthetic validation set with known clustering structure, and on a smaller set of 268 trajectories extracted from the longitudinal Health and Retirement Survey. The proposed method can be implemented quite simply using standard packages in R and Matlab and may be a good candidate for solving the difficult problem of clustering multivariate time series with categorical variables using tools that do not require advanced statistic knowledge, and therefore are accessible to a wide range of researchers.

Suggested Citation

  • Shima Ghassempour & Federico Girosi & Anthony Maeder, 2014. "Clustering Multivariate Time Series Using Hidden Markov Models," IJERPH, MDPI, vol. 11(3), pages 1-23, March.
    • Handle: RePEc:gam:jijerp:v:11:y:2014:i:3:p:2741-2763:d:33778
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    References listed on IDEAS

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    1. Jeng‐Min Chiou & Pai‐Ling Li, 2007. "Functional clustering and identifying substructures of longitudinal data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 679-699, September.
    2. Konrad Banachewicz & André Lucas & Aad van der Vaart, 2008. "Modelling Portfolio Defaults Using Hidden Markov Models with Covariates," Econometrics Journal, Royal Economic Society, vol. 11(1), pages 155-171, March.
    3. Visser, Ingmar & Speekenbrink, Maarten, 2010. "depmixS4: An R Package for Hidden Markov Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 36(i07).
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