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Int. J. Environ. Res. Public Health 2014, 11(3), 2741-2763; doi:10.3390/ijerph110302741

Clustering Multivariate Time Series Using Hidden Markov Models

1,2,* , 2
1 School of Computing, Engineering and Mathematics, University of Western Sydney, Campbelltown, NSW 2751 , Australia 2 Centre for Health Research, University of Western Sydney, Campbelltown, NSW 2751 , Australia
* Author to whom correspondence should be addressed.
Received: 4 December 2013 / Revised: 6 February 2014 / Accepted: 19 February 2014 / Published: 6 March 2014
(This article belongs to the Special Issue Public Health Informatics)
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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.
Keywords: health trajectory; HMM; clustering health trajectory; HMM; clustering
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Ghassempour, S.; Girosi, F.; Maeder, A. Clustering Multivariate Time Series Using Hidden Markov Models. Int. J. Environ. Res. Public Health 2014, 11, 2741-2763.

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