Abstract
Recently, the use of finite mixture models to cluster three-way data sets has become popular. A natural extension of mixture models to model time dependent data is represented by Hidden Markov models (HMMs) (Cappé et al. 2005); thus, a direct generalization in the finite mixture context for solving the problem of mixing in the time dimension may be given adapting HMMs to three way data clustering. We discuss the issue of longitudinal multivariate data allowing for both time and local dependence.
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References
Basford, K. E., & McLachlan, G. J. (1985). The mixture method for clustering applies to three-way data. Journal of Classification, 2, 109–125.
Cappé, O., Moulines, E., & Rydén, T. (2005). Inference in hidden Markov models. Springer series in statistics. Berlin: Springer.
Carroll, J. D., & Arabie, P. (1980). Multidimensional scaling. Annaual Review of Psychology, 31, 607–649.
Everitt, B. S. (1993). Cluster analysis. London: Edward Arnold.
Giudici, P., Rydén, T., & Vandekerkhove, P. (2000). Likelihood-ratio tests for hidden Markov models. Biometrics, 56, 742–747.
Hunt, L. A., & Basford, K. E. (2001). Fittinga a mixture model to three-mode three-way data with missing information. Journal of Classification, 18, 209–226.
McLachlan, G. J., & Basford, K. E. (1988). Mixture models: Inference and applications to clustering. New York: Marcel Dekker.
McLachlan, G. J., & Peel, D. (2000a). Finite mixture models. New York: Wiley.
McLachlan, G. J., & Peel, D. (2000b). Mixture of factor analyzers. In P. Langley (Ed.), Proceedings of the seventeenth international conference on Machine Learnings. San Francisco: Morgan Kauffmann.
Meulders, M., De Boeck, P., Kuppens, P., & Van Mechelen, I. (2002). Constrained latent class analysis of three-way three-mode data. Journal of Classification, 19, 277–302.
Pearl, J. (1988). Probabilistic reasoning in intelligent systems: Networks of plausible inference. San Matteo, CA: Morgan Kauffmann.
Rijmen, F., Vansteelandt, K., & De Boeck, P. (2008). Latent class models for diary method data: Parameter estimation by local computations. Psychometrika, 73(2), 167–182.
Vermunt, J. K. (2007). A hierarchical mixture model for clustering three-way data sets. Computational Statistics and Data Analysis, 51, 5368–5376.
Vermunt, J. K., Tran, B., & Magidson, J. (2008). Latent class models in longitudinal research. In S. Menard (Ed.), Handbook of longitudinal research: Design, measurement, and analysis (pp. 373–385). Burlington, MA: Elsevier.
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Alfò, M., Maruotti, A. (2010). A Hierarchical Model for Time Dependent Multivariate Longitudinal Data. In: Palumbo, F., Lauro, C., Greenacre, M. (eds) Data Analysis and Classification. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03739-9_31
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DOI: https://doi.org/10.1007/978-3-642-03739-9_31
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