Clustering multivariate functional data in group-specific functional subspaces
- 5 Downloads
With the emergence of numerical sensors in many aspects of everyday life, there is an increasing need in analyzing multivariate functional data. This work focuses on the clustering of such functional data, in order to ease their modeling and understanding. To this end, a novel clustering technique for multivariate functional data is presented. This method is based on a functional latent mixture model which fits the data into group-specific functional subspaces through a multivariate functional principal component analysis. A family of parsimonious models is obtained by constraining model parameters within and between groups. An Expectation Maximization algorithm is proposed for model inference and the choice of hyper-parameters is addressed through model selection. Numerical experiments on simulated datasets highlight the good performance of the proposed methodology compared to existing works. This algorithm is then applied to the analysis of the pollution in French cities for 1 year.
KeywordsMultivariate functional curves Multivariate functional principal component analysis Model-based clustering EM algorithm
Compliance with ethical standards
Conflicts of interest
The authors declare that they have no conflict of interest.
- Hennig C, Coretto P (2007) The noise component in model-based cluster analysis. Springer, Berlin, pp 127–138Google Scholar
- Petersen KB, Pedersen MS (2012) The matrix cookbook. http://www2.imm.dtu.dk/pubdb/p.php?3274, version 20121115
- R Core Team (2017) R: a language and environment for statistical computing. R foundation for statistical computing, Vienna, Austria, https://www.R-project.org/
- Saporta G (1981) Méthodes exploratoires d’analyse de données temporelles. Cahiers du Bureau universitaire de recherche opérationnelle Série Recherche 37–38:7–194Google Scholar