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Title: Functional data clustering with outlier detection Authors:  Julien Jacques - Universite de Lyon (France) [presenting]
Martial Amovin - Univeriste de Lyon (France)
Irene Gannaz - INSA Lyon (France)
Abstract: With the emergence of numerical sensors in many aspects of everyday life, there is an increasing need to analyze high-frequency data, which can be seen as discrete observations of functional data. The focus will be 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 in group-specific functional subspaces through a multivariate functional principal component analysis. In such clustering analysis, the presence of outliers can confuse the notion of cluster. Consequently, a contaminated version of the previous mixture model is proposed. This model both clusters the multivariate functional data into homogeneous groups and detects outliers. The main advantage of this procedure over its competitors is that it does not require us to specify the proportion of outliers. The model inference is performed through an Expectation-Conditional Maximization algorithm, and the BIC criterion is used to select the number of clusters. Numerical experiments on simulated data demonstrate the high performance achieved by the inference algorithm. In particular, the proposed model outperforms competitors. Its application on the real data, which motivated this study allows us to detect abnormal behaviors correctly.