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Title: A clustering procedure for multivariate functional data based on a Mahalanobis type distance Authors:  Andrea Martino - Politecnico di Milano (Italy) [presenting]
Andrea Ghiglietti - Universita degli Studi di Milano (Italy)
Francesca Ieva - Politecnico di Milano (Italy)
Anna Maria Paganoni - MOX-Politecnico di Milano (Italy)
Abstract: Clustering functional data can be a difficult task, because of the dimensionality of the space the data belongs to. To address the difficulties arising from the study of functional data, several approaches have been proposed along the years. A standard procedure consists in reducing the infinite dimensional problem to a finite one, approximating the data with elements from a finite dimensional space. Since this approach may lead to losing some important information about the data, we propose a novel clustering technique for samples of multivariate functions. The method consists in a $k$-means algorithm in which the distance between the curves is measured using a metric that generalizes the Mahalanobis distance in Hilbert spaces. This procedure is able to consider the correlation and the variability along all the components of the functional data. The proposed algorithm is tested in a simulation study and compared with the $k$-means based on other distances commonly used for clustering multivariate functional data. Finally, the method is applied to two case studies, concerning growth curves and ECG signals.