Nonparametric Hierarchical Clustering of Functional Data

In this paper, we deal with the problem of curves clustering. We propose a nonparametric method which partitions the curves into clusters and discretizes the dimensions of the curve points into intervals. The cross-product of these partitions forms a data-grid which is obtained using a Bayesian model selection approach while making no assumptions regarding the curves. Finally, a post-processing technique, aiming at reducing the number of clusters in order to improve the interpretability of the clustering, is proposed. It consists in optimally merging the clusters step by step, which corresponds to an agglomerative hierarchical classification whose dissimilarity measure is the variation of the criterion. Interestingly this measure is none other than the sum of the Kullback-Leibler divergences between clusters distributions before and after the merges. The practical interest of the approach for functional data exploratory analysis is presented and compared with an alternative approach on an artificial and a real world data set.