Sparse clustering of functional data

Abstract

We consider the problem of clustering functional data while jointly selecting the most relevant features for classification. Functional sparse clustering is here analytically defined as a variational problem with a hard thresholding constraint ensuring the sparsity of the solution. First, a unique solution to sparse clustering with hard thresholding in finite dimensions is proved to exist. Then, the infinite-dimensional generalization is given and proved to have a unique solution under reasonable assumptions. Both the multivariate and the functional versions of sparse clustering with hard thresholding exhibit improvements on other standard and sparse clustering strategies on simulated data. A real functional data application is also shown.