Model-Based Co-Clustering of Multivariate Functional Data

High dimensional data clustering is an increasingly interesting topic in the statistical analysis of heterogeneous large-scale data. In this paper, we consider the problem of clustering heterogeneous high-dimensional data where the individuals are described by functional variables which exhibit a dynamical longitudinal structure. We address the issue in the framework of model-based co-clustering and propose the functional latent block model (FLBM). The introduced FLBM model allows to simultaneously cluster a sample of multivariate functions into a finite set of blocks, each block being an association of a cluster over individuals and a cluster over functional variables. Furthermore, the homogeneous set within each block is modeled with a dedicated latent process functional regression model which allows its segmentation according to an underlying dynamical structure. The proposed model allows thus to fully exploit the structure of the data, compared to classical latent block clustering models for continuous non functional data, which ignores the functional structure of the observations. The FLBM can therefore serve for simultaneous co-clustering and segmentation of multivariate non-stationary functions. We propose a variational expectation-maximization (EM) algorithm (VEM-FLBM) to monotonically maximize a variational approximation of the observed-data log-likelihood for the unsupervised inference of the FLBM model.