Co-clustering of time-dependent data via Shape Invariant Model

Multivariate time-dependent data, where multiple features are observed over time for a set of individuals, are increasingly widespread in many application domains. To model these data we need to account for relations among both time instants and variables and, at the same time, for subjects heterogeneity. We propose a new co-clustering methodology for clustering individuals and variables simultaneously that is designed to handle both functional and longitudinal data. Our approach borrows some concepts from the curve registration framework by embedding the Shape Invariant Model in the Latent Block Model, estimated via a suitable modification of the SEM-Gibbs algorithm. The resulting procedure allows for several user-defined specifications of the notion of cluster that could be chosen on substantive grounds and provides parsimonious summaries of complex longitudinal or functional data by partitioning data matrices into homogeneous blocks.