Abstract:
Functional data, when represented as curves or surfaces, are characterized by shapes. While harder to analyze than typical multivariate data, the information in shapes is rich. In this talk, we introduce two new biclustering-inspired FDA methods which exploit this information to perform functional motif discovery and functional triclustering. Functional motif discovery aims at identifying functional motifs, i.e., typical “shapes” or “patterns” repeated multiple times in different portions of a single curves and/or in misaligned portions of several curves. Functional triclustering collects functional triclusters, i.e., data cubes defined by a subset of observations which exhibit similar behavior across a subset of attributes and a subset of contexts. Both proposed methods rely on additive models inspired by the multivariate biclustering (and triclustering) literature. Moreover, the methods employ two functional versions of the mean squared residue score (fMSR) to identify and validate their results. Method performance is assessed through simulations and real-data case studies.