Title: funBIalign: A hierarchical algorithm for functional motif discovery Authors:  Marzia Cremona - Universite Laval (Canada) [presenting]
Jacopo Di Iorio - Emory University (United States)
Francesca Chiaromonte - The Pennsylvania State University (United States)
Abstract: Motif discovery is gaining increasing attention in the domain of functional data analysis. Functional motifs are typical shapes or patterns that recur multiple times in different portions of a single curve and/or in misaligned portions of multiple curves. We define functional motifs using an additive model and propose funBIalign for their discovery and evaluation. Inspired by clustering and biclustering techniques, funBIalign is a multi-step procedure that uses agglomerative hierarchical clustering with complete linkage and a functional distance based on mean squared residue scores to discover functional motifs, both in a single curve (e.g., time series) and in a set of curves. We assess its performance and compare it to other recent methods through extensive simulations. Moreover, we use funBIalign for discovering motifs in two real-data case studies; one on food price inflation and one on temperature changes. Finally, we introduce another definition of motifs based on a multiplicative model that includes the more challenging scenario of motifs composed of portions sharing the same shape but having different amplitudes, and we extend funBIalign to discover amplitude-invariant functional motifs.