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Title: An agglomerative hierarchical local clustering algorithm for functional motif discovery Authors:  Jacopo Di Iorio - Penn State University (United States) [presenting]
Marzia Cremona - Université Laval (Canada)
Francesca Chiaromonte - The Pennsylvania State University (United States)
Abstract: Two of the new issues that functional data analysis is recently dealing with are the identification of local clusters, i.e., clusters defined only on a portion of the domain, and the discovery of functional motifs, i.e. typical ``shapes'' that may be repeated - scaled or not along the y axis - multiple times within each curve, or across several curves belonging to the same set. We propose a new algorithm to solve these problems, leveraging ideas from multivariate and functional data analysis - especially curve alignment, functional clustering and biclustering. funBIalign is a multi-step algorithm based on agglomerative hierarchical clustering with complete linkage, which is able to discover local clusters and/or functional motifs both in a set of misaligned curves or in a single curve (e.g., time series). Differently from other alternatives, funBIalign is able to detect both shifting and scaling functional patterns thanks to the use of metrics based on functional and adjusted versions of widely used multivariate biclustering validation measures such as the mean squared residue score (or H-score) and the virtual error. Simulations and case studies results are shown to assess the goodness of the methodology proposed.