Sequential Clustering for Functional Data

Abstract: This paper presents SeqClusFD, a top-down sequential clustering method for functional data. The clustering algorithm extracts the splitting information either from trajectories, first or second derivatives. Initial partition is based on gap statistic that provides local information to identify the instant with more clustering evidence in trajectories or derivatives. Then functional boxplots allow reconsidering overall allocation and each observation is finally assigned to the cluster where it spends most of the time within whiskers. These local and global searches are repeated recursively until there is no evidence of clustering at any time on trajectories or first and second derivatives. SeqClusFD simultaneously estimates the number of groups and provides data allocation. It also provides valuable information about the most important features that determine cluster structure. Computational aspects have been analyzed and the new method is tested on synthetic and real data sets.