ABSTRACT
This chapter introduces methods for clustering functional data with emphasis on the interface between functional data smoothing and existing methods for clustering. Standard clustering tools including K-means, hierarchical clustering, and distributional clustering are considered on both the observed and smoothed data. Methods introduced for smoothing in Chapters 2 and 3 can be directly used on the observed functions, and then any method for clustering can be used on the resulting functions or scores (projections on prespecified or data-driven bases). Results indicate that when data is observed with moderate to significant noise, clustering after smoothing performs better than clustering before smoothing. Moreover, clustering of sparse functional data cannot be conducted, at least in its traditional form, without smoothing the data first. Methods are illustrated using the COVID-19 US mortality data set and the CD4 count data set.
