Phase and Amplitude-Based Clustering for Functional Data

Abstract

Functional data that are not perfectly aligned in the sense of not showing peaks and valleys at the precise same locations possess phase variation. This is commonly addressed by preprocessing the data via a warping procedure. As opposed to treating phase variation as a nuisance effect, we explicitly recognize it as a possible important source of information for clustering. We illustrate how results from a multiresolution warping procedure can be used for clustering. This approach allows to address detailed questions to find local clusters that differ in phase, or clusters that differ in amplitude, or both simultaneous.

Keywords: Functional data, clustering, phase variation, amplitude variation, warping