Probabilistic $K$-mean with local alignment for clustering and motif discovery in functional data

TL;DR

This paper introduces a probabilistic $K$-mean clustering method with local alignment for functional data, enabling the discovery of recurring local motifs and shapes within curves, with applications across biological and epidemiological datasets.

Contribution

It presents a novel clustering and motif discovery approach that combines functional data analysis, bioinformatics, and fuzzy clustering, allowing for flexible, local shape-based analysis of curves.

Findings

Effective in identifying local motifs in simulated data

Generalizes existing functional data clustering methods

Successfully applied to real biological and epidemiological data

Abstract

We develop a new method to locally cluster curves and discover functional motifs, i.e.~typical ``shapes'' that may recur several times along and across the curves capturing important local characteristics. In order to identify these shared curve portions, our method leverages ideas from functional data analysis (joint clustering and alignment of curves), bioinformatics (local alignment through the extension of high similarity seeds) and fuzzy clustering (curves belonging to more than one cluster, if they contain more than one typical ``shape''). It can employ various dissimilarity measures and incorporate derivatives in the discovery process, thus exploiting complex facets of shapes. We demonstrate the performance of our method with an extensive simulation study, and show how it generalizes other clustering methods for functional data. Finally, we provide real data applications to Berkeley growth data, Italian Covid-19 death curves and ``Omics'' data related to mutagenesis.