funLOCI: A Local Clustering Algorithm for Functional Data

Abstract

Nowadays, an increasing number of problems involve data with one infinite continuous dimension known as functional data. In this paper, we introduce the funLOCI algorithm, which enables the identification of functional local clusters or functional loci, i.e, subsets or groups of curves that exhibit similar behavior across the same continuous subset of the domain. The definition of functional local clusters incorporates ideas from multivariate and functional clustering and biclustering and is based on an additive model that takes into account the shape of the curves. funLOCI is a multi-step algorithm that relies on hierarchical clustering and a functional version of the mean squared residue score to identify and validate candidate loci. Subsequently, all the results are collected and ordered in a post-processing step. To evaluate our algorithm performance, we conduct extensive simulations and compare it with other recently proposed algorithms in the literature. Furthermore, we apply funLOCI to a real-data case regarding inner carotid arteries.