Robust Functional Ward's Linkages with Applications in EEG data Clustering

Abstract

This paper proposes two robust linkage criteria, termed functional Ward-type linkages, for hierarchical clustering of grouped functional data, where each clustering unit is represented by a set of curves. Ordinary Ward\textquotesingle s linkage defines the cluster dissimilarity between two clusters as the increase in the sum of squared errors (SSE) upon merging, which can be interpreted graphically as an increase in within-cluster dispersion. Motivated by this principle, the proposed linkages measure the weighted increase in band width required to construct a common band containing the central representatives of two candidate clusters. To reduce the influence of outliers, the central curves are selected separately within each cluster by leveraging the magnitude-shape outlyingness measure and the modified band depth, respectively. Simulations and two EEG data analyses demonstrate the robustness and competitive performance of the proposed methods under a range of contamination settings.