Robust Functional Ward's Linkages With Applications in EEG Data Clustering

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'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.