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

Abstract: This paper proposes two new distance measures, called functional Ward's linkages, for functional data clustering that are robust against outliers. Conventional Ward's linkage defines the distance between two clusters as the increase in sum of squared errors (SSE) upon merging, which can be interpreted graphically as an increase in the diameter. Analogously, functional Ward's linkage defines the distance of two clusters as the increased width of the band delimited by the merged clusters. To address the limitations of conventional Ward's linkage in handling outliers and contamination, the proposed linkages focus exclusively on the most central curves by leveraging magnitude-shape outlyingness measures and modified band depth, respectively. Simulations and real-world electroencephalogram (EEG) data analysis demonstrate that the proposed methods outperform other competitive approaches, particularly in the presence of various types of outliers and contamination.