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

TL;DR

This paper introduces robust functional Ward's linkages for clustering functional data, especially EEG signals, that effectively handle outliers by focusing on central curves, improving clustering accuracy under contamination.

Contribution

The paper develops two novel distance measures for functional clustering that enhance robustness against outliers using magnitude-shape outlyingness and modified band depth.

Findings

Outperforms existing methods in simulations with outliers.

Effectively clusters EEG data with contamination.

Robustness verified through real-world EEG analysis.

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.