Robust Spectral Fuzzy Clustering of Multivariate Time Series with Applications to Electroencephalogram

Clustering multivariate time series (MTS) is challenging due to non-stationary cross-dependencies, noise contamination, and gradual or overlapping state boundaries. We introduce a robust fuzzy clustering framework in the spectral domain that leverages Kendall's tau-based canonical coherence to extract frequency-specific monotonic relationships across variables. Our method takes advantage of dominant frequency-based cross-regional connectivity patterns to improve clustering accuracy while remaining resilient to outliers, making the approach broadly applicable to noisy, high-dimensional MTS. Each series is projected onto vectors generated from a spectral matrix specifically tailored to capture the underlying fuzzy partitions. Numerical experiments demonstrate the superiority of our framework over existing methods. As a flagship application, we analyze electroencephalogram recordings, where our approach uncovers frequency- and connectivity-specific markers of latent cognitive states such as alertness and drowsiness, revealing discriminative patterns and ambiguous transitions.