Robust fuzzy clustering for high-dimensional multivariate time series with outlier detection

TL;DR

This paper introduces RFCPCA, a novel robust fuzzy clustering method for high-dimensional multivariate time series that effectively handles outliers, temporal dependence, and unequal sequence lengths, improving clustering accuracy and uncertainty estimation.

Contribution

RFCPCA is the first method to simultaneously learn membership-informed subspaces, handle unequal lengths, achieve robustness, and automatically select hyperparameters for MTS clustering.

Findings

RFCPCA improves clustering accuracy on driver drowsiness EEG data.

RFCPCA provides calibrated membership uncertainty and outlier detection.

RFCPCA remains stable under contamination and noise.

Abstract

Fuzzy clustering provides a natural framework for modeling partial memberships, particularly important in multivariate time series (MTS) where state boundaries are often ambiguous. For example, in EEG monitoring of driver alertness, neural activity evolves along a continuum (from unconscious to fully alert, with many intermediate levels of drowsiness) so crisp labels are unrealistic and partial memberships are essential. However, most existing algorithms are developed for static, low-dimensional data and struggle with temporal dependence, unequal sequence lengths, high dimensionality, and contamination by noise or artifacts. To address these challenges, we introduce RFCPCA, a robust fuzzy subspace-clustering method explicitly tailored to MTS that, to the best of our knowledge, is the first of its kind to simultaneously: (i) learn membership-informed subspaces, (ii) accommodate unequal lengths and moderately high dimensions, (iii) achieve robustness through trimming, exponential reweighting, and a dedicated noise cluster, and (iv) automatically select all required hyperparameters. These components enable RFCPCA to capture latent temporal structure, provide calibrated membership uncertainty, and flag series-level outliers while remaining stable under contamination. On driver drowsiness EEG, RFCPCA improves clustering accuracy over related methods and yields a more reliable characterization of uncertainty and outlier structure in MTS.