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

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.

FCPCA: Fuzzy clustering of high-dimensional time series based on common principal component analysis

Clustering multivariate time series data is a crucial task in many domains, as it enables the identification of meaningful patterns and groups in time-evolving data. Traditional approaches, such as crisp clustering, rely on the assumption that clusters are sufficiently separated with little overlap. However, real-world data often defy this assumption, exhibiting overlapping distributions or overlapping clouds of points and blurred boundaries between clusters. Fuzzy clustering offers a compelling alternative by allowing partial membership in multiple clusters, making it well-suited for these ambiguous scenarios. Despite its advantages, current fuzzy clustering methods primarily focus on univariate time series, and for multivariate cases, even datasets of moderate dimensionality become computationally prohibitive. This challenge is further exacerbated when dealing with time series of varying lengths, leaving a clear gap in addressing the complexities of modern datasets. This work introduces a novel fuzzy clustering approach based on common principal component analysis to address the aforementioned shortcomings. Our method has the advantage of efficiently handling high-dimensional multivariate time series by reducing dimensionality while preserving critical temporal features. Extensive numerical results show that our proposed clustering method outperforms several existing approaches in the literature. An interesting application involving brain signals from different drivers recorded from a simulated driving experiment illustrates the potential of the approach.