ROBCPCA: A Robust Multivariate Time Series Clustering Method Based on Common Principal Component Analysis

Multivariate time series (MTS) clustering is crucial for analyzing complex temporal data across various fields. Principal component analysis (PCA)-based methods are popular for their effectiveness in dimensionality reduction, but they are often sensitive to outliers and can not properly handle varying observation lengths. Common principal component analysis (CPCA) addresses the latter limitation by identifying a common set of principal components that capture the shared variance structure across multiple objects. In this paper, we develop a robust MTS clustering method based on CPCA (which we call ROBCPCA), enhancing existing CPCA-based algorithms through the use of an initial grouping mechanism, the detection of richer temporal dependence structures using cross-covariance matrices for several lags, and the introduction of robustness against outliers. Compared to the classical CPCA-based approach, the proposed ROBCPCA method demonstrates improved performance on both non-temporal and temporal, uncontaminated and contaminated data. In addition, ROBCPCA produced good results when applied to multichannel electroencephalogram time series.