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

TL;DR

This paper introduces FCPCA, a fuzzy clustering method for high-dimensional multivariate time series that leverages common principal component analysis to improve efficiency and accuracy in complex, overlapping data scenarios.

Contribution

The paper proposes a novel fuzzy clustering technique based on common principal component analysis, effectively handling high-dimensional multivariate time series with varying lengths.

Findings

Outperforms existing clustering methods in numerical experiments.

Efficiently manages high-dimensional multivariate time series.

Demonstrates applicability to brain signal data in driving simulations.

Abstract

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.