Multivariate Time Series Clustering with State Space Dynamical Modeling and Grassmann Manifold Learning: A Systematic Review on Human Motion Data

Abstract

Multivariate time series (MTS) clustering has been an essential research topic in various domains over the past decades. However, inherent properties of MTS data—namely, temporal dynamics and inter-variable correlations—make MTS clustering challenging. These challenges can be addressed in Grassmann manifold learning combined with state-space dynamical modeling, which allows existing clustering techniques to be applicable using similarity measures defined on MTS data. In this paper, we present a systematic overview of Grassmann MTS clustering from a geometrical perspective, categorizing the methods into three approaches: (i) extrinsic, (ii) intrinsic, and (iii) semi-intrinsic. Consequently, we outline 11 methods for Grassmann clustering and demonstrate their effectiveness through a comparative experimental study using human motion gesture-derived MTS data.

Keywords

• clustering
• geodesic distance
• Grassmann manifold
• Karcher mean
• kernel method
• multivariate time series