Exploring Dynamic Structures in Matrix-Valued Time Series via Principal Component Analysis
Lynne Billard, Ahlame Douzal-Chouakria, S. Yaser Samadi
Abstract
Time-series data are widespread and have inspired numerous research works in machine learning and data analysis fields for the classification and clustering of temporal data. While there are several clustering methods for univariate time series and a few for multivariate series, most methods are based on distance and/or dissimilarity measures that do not fully utilize the time-dependency information inherent to time-series data. To highlight the main dynamic structure of a set of multivariate time series, this study extends the use of standard variance–covariance matrices in principal component analysis to cross-autocorrelation matrices at time lags k=1,2,…. This results in “principal component time series”. Simulations and a sign language dataset are used to demonstrate the effectiveness of the proposed method and its benefits in exploring the main structural features of multiple time series.