A Simulation Study on Clustering Multivariate Time Series Using Kernel Variant Multi-Way Principal Component Analysis

Abstract

Conventional time series modeling may not satisfy the model validity for short-period time series data. In this study, we apply the Kernel Variant Multi-Way Principal Component Analysis (KMPCA) to cluster multivariate time series data which havemultiple dimensions with auto- and cross-correlations. We then check whether this method works well in clustering those data by employing simulation for generalization. Two simulation studies with two different mean structures with nine combinations of auto- and cross-correlations were conducted. The results showed that KMPCA cluster two different mean structure groups over 90% success rates with an appropriate kernel function. We also found that when the mean structures are the same, auto-correlation, the number of temporal points, and the kernel function parameter have the statistically significant effects on clustering performance. The second and third order interaction effects with each of those factors also have effects on clustering success rates. Among the effects of the main factors, the kernel function parameter is the most critical factor to consider for obtaining better performance. A similar error structure may obstruct the clustering performance: strong cross-correlation, weak auto-correlation, and a larger number of temporal points. The paper also discussed some limitations of the KMPCA model and suggested directions for future research that could improve the model.