Learning Wasserstein Distance-Based Gaussian Graphical Model for Multivariate Time Series Classification

Abstract

Multivariate time series classification occupies an important position in time series data mining tasks and has been applied in many fields. However, due to the statistical coupling between different variables of Multivariate Time Series (MTS) data, traditional classification methods cannot find complex dependencies between different variables, so most existing methods perform not well in MTS classification with many variables. Thus, in this paper, a novel model-based classification method is proposed, called Wasserstein Distance-based Gaussian Graphical Model classification (WD-GGMC), which converts the original MTS data into two important parameters of the Gaussian Graphical Model: the sparse inverse covariance matrix and the mean vector. Among them, the former is the most important parameter, which contains the information between variables and solved by Alternating Direction Method of Multipliers (ADMM). Furthermore, the Wasserstein Distance is applied as the similarity measure for different subsequences because it can measure the similarity between different distributions. Experimental results on the eight public MTS datasets demonstrate the effectiveness of the proposed method in MTS classification.