Adaptive State Continuity-Based Sparse Inverse Covariance Clustering for Multivariate Time Series

Compared with univariate time series clustering, multivariate time series (MTS) clustering has become a challenging research topic on the data mining of time series. In this paper, a novel model-based approach Adaptive State Continuity-Based Sparse Inverse Covariance Clustering (ASCSICC) is proposed for MTS clustering. Specifically, the state continuity is introduced to make the traditional Gaussian mixture model (GMM) applicable to time series clustering. To prevent overfitting, the alternating direction method of multipliers (ADMM) is applied to optimize the parameter of GMM inverse covariance. In addition, the proposed approach simultaneously segments and clusters the time series. Technically, first, the adaptive state continuity is estimated based on the distance similarity of adjacent time series data. Then, a dynamic programming algorithm of cluster assignment by adaptive state continuity is taken as the E-step, and the ADMM for solving sparse inverse covariance is taken as the M-step. E-step and M-step are combined into an Expectation-Maximization (EM) algorithm to conduct the clustering process. Finally, we show the effectiveness of the proposed approach by comparing the ASC-SICC with several state-of-the-art approaches in experiments on two datasets from real applications.