A Temporal Proximity Regularized Clusterwise Vector Autoregressive Method for Multivariate Time Series Clustering

Repeated patterns often appear in time series data. Discovering these patterns is challenging because time series need to be segmented and clustered simultaneously. Clusterwise regression is a useful approach that enables the segmentation and clustering of the time series simultaneously. In this paper, we consider the multivariate time series generated by vector autoregressive (VAR) models. By introducing a weight function matrix and using the clusterwise VAR method, we propose a minimization model that consists of the sum of weighted squared regression errors and the total variation of the weight function matrix. The total variation of the weight function matrix enforces temporal proximity on the clustering results. Based on alternating minimization, we design an expectation maximization (EM)-like method to estimate the weights and the VAR regression parameters alternatively. Experimental results for both synthetic and real-world time series show the effectiveness of the proposed method and its competitiveness compared with existing methods.