Clustering Multivariate Time Series Data via Multi-Nonnegative Matrix Factorization in Multi-Relational Networks

In multivariate time series clustering, the inter-similarity across distinct variates and the intra-similarity within each variate pose analytical challenges. Here, we propose a novel multivariate time series clustering method using multi-nonnegative matrix factorization (MNMF) in multi-relational networks. Specifically, a set of multivariate time series is transformed from the time–space domain into a multi-relational network in the topological domain. Then, the multi-relational network is factorized to identify time series clusters. The transformation from the time–space domain to the topological domain benefits from the ability of networks to characterize both the local and global relationships between the nodes, and MNMF incorporates inter-similarity across distinct variates into clustering. Furthermore, to trace the evolutionary trends of clusters, time series is transformed into a dynamic multi-relational network, thereby extending MNMF to dynamic MNMF. Extensive experiments illustrate the superiority of our approach compared with the current state-of-the-art algorithms.