Clustering Multivariate Time Series Data a 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.