Tensor Decomposition for Multilayer Networks Clustering

Clustering on multilayer networks has been shown to be a promising approach to enhance the accuracy. Various multilayer networks clustering algorithms assume all networks derive from a latent clustering structure, and jointly learn the compatible and complementary information from different networks to excavate one shared underlying structure. However, such an assumption is in conflict with many emerging real-life applications due to the existence of noisy/irrelevant networks. To address this issue, we propose Centroid-based Multilayer Network Clustering (CMNC), a novel approach which can divide irrelevant relationships into different network groups and uncover the cluster structure in each group simultaneously. The multilayer networks is represented within a unified tensor framework for simultaneously capturing multiple types of relationships between a set of entities. By imposing the rank-(L-r;L-r; 1) block term decomposition with nonnegativity, we are able to have well interpretations on the multiple clustering results based on graph cut theory. Numerically, we transform this tensor decomposition problem to an unconstrained optimization, thus can solve it efficiently under the nonlinear least squares (NLS) framework. Extensive experimental results on synthetic and real-world datasets show the effectiveness and robustness of our method against noise and irrelevant data.