Multikernel Clustering via Non-Negative Matrix Factorization Tailored Graph Tensor Over Distributed Networks

Next-generation wireless networks are witnessing an increasing number of clustering applications, and produce a large amount of non-linear and unlabeled data. In some degree, single kernel methods face the challenging problem of kernel choice. To overcome this problem for non-linear data clustering, multiple kernel graph-based clustering (MKGC) has attracted intense attention in recent years. However, existing MKGC methods suffer from two common problems: (1) they mainly aim to learn a consensus kernel from multiple candidate kernels, slight affinity graph learning, such that cannot fully exploit the underlying graph structure of non-linear data; (2) they disregard the high-order correlations between all base kernels, which cannot fully capture the consistent and complementary information of all kernels. In this paper, we propose a novel non-negative matrix factorization (NMF) tailored graph tensor MKGC method for non-linear data clustering, namely TMKGC. Specifically, TMKGC integrates NMF and graph learning together in kernel space so as to learn multiple candidate affinity graphs. Afterwards, the high-order structure information of all candidate graphs is captured in a 3-order tensor kernel space by introducing tensor singular value decomposition based tensor nuclear norm, such that an optimal affinity graph can be obtained subsequently. Based on the alternating direction method of multipliers, the effective local and distributed solvers are elaborated to solve the proposed objective function. Extensive experiments have demonstrated the superiority of TMKGC compared to the state-of-the-art MKGC methods.