Joint nonnegative matrix factorization and network embedding for graph co-clustering

Abstract

Graph co-clustering aims to simultaneously group heterogeneous vertices in bipartite networks. The current algorithms measure similarity of vertices by either topology or latent feature of networks, which is insufficient to fully characterize the structure of bipartite graphs. To overcome this problem, we propose a novel co-clustering algorithm by jointly integrating network embedding and NMF (called NENMF) based on the fact that graph representation learning implicitly implies matrix factorizations, where multiple views of bipartite networks are integrated for graph co-clustering. Specifically, the equivalence between nonnegative matrix factorization (NMF) graph embedding for co-clustering is proven, which serves as the theoretical foundation for the proposed algorithm. Then, two auxiliary graphs are generated to fully characterize the topology structure of bipartite networks. Finally, NENMF jointly learns low-rank approximation matrices for bipartite networks and network embedding of auxiliary graphs, where network embedding is regularized into objective function of NMF. The main advantage of the proposed algorithm is to boost the accuracy by combining the low-dimensional approximation and graph representation of bipartite networks without increasing time complexity. The experimental results demonstrate that NENMF outperforms state-of-the-art approaches in terms of accuracy.