End-to-end Modularity-based Community Co-partition in Bipartite Networks

Resolving community structure in networks is of significant benefit for both scientific inquiries and practical applications. Recently, deep neural networks have demonstrated excellent performance on various graph mining tasks, including community detection. However, there are still some challenges that are urgent to be addressed. First, being frequently formulated in an unsupervised setting, community detection has been proved to be more resistant to the advantages of end-to-end learning. Many deep methods carry out clustering algorithms after the acquisition of node representations. Second, very few studies consider the heterogeneity of a large number of real-world networks in end-to-end community detection. For instance, the building blocks of general heterogeneous networks are the bipartite model, which is a ubiquitous structure where two types of nodes co-exist. In view of these challenges, we study the end-to-end community co-partition of two types of nodes in bipartite networks. Specifically, we extend both spectral and spatial graph convolution operators to bipartite structures for node feature encoding. Then we formulate a novel loss function with a modularity-based objective, as well as two collapsed regularizations for producing more informative community assignment matrices. Co-partitions of nodes can be directly achieved by optimization with stochastic gradient descent under the proposed framework. Comprehensive empirical analysis, compared with various types of classic and deep methods, demonstrates the efficacy and the scalability of the proposed method.