Structural Deep Nonnegative Matrix Factorization for community detection

Abstract

Due to the important role in analyzing the topological structure of complex networks, community detection has attracted increasing attention recently. The network embedding methods have shown promising performances in community detection, aiming to learn low-dimensional representations of nodes in networks. Among them, Nonnegative Matrix Factorization (NMF) is proved to be an efficient approach. However, considering that the mapping between the original network and the community membership space contains rather complex hierarchical information, classic shallow-NMF approaches often fail to capture the complex underlying network structure, resulting in sub-optimal network representations. Therefore, how to find a method that is able to effectively capture the complex underlying network structure and preserve the global and local structure is an open and important topic. Inspired by the excellent ability of representation learning in deep autoencoder, we propose a Structural Deep Nonnegative Matrix Factorization model, named SDNMF, for community detection. Similar to deep autoencoder, the proposed multi-layer NMF-based model consists of a decoder module and an encoder module. Further, we propose to exploit the first-order similarity and second-order similarity jointly to preserve the structural information. The first-order similarity characterizes the local network information. Meanwhile, the global network information can be captured and the sparsity problem is alleviated by the second-order similarity. An efficient learning algorithm is developed to optimize the proposed DANMF model, which simultaneously optimizes the first-order and second-order similarity. The effectiveness of the proposed SDNMF is verified by comparing it with several state-of-the-art approaches for community detection on six real-word networks. The comparison is based on three performance metrics. Experimental results demonstrate that the proposed SDNMF can obtain a more accurate community membership matrix compared with the baselines. The convergence analysis is also performed to verify the efficiency of our approach.