Uncovering community structures is a fundamental and important problem in analyzing the complex networks. While most of the methods focus on identifying node communities, recent works show the intuitions and advantages of detecting link communities in networks. In this paper, we propose a non-negative matrix factorization (NMF) based method to detect the link community structures. Traditional NMF-based methods mainly consider the adjacency matrix as the representation of network topology, while the adjacency matrix only shows the relationship between immediate neighbor nodes, which does not take the relationship between non-neighbor nodes into consideration. This may greatly reduce the information contained in the network topology, and thus leads to unsatisfactory results. Here, we address this by introducing multi-step similarities using the graph random walk approach so that the similarities between non-neighbor nodes can be captured. Meanwhile, in order to reduce impact caused by self-similarities (similarities between nodes themselves) and increase importance gained from similarities between other different nodes, we add a penalty term to our objective function. Then an efficient optimization scheme for the objective function is derived. Finally, we test the proposed method on both synthetic and real networks. Experimental results demonstrate the effectiveness of the proposed approach.
A Mathematical Comparison of Non‐negative Matrix Factorization‐Related Methods with Practical Implications for the Analysis of Mass Spectrometry Imaging Data