Optimizing modularity with nonnegative matrix factorization

Abstract

Community structure detection is one of the fundamental problems in complex network analysis towards understanding the topology structure and function of the network. Modularity is a criterion to evaluate the quality of community structures, and optimization of this quality function over the possible divisions of a network is a sensitive detection method for community structure. However, the direct application of this method is computationally costly. Nonnegative matrix factorization (NMF) is a widely used method for community detection. In this paper, we show that modularity maximization can be approximately reformulated under the framework of NMF with Frobenius norm, especially when [Formula: see text] is large. A new algorithm for detecting community structure is proposed based on the above finding. The new method is compared with four state-of-the-art methods on both synthetic and real-world networks, showing its higher clustering quality over the existing methods.