Optimizing modularity with nonnegative matrix factorization

Zhenhai Chang, Zhong-Yuan Zhang, Huimin Cheng, Chao Yan and Xianjun Yin
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Zhenhai Chang: School of Mathematics and Statistics, Tianshui Normal University, No. 60, Lian-Ting Road Gansu, P. R. China
Zhong-Yuan Zhang: School of Statistics and Mathematics, Central University of Finance and Economics, No. 39, Xue-Yuan South Road, Beijing, P. R. China
Huimin Cheng: School of Statistics and Mathematics, Central University of Finance and Economics, No. 39, Xue-Yuan South Road, Beijing, P. R. China
Chao Yan: School of Statistics and Mathematics, Central University of Finance and Economics, No. 39, Xue-Yuan South Road, Beijing, P. R. China
Xianjun Yin: School of Statistics and Mathematics, Central University of Finance and Economics, No. 39, Xue-Yuan South Road, Beijing, P. R. China

International Journal of Modern Physics C (IJMPC), 2021, vol. 32, issue 11, 1-18

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 n 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.

Keywords: Complex network; community structure; modularity; nonnegative matrix factorization (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0129183121501424

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