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A semi-orthogonal nonnegative matrix tri-factorization algorithm for overlapping community detection

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Abstract

In this paper, we focus on overlapping community detection and propose an efficient semi-orthogonal nonnegative matrix tri-factorization (semi-ONMTF) algorithm. This method factorizes a matrix X into an orthogonal matrix U, a nonnegative matrix B, and a transposed matrix \(U^\mathrm {\scriptscriptstyle T} \). We use the Cayley Transformation to maintain strict orthogonality of U that each iteration stays on the Stiefel Manifold. This algorithm is computationally efficient because the solutions of U and B are simplified into a matrix-wise update algorithm. Applying this method, we detect overlapping communities by the belonging coefficient vector and analyse associations between communities by the unweighted network of communities. We conduct simulations and applications to show that the proposed method has wide applicability. In a real data example, we apply the semi-ONMTF to a stock data set and construct a directed association network of companies. Based on the modularity for directed and overlapping communities, we obtain five overlapping communities, 17 overlapping nodes, and five outlier nodes in the network. We also discuss the associations between communities, providing insights into the overlapping community detection on the stock market network.

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Notes

  1. Arthur J.Gallagher &Corporation, Verisk Analytics Incorporated, Aon Corporation, Equity Residential Company, UDR Incorporated.

  2. Abbott Laboratories, Centene Corporation.

  3. Schlumberger Company Limited, Waste Management Incorporated, DTE Energy Corporation, American Electric Power Company Incorporated, Atmos Energy Corporation, AES Corporation.

  4. Tapestry Incorporated, Hershey Company.

  5. Ball Corporation.

  6. Microsoft Corporation.

  7. AutoZone Incorporated, Eversource Energy, Entergy Corporation, Copart Incorporated, Starbucks Corporation.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 12001557,12371281); the Emerging Interdisciplinary Project, Program for Innovation Research, and the Disciplinary Funds of Central University of Finance and Economics.

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Authors and Affiliations

  1. Department of Biostatistics, School of Public Health, Fudan University, Shanghai, 200433, China

    Zhaoyang Li

  2. School of Statistics and Mathematics, Central University of Finance and Economics, Beijing, 100081, China

    Yuehan Yang

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  1. Zhaoyang Li
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  2. Yuehan Yang
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Correspondence to Yuehan Yang.

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Li, Z., Yang, Y. A semi-orthogonal nonnegative matrix tri-factorization algorithm for overlapping community detection. Stat Papers (2024). https://doi.org/10.1007/s00362-024-01537-1

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