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Symmetric Nonnegative Matrix Factorization-Based Community Detection Models and Their Convergence Analysis.

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    Summary
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    This study enhances community detection accuracy by adjusting the scaling factor in nonnegative matrix factorization (SNMF) learning schemes. Novel methods improve SNMF models, leading to significant gains in identifying social network communities.

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    Area of Science:

    • Social Network Analysis
    • Machine Learning
    • Data Mining

    Background:

    • Community detection is crucial in social network analysis.
    • Symmetric and nonnegative matrix factorization (SNMF) with nonnegative multiplicative update (NMU) schemes are common methods.
    • Existing research often overlooks the impact of learning schemes on SNMF accuracy.

    Purpose of the Study:

    • To improve community detection accuracy by exploring the relationship between SNMF detection accuracy and NMU scaling factors.
    • To introduce novel SNMF-based community detectors by adjusting the NMU scheme's scaling factor.

    Main Methods:

    • Implemented linear and nonlinear strategies to adjust the NMU scheme's scaling factor.
    • Developed four new SNMF-based community detectors by applying adjusted NMU schemes to SNMF and graph-regularized SNMF models.
    • Conducted theoretical analyses to ensure model convergence and nonincreasing loss functions.

    Main Results:

    • Theoretical analysis confirmed that proposed schemes ensure nonincreasing loss functions and convergence to stationary points.
    • Empirical studies on eight social networks demonstrated significant accuracy improvements in community detection.
    • The novel detectors outperformed existing state-of-the-art community detection methods.

    Conclusions:

    • Adjusting the NMU scheme's scaling factor is an effective strategy for enhancing SNMF-based community detection.
    • The proposed methods offer a promising approach for accurate and robust community detection in social networks.
    • This work opens new avenues for research in optimizing learning schemes for matrix factorization-based network analysis.