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Robust Exponential Graph Regularization Non-Negative Matrix Factorization Technology for Feature Extraction

Author

Listed:
  • Minghua Wan

    (School of Computer Science (School of Intelligent Auditing), Nanjing Audit University, Nanjing 211815, China
    Jiangsu Key Lab of Image and Video Understanding for Social Security, and Key Lab of Intelligent Perception and Systems for High-Dimensional Information of Ministry of Education, Nanjing University of Science and Technology, Nanjing 210094, China
    Jiangsu Modern Intelligent Audit Integrated Application Technology Engineering Research Center, Nanjing Audit University, Nanjing 211815, China
    Key Laboratory of Intelligent Information Processing, Nanjing Xiaozhuang University, Nanjing 211171, China)

  • Mingxiu Cai

    (School of Computer Science (School of Intelligent Auditing), Nanjing Audit University, Nanjing 211815, China
    Jiangsu Modern Intelligent Audit Integrated Application Technology Engineering Research Center, Nanjing Audit University, Nanjing 211815, China)

  • Guowei Yang

    (School of Computer Science (School of Intelligent Auditing), Nanjing Audit University, Nanjing 211815, China
    Jiangsu Modern Intelligent Audit Integrated Application Technology Engineering Research Center, Nanjing Audit University, Nanjing 211815, China
    School of Electronic Information, Qingdao University, Qingdao 266071, China)

Abstract

Graph regularized non-negative matrix factorization (GNMF) is widely used in feature extraction. In the process of dimensionality reduction, GNMF can retain the internal manifold structure of data by adding a regularizer to non-negative matrix factorization (NMF). Because Ga NMF regularizer is implemented by local preserving projections (LPP), there are small sample size problems (SSS). In view of the above problems, a new algorithm named robust exponential graph regularized non-negative matrix factorization (REGNMF) is proposed in this paper. By adding a matrix exponent to the regularizer of GNMF, the possible existing singular matrix will change into a non-singular matrix. This model successfully solves the problems in the above algorithm. For the optimization problem of the REGNMF algorithm, we use a multiplicative non-negative updating rule to iteratively solve the REGNMF method. Finally, this method is applied to AR, COIL database, Yale noise set, and AR occlusion dataset for performance test, and the experimental results are compared with some existing methods. The results indicate that the proposed method is more significant.

Suggested Citation

  • Minghua Wan & Mingxiu Cai & Guowei Yang, 2023. "Robust Exponential Graph Regularization Non-Negative Matrix Factorization Technology for Feature Extraction," Mathematics, MDPI, vol. 11(7), pages 1-14, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:7:p:1716-:d:1115040
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    References listed on IDEAS

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    1. Ivanovs, Jevgenijs & Boxma, Onno & Mandjes, Michel, 2010. "Singularities of the matrix exponent of a Markov additive process with one-sided jumps," Stochastic Processes and their Applications, Elsevier, vol. 120(9), pages 1776-1794, August.
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