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Research on clustering based on orthogonal non-negative matrix factorization under noisy conditions

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Abstract

An orthogonal non-negative matrix factorization model based on graph regularization under noisy conditions (NGONMF) is proposed in this paper. The main result of this paper lies in introducing a noise matrix in the non-negative decomposition process and iteratively updating the noise in the algorithm, and its purpose is to capture the sparsity damage caused by noise or outliers, while using graph regularization terms and orthogonal penalty terms to consider the graph structure information of the data, improving the sparsity of low dimensional representations. At the same time, we have developed corresponding iterative update algorithms and theoretically proved their convergence, which is one of the innovations of this paper. Extensive clustering experiments have been conducted on multiple datasets under the interference of Gaussian noise, non Gaussian noise, and anomalous destruction. The real and reliable empirical results confirm the robustness and competitive advantage of the proposed algorithm. This is another innovation. Therefore, the proposed model can effectively reduce the adverse effects of noise or outliers and obtain robust decomposition results.

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Data Availability

All experimental data have no ethical or moral issues, and all data have been downloaded from public websites and labeled with URLs for inspection.

Notes

  1. https://www.cl.cam.ac.uk/research/dtg/attarchive/facedatabase.html

  2. http://images.ee.umist.ac.uk/danny/database.html

  3. http://www.anefian.com/research/face_reco.htm

  4. https://yann.lecun.com/exdb/mnist/

  5. http://www.cs.toronto.edu/~kriz/cifar.html

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Acknowledgements

The authors would like to thank the editors and anonymous referees for carefully reading the manuscript, giving valuable comments and suggestions to improve the results as well as the exposition of the paper.

Funding

The author of Junjian Zhao is partially supported by the Natural Science Foundations of Tianjin City, China (Grant Nos. 24JCYBJC00430, 18JCYBJC16300 and 22JCYBJC01470).

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, TianGong University, Tianjin, 300387, People’s Republic of China

    Junjian Zhao, Jiaxi Cai & Yasong Chen

Authors
  1. Junjian Zhao
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  2. Jiaxi Cai
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  3. Yasong Chen
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Contributions

All authors contributed equally to this manuscript. Y.C. primarily generated writing original manuscript, methodology, software program. J.C. primarily generated original model, formal analysis, software program. J.Z. mainly contributed to formal analysis, software program, writing and revising the manuscript. All authors read and approved the final manuscript.

Corresponding authors

Correspondence to Junjian Zhao or Yasong Chen.

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Zhao, J., Cai, J. & Chen, Y. Research on clustering based on orthogonal non-negative matrix factorization under noisy conditions. Optim Eng (2025). https://doi.org/10.1007/s11081-025-10030-z

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