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Orthogonal Graph Regularized Nonnegative Matrix Factorization for Image Clustering

  • Jinrong He
  • Dongjian HeEmail author
  • Bin Liu
  • Wenfa Wang
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 1120)

Abstract

Since high-dimensional data can be represented as vectors or matrices, matrix factorization is a common useful data modeling technique for high-dimensional feature representation, which has been widely applied in feature extraction, image processing and text clustering. Graph regularized nonnegative matrix factorization (GNMF) incorporates the non-negativity constraint and manifold regularization simultaneously to achieve a parts-based meaningful high-dimensional data representation, which can discover the underlying local geometrical structure of the original data space. In order to reduce the redundancy between bases and representations, and enhance the clustering power of NMF, three orthogonal variants of GNMF are proposed, which incorporates the orthogonal constraints into GNMF model. The optimization algorithms are developed to solve the objective functions of Orthogonal GNMF (OGNMF). The extensive experimental results on four real-world face image data sets have confirmed the effectiveness of the proposed OGNMF methods.

Keywords

Image representation Nonnegative Matrix Factorization Manifold regularization Orthogonal projection 

Notes

Acknowledgement

This work was partially supported by National Natural Science Foundation of China (61902339, 61602388), China Postdoctoral Science Foundation (2018M633585, 2017M613216), Natural Science Basic Research Plan in Shaanxi Province of China (2018JQ6060, 2017JM6059), Fundamental Research Funds for the Central Universities (2452019064), Key Research and Development Program of Shaanxi (2019ZDLNY07-06-01), and the Doctoral Starting up Foundation of Yan’an University (YDBK2019-06).

References

  1. 1.
    Lee, D.D., Seung, H.S.: Learning the parts of objects by nonnegative matrix factorization. Nature 401(6755), 788–791 (1999)CrossRefGoogle Scholar
  2. 2.
    Hamza, A.B., Brady, D.J.: Reconstruction of reflectance spectra using robust non-negative matrix factorization. IEEE Trans. Sig. Process. 54(9), 3637–3642 (2006)CrossRefGoogle Scholar
  3. 3.
    Lam, E.Y.: Non-negative matrix factorization for images with Laplacian noise. In: IEEE Asia Pacific Conference on Circuits and Systems, pp. 798–801 (2008)Google Scholar
  4. 4.
    Zhang, L., Chen, Z., Zheng, M., He, X.: Robust non-negative matrix factorization. Front. Electr. Electron. Eng. China 6(2), 192–200 (2011)CrossRefGoogle Scholar
  5. 5.
    Kong, D., Ding, C., Huang, H.: Robust non-negative matrix factorization using L21-norm. In: Proceedings of the 20th ACM International Conference on Information and Knowledge Management, pp. 673–682 (2011)Google Scholar
  6. 6.
    Gao, H., Nie, F., Cai, W., Huang, H.: Robust capped norm nonnegative matrix factorization. In: Proceedings of the 24th ACM International Conference on Information and Knowledge Management, Melbourne, Australia, 19–23 October 2015Google Scholar
  7. 7.
    Guan, N., Liu, T., Zhang, Y., et al.: Truncated cauchy non-negative matrix factorization for robust subspace learning. IEEE Trans. Pattern Anal. Mach. Intell. 41(1), 246–259 (2019)CrossRefGoogle Scholar
  8. 8.
    Cai, D., He, X., Han, J., et al.: Graph regularized nonnegative matrix factorization for data representation. IEEE Trans. Pattern Anal. Mach. Intell. 33(8), 1548–1560 (2011)CrossRefGoogle Scholar
  9. 9.
    Zeng, K., Yu, J., Li, C., You, J., Jin, T.: Image clustering by hyper-graph regularized non-negative matrix factorization. Neurocomputing 138(11), 209–217 (2014)CrossRefGoogle Scholar
  10. 10.
    Huang, S., Wang, H., Ge, Y., et al.: Improved hypergraph regularized nonnegative matrix factorization with sparse representation. Pattern Recogn. Lett. 102(15), 8–14 (2018)CrossRefGoogle Scholar
  11. 11.
    Wang, W., Qian, Y., Tang, Y.Y.: Hypergraph-regularized sparse NMF for hyper-spectral unmixing. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 9(2), 681–694 (2016)CrossRefGoogle Scholar
  12. 12.
    Wang, J.Y., Bensmail, H., Gao, X.: Multiple graph regularized nonnegative matrix factorization. Pattern Recogn. 46(10), 2840–2847 (2013)CrossRefGoogle Scholar
  13. 13.
    Xu, Y., Li, Z., Zhang, B., Yang, J., You, J.: Sample diversity, representation effectiveness and robust dictionary learning for face recognition. Inform. Sci. 375(1), 171–182 (2017)CrossRefGoogle Scholar
  14. 14.
    Wang, C., Song, X., Zhang, J.: Graph regularized nonnegative matrix factorization with sample diversity for image representation. Eng. Appl. Artif. Intell. 68(2), 32–39 (2018)CrossRefGoogle Scholar
  15. 15.
    Wenhui, W., Sam Kwong, Yu., Zhou, Y.J., Gao, W.: Nonnegative matrix factorization with mixed hypergraph regularization for community detection. Inf. Sci. 435(4), 263–281 (2018)MathSciNetGoogle Scholar
  16. 16.
    Ding, C., Li, T., Peng, W., Park, H.: Orthogonal nonnegative matrix t-factorizations for clustering. In: Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 126–135. ACM (2006)Google Scholar
  17. 17.
    Li, B., Zhou, G., Cichocki, A.: Two efficient algorithms for approximately orthogonal nonnegative matrix factorization. IEEE Sig. Process. Lett. 22(7), 843–846 (2015)CrossRefGoogle Scholar
  18. 18.
    Yoo, J., Choi, S.: Orthogonal nonnegative matrix factorization: multiplicative updates on Stiefel manifolds. In: Fyfe, C., Kim, D., Lee, S.-Y., Yin, H. (eds.) IDEAL 2008. LNCS, vol. 5326, pp. 140–147. Springer, Heidelberg (2008).  https://doi.org/10.1007/978-3-540-88906-9_18CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Jinrong He
    • 1
    • 2
    • 3
  • Dongjian He
    • 1
    • 3
    Email author
  • Bin Liu
    • 1
    • 3
  • Wenfa Wang
    • 2
  1. 1.Key Laboratory of Agricultural Internet of ThingsMinistry of Agriculture and Rural Affairs, Northwest A&F UniversityYanglingChina
  2. 2.College of Mathematics and Computer ScienceYan’an UniversityYan’anChina
  3. 3.Shaanxi Key Laboratory of Agricultural Information Perception and Intelligent ServiceNorthwest A&F UniversityYanglingChina

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