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Robust Feature Selection Based on Fuzzy Rough Sets with Representative Sample

  • Zhimin Zhang
  • Weitong Chen
  • Chengyu Liu
  • Yun Kang
  • Feng Liu
  • Yuwen LiEmail author
  • Shoushui WeiEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11888)

Abstract

Fuzzy rough set theory is not only an objective mathematical tool to deal with incomplete and uncertain information but also a powerful computing paradigm to realize feature selection. However, the existing fuzzy rough set models are sensitive to noise in feature selection. To solve this problem, a novel fuzzy rough set model that is robust to noise is studied in this paper, which expands the research of fuzzy rough set theory and broadens the application of feature selection. In this study, we propose a fuzzy rough set model with representative sample (RS-FRS), and it deals better with noise. Firstly, the fuzzy membership of the sample is defined, and it is added into the construction of RS-FRS model, which could increase the upper and lower approximation of RS-FRS and reduce the influence of the noise samples. The proposed model considers the fuzziness of the sample membership degree, and it can approximate other subsets of the domain space with the fuzzy equivalent approximation space more precisely. Furthermore, RS-FRS model does not need to set parameters for the model in advance, which helps reduce the model complexity and human intervention effectively. At the same time, we also give a careful study to the related properties of RS-FRS model, and a robust feature selection based on RS-FRS with sample pair selection is designed. Extensive experiments are given to illustrate the robustness and effectiveness of the proposed model.

Keywords

Feature selection Fuzzy rough sets Representative sample 

Notes

Acknowledgement

This work was supported by Shandong Province Key Research and Development Plan (2018GSF118133) and China Postdoctoral Science Foundation (2018M642144).

References

  1. 1.
    Murthy, C.A.: Bridging feature selection and extraction: compound feature generation. IEEE Trans. Knowl. Data Eng. 29(4), 757–770 (2017)CrossRefGoogle Scholar
  2. 2.
    Chen, X.J., Yuan, G.W., Wang, W.T., Nie, F.P., Chang, X.J., Huang, J.Z.: Local adaptive projection framework for feature selection of labeled and unlabeled data. IEEE Trans. Neural Netw. Learn. Syst. 29(12), 6362–6373 (2018)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Chen, H.M., Li, T.R., Fan, X., Luo, C.: Feature selection for imbalanced data based on neighborhood rough sets. Inf. Sci. 483, 1–20 (2019)CrossRefGoogle Scholar
  4. 4.
    Zhou, P., Hu, X.G., Li, P.P., Wu, X.D.: Online streaming feature selection using adapted Neighborhood Rough Set. Inf. Sci. 481, 258–279 (2019)CrossRefGoogle Scholar
  5. 5.
    Wang, C.Z., Huang, Y., Shao, M.W., Chen, D.G.: Uncertainty measures for general fuzzy relations. Fuzzy Sets Syst. 360, 82–96 (2019)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Liu, K.Y., Yang, X.B., Yu, H.L., Mi, J.S., Wang, P.X., Chen, X.J.: Rough set based semi-supervised feature selection via ensemble selector. Knowl.-Based Syst. 165, 282–296 (2019)CrossRefGoogle Scholar
  7. 7.
    Zhou, P., Hu, X.G., Li, P.P., Wu, X.D.: OFS-density: a novel online streaming feature selection method. Pattern Recogn. 86, 48–61 (2019)CrossRefGoogle Scholar
  8. 8.
    Pawlak, Z.: Rough sets. Int. J. Comput. Inform. Sci. 11, 341–356 (1982)CrossRefGoogle Scholar
  9. 9.
    Pawlak, Z., Skowron, A.: Rough sets and boolean reasoning. Inf. Sci. 177, 41–73 (2007)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Pawlak, Z., Skowron, A.: Rough sets: some extensions. Inf. Sci. 177, 28–40 (2007)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Lin, Y.J., Hu, Q.H., Liu, J.H., Chen, J.K., Duan, J.: Multi-label feature selection based on neighborhood mutual information. Appl. Soft Comput. 38, 244–256 (2016)CrossRefGoogle Scholar
  12. 12.
    Li, Y.W., Wu, S.X., Lin, Y.J., Liu, J.H.: Different classes’ ratio fuzzy rough set based robust feature selection. Knowl.-Based Syst. 120, 74–86 (2017)CrossRefGoogle Scholar
  13. 13.
    Li, Y.W., Lin, Y.J., Liu, J.H., Weng, W., Shi, Z.K., Wu, S.X.: Feature selection for multi-label learning based on kernelized fuzzy rough sets. Neurocomputing 318, 217–286 (2018)Google Scholar
  14. 14.
    Dubois, D., Prade, H.: Rough fuzzy sets and fuzzy rough sets. Int. J. Gen. Syst. 17, 191–209 (1990)CrossRefGoogle Scholar
  15. 15.
    Dubois, D., Prade, H.: Putting rough sets and fuzzy sets together. Intell. Decis. Support 11, 203–232 (1992)CrossRefGoogle Scholar
  16. 16.
    Wu, W.Z., Leung, Y., Shao, M.W.: Generalized fuzzy rough approximation operators determined by fuzzy implicators. Int. J. Approx. Reason. 54, 1388–1409 (2013)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Wu, W.Z., Mi, J.S., Zhang, W.X.: Constructive and axiomatic approaches of fuzzy approximation operators. Inf. Sci. 159, 233–254 (2004)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Salido, J.M.F., Murakami, S.: Rough set analysis of a general type of fuzzy data using transitive aggregations of fuzzy similarity relations. Fuzzy Sets Syst. 139, 635–660 (2003)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Hu, Q.H., An, S., Yu, D.R.: Soft fuzzy rough sets for robust feature evaluation and selection. Inf. Sci. 180, 4384–4400 (2010)MathSciNetCrossRefGoogle Scholar
  20. 20.
    An, S., Hu, Q.H., Yu, D.R., Liu, J.F.: Soft minimum-enclosing-ball based robust fuzzy rough sets. Fundam. Inf. 115, 189–202 (2012)MathSciNetzbMATHGoogle Scholar
  21. 21.
    An, S., Hu, Q.H., Pedrycz, W., Zhu, P.F., Tsang, E.C.C.: Data-distribution-aware fuzzy rough set model and its application to robust classification. IEEE Trans. Cybern. 99, 1–13 (2015)CrossRefGoogle Scholar
  22. 22.
    Hu, Q.H., Zhang, L., An, S., Zhang, D., Yu, D.R.: On robust fuzzy rough set models. IEEE Trans. Fuzzy Syst. 20, 636–651 (2012)CrossRefGoogle Scholar
  23. 23.
    Cornelis, C., De Cock, M., Radzikowska, A.M.: Vaguely quantified rough sets. In: An, A., Stefanowski, J., Ramanna, S., Butz, C.J., Pedrycz, W., Wang, G. (eds.) RSFDGrC 2007. LNCS (LNAI), vol. 4482, pp. 87–94. Springer, Heidelberg (2007).  https://doi.org/10.1007/978-3-540-72530-5_10CrossRefGoogle Scholar
  24. 24.
    Zhao, S.Y., Tsang, E.C.C., Chen, D.G.: The model of fuzzy variable precision rough sets. IEEE Trans. Fuzzy Syst. 17, 451–467 (2009)CrossRefGoogle Scholar
  25. 25.
    Verbiest, N., Cornelis, C., Herrera, F.: OWA-FRPS: a prototype selection method based on ordered weighted average fuzzy rough set theory. In: Ciucci, D., Inuiguchi, M., Yao, Y., Ślęzak, D., Wang, G. (eds.) RSFDGrC 2013. LNCS (LNAI), vol. 8170, pp. 180–190. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-41218-9_19CrossRefGoogle Scholar
  26. 26.
    Hu, Q.H., Yu, D.R., Liu, J.F., Wu, C.X.: Neighborhood rough set based heterogeneous feature subset selection. Inf. Sci. 178, 3577–3594 (2008)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Wang, C.Z., et al.: A fitting model for feature selection with fuzzy rough sets. IEEE Trans. Fuzzy Syst. 25, 741–753 (2017)CrossRefGoogle Scholar
  28. 28.
    Hu, X.H., Cercone, N.: Learning in relational databases: a rough set approach. Int. J. Comput. Intell. 11, 323–338 (1995)CrossRefGoogle Scholar
  29. 29.
    Yao, Y.Y., Zhao, Y.: Discernibility matrix simplification for constructing attribute reducts. Inf. Sci. 179, 867–882 (2009)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Jensen, R., Tuson, A., Shen, Q.: Finding rough and fuzzy-rough set reducts with SAT. Inf. Sci. 255, 100–120 (2014)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Liang, J.Y., Xu, Z.B.: The algorithm on knowledge reduction in incomplete information systems. Int. J. Uncertainty Fuzziness Knowl.-Based Syst. 12, 651–672 (2004)CrossRefGoogle Scholar
  32. 32.
    Chen, D.G., Zhao, S.Y., Zhang, L., Yang, Y.P., Zhang, X.: Sample pair selection for attribute reduction with rough set. IEEE Trans. Knowl. Data Eng. 24, 2080–2093 (2012)CrossRefGoogle Scholar
  33. 33.
    Chen, D.G., Zhang, L., Zhao, S.Y., Hu, Q.H., Zhu, P.F.: A novel algorithm for finding reducts with fuzzy rough sets. IEEE Trans. Fuzzy Syst. 20, 385–389 (2012)CrossRefGoogle Scholar
  34. 34.
    Asuncion, A., Newman, D.J.: UCI Machine Learning Repository. School of Information and Computer Science, University of California, Irvine (2007). http://www.ics.uci.edu/mlearn/MLRepository.html
  35. 35.
    Aha, D.W., Kibler, D., Albert, M.K.: Instance-based learning algorithms. Mach. Learn. 6, 37–66 (1991)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Control Science and EngineeringShandong UniversityJinanChina
  2. 2.School of Information Technology and Electrical EngineeringThe University of QueenslandBrisbaneAustralia
  3. 3.School of Instrument Science and EngineeringSoutheast UniversityNanjingChina
  4. 4.College of Information Science and EngineeringHunan Normal UniversityChangshaChina

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