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Clustering Validity Function Fusion Method of FCM Clustering Algorithm Based on Dempster–Shafer Evidence Theory

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Abstract

With the deepening of the research on clustering algorithm, clustering validity has become an indispensable part of cluster analysis. However, due to the complexity of data structure and different attributes, any clustering validity function cannot be applied to all datasets, so clustering validity function has been bringing forth new ones. Therefore, this paper proposes a clustering validity function fusion model based on D–S evidence theory (DS-CVFFM), which adopts FCM clustering algorithm as the base algorithm, calculates the values of different validity functions, and then uses the values of different clustering validity functions as the evidence source to construct the basic probability assignment function (BPA). Finally, it integrates with the fusion rules of D–S evidence theory, and outputs the optimal clustering number according to the decision conditions. DS-CVFFM uses the information fusion of multiple clustering validity functions to judge the number of optimal clusters without the need to propose complex validity functions, and avoid the influence of expert factors in the weighted combination clustering validity evaluation method. Finally, 4 sets of artificial datasets and 14 sets of UCI datasets are selected to verify the effectiveness of the proposed model. The experimental results show that compared with the traditional clustering validity evaluation methods, the proposed fusion model has a significant improvement in the accuracy of judging the optimal number of clusters, and the stability is improved under different values of fuzzy exponent, which can overcome the shortcomings of traditional clustering validity evaluation methods.

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References

  1. Frossyniotis, D., Likas, A., Stafylopatis, A.: A clustering method based on boosting. Pattern Recogn. Lett. 25(6), 641–654 (2004)

    Article  Google Scholar 

  2. Li, W.C., Zhou, Y., Xia, S.X.: A novel clustering algorithm based on hierarchical and K-means clustering. In: 2007 Chinese Control Conference, pp. 605–609. IEEE (2007)

  3. Kriegel, H.P.: Density-based clustering. Wiley Interdisciplinary Rev. Data Mining Knowledge Discovery 1(3), 231–240 (2011)

    Article  Google Scholar 

  4. Gurrutxga, I.: SEP/COP: An efficient method to find the best partition in hierarchical clustering based on a new cluster validity index. Pattern Recogn. 43(10), 3364–3373 (2010)

    Article  Google Scholar 

  5. Gertraud, M.W., Sylvia, F.S., Bettina, G.: Model-based clustering based on sparse finite Gaussian mixtures. Stat. Comput. 26(1–2), 303–324 (2016)

    Article  MathSciNet  Google Scholar 

  6. Bezdek, J.C., Ehrlich, R., Full, W.: FCM: The fuzzy c-means clustering algorithm. Comput. Geosci. 10(2–3), 191–203 (1984)

    Article  Google Scholar 

  7. Hartigan, J.A., Wong, M.A.: Algorithm AS 136: A k-means clustering algorithm. J. R. Stat. Soc. Ser. C 28(1), 100–108 (1979)

    MATH  Google Scholar 

  8. Zadeh, L.A.: Fuzzy sets. In: Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems: selected papers by Lotfi A Zadeh. pp. 394–432 (1996)

  9. Huang, H.: Brain image segmentation based on FCM clustering algorithm and rough set. IEEE Access 7, 12386–12396 (2019)

    Article  Google Scholar 

  10. Nayak, J., Naik, B., Behera, H.: Fuzzy C-means (FCM) clustering algorithm: a decade review from 2000 to 2014. Comput. Intell. Data Mining 2, 133–149 (2015)

    Google Scholar 

  11. Bezdek, J.C., Pal, N.R.: Some New indexes of cluster validity. IEEE Trans. Syst. Man Cybernetics 28(Part B), 301–315 (1998)

    Article  Google Scholar 

  12. Dos, S., Roberto, J.V.: Generalization of Shannon’s theorem for Tsallis entropy. J. Math. Phys. 38(8), 4104–4107 (1997)

    Article  MathSciNet  Google Scholar 

  13. Simovici, D.A., Jaroszewicz, S.: An axiomatization of partition entropy. IEEE Trans. Inf. Theory 48(7), 2138–2142 (2002)

    Article  MathSciNet  Google Scholar 

  14. Silva, L.: An interval-based framework for fuzzy clustering applications. IEEE Trans. Syst. 23(6), 2174–2187 (2015)

    Google Scholar 

  15. Chen, M.Y., Linkens, D.A.: Rule-base self-generation and simplification for data-driven fuzzy models. Fuzzy Sets Syst. 142(2), 243–265 (2004)

    Article  MathSciNet  Google Scholar 

  16. Xie, X.L., Beni, G.: A validity measure for fuzzy clustering. IEEE Trans. Pattern Anal. Mach. Intell. 13(8), 841–847 (1991)

    Article  Google Scholar 

  17. Fukuyama, Y., Sugeno, M.: A new method of choosing the number of clusters for the fuzzy c-means method. In: 5th Fuzzy Systems Symposium, pp. 247–250 (1989)

  18. Kwon, S.H.: Cluster validity index for fuzzy clustering. Electron. Lett. 34(22), 2176–2177 (1998)

    Article  Google Scholar 

  19. Wang, J.S.: A new clustering validity function for the fuzzy C-means algorithm. In: IEEE Conference on Control & Decision. IEEE (2008)

  20. Zhu, L.F., Wang, J.S., Wang, H.Y.: A novel clustering validity function of FCM clustering algorithm. IEEE Access 7, 152289–152315 (2019)

    Article  Google Scholar 

  21. Sheng, W. G. A weighted sum validity function for clustering with a hybrid niching genetic algorithm. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 2005, 35.6: 1156–1167.

  22. Xu, R.; Xu, J.; Wunsch, D. C. A comparison study of validity indices on swarm-intelligence-based clustering. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 2012, 42.4: 1243–1256.

  23. Dong, H.B., Hou, W., Yin, G.S.: An evolutionary clustering algorithm based on adaptive fuzzy weighted sum validity function. In: 2010 Third International Joint Conference on Computational Science and Optimization, pp. 357–361. IEEE (2010)

  24. Wu, Z.F., Huang, H.K.: A dynamic weighted sum validity function for fuzzy clustering with an adaptive differential evolution algorithm. In: 2010 Third International Joint Conference on Computational Science and Optimization, pp. 362–366. IEEE (2010)

  25. Zhou, K.L.: Comparison and weighted summation type of fuzzy cluster validity indices. Int. J. Comput. Commun. Control 9(3), 370–378 (2014)

    Article  Google Scholar 

  26. Wang, H.Y., Wang, J.S.: Combination evaluation method of fuzzy c-mean clustering validity based on hybrid weighted strategy. IEEE Access 9, 27239–27261 (2021)

    Article  Google Scholar 

  27. Shafer, G.: A Mathematical Theory of Evidence, vol. 42. Princeton University Press, Princeton (1976)

    Book  Google Scholar 

  28. Fixsen, D., Mahler, R.P.S.: The modified Dempster-Shafer approach to classification. Syst. Man Cybernetics Part A 27(1), 96–104 (1997)

    Article  Google Scholar 

  29. Fan, X., Guo, Y., Ju, Y., Bao, J.: Multi sensor fusion method based on the belief entropy and DS evidence theory. J. Sens. (2020). https://doi.org/10.1155/2020/7917512

    Article  Google Scholar 

  30. Wu, Z.H., Wu, Z.C., Zhang, J.: An improved FCM algorithm with adaptive weights based on SA-PSO. Neural Comput. Appl. 28(10), 3113–3118 (2017)

    Article  Google Scholar 

  31. Lin, G.P., Qian, Y.H., Liang, J.Y.: An information fusion approach by combining multi granulation rough sets and evidence theory. Inf. Sci. 314, 184–119 (2015)

    Article  Google Scholar 

  32. Park, D.C., Dagher, I.: Gradient based fuzzy c-means (GBFCM) algorithm. In: Proceedings of 1994 IEEE International Conference on Neural Networks (ICNN'94), pp. 1626–1631. IEEE (1994)

  33. Wu, Z.D., Xie, W.X., Yu, J.P.: Fuzzy c-means clustering algorithm based on kernel method. In: Proceedings Fifth International Conference on Computational Intelligence and Multimedia Applications. ICCIMA 2003, pp: 49–54. IEEE (2003)

  34. Sanchez, M.A.: Fuzzy granular gravitational clustering algorithm for multivariate data. Inf. Sci. 279, 498–511 (2014)

    Article  MathSciNet  Google Scholar 

  35. Ding, Y., Fu, X.: Kernel-based fuzzy c-means clustering algorithm based on genetic algorithm. Neurocomputing 188, 233–238 (2016)

    Article  Google Scholar 

  36. Rubio, E., Castillo, O., Valdez, F., Melin, P., Gonzalez, C.I., Martinez, G.: An extension of the fuzzy possibilistic clustering algorithm using type-2 fuzzy logic techniques. In: Advances in Fuzzy Systems (2017)

  37. Kuo, R.J.: A hybrid metaheuristic and kernel intuitionistic fuzzy c-means algorithm for cluster analysis. Appl. Soft Comput. 67, 299–308 (2018)

    Article  Google Scholar 

  38. Moreno, J.E., Sanchez, M.A., Mendoza, O., Rodriguez-Diaz, A., Castillo, O., Melin, P., Castro, J.R.: Design of an interval Type-2 fuzzy model with justifiable uncertainty. Inf. Sci. 513, 206–221 (2020)

    Article  Google Scholar 

  39. Wu, K.L., Yang, M.S.: A cluster validity index for fuzzy clustering. Pattern Recogn. Lett. 26(9), 1275–1291 (2005)

    Article  MathSciNet  Google Scholar 

  40. Bensaid, A.M., Hall, L.O., Bezdek, J.C., Clarke, L.P., Silbiger, M.L., Arrington, J.A.: Validity-guided (re) clustering with applications to image segmentation. IEEE Trans. Fuzzy Syst. 4(2), 112–123 (1996)

    Article  Google Scholar 

  41. Pakhira, M.K., Bandyopadhyay, S., Maulik, U.: Validity index for crisp and fuzzy clusters. Pattern Recogn. 37(3), 487–501 (2004)

    Article  Google Scholar 

  42. Wu, C.H.: A new fuzzy clustering validity index with a median factor for centroid-based clustering. IEEE Trans. Fuzzy Syst. 23(3), 701–718 (2014)

    Article  Google Scholar 

  43. Feng, Z., Fan, J.C.: A novel validity index in fuzzy clustering algorithm. Int. J. Wirel. Mob. Comput. 10(2), 183–190 (2016)

    Article  Google Scholar 

  44. Haouas, F.: A new efficient fuzzy cluster validity index: Application to images clustering. In: 2017 IEEE International Conference on Fuzzy Systems, pp. 1–6. IEEE (2017)

  45. Geng, J.Y., Qian, X.Z., Zhou, S.B.: New fuzzy clustering validity index. Appl. Res. Comput. 36(4), 1001–1005 (2019)

    Google Scholar 

  46. Ouchicha, C., Ammor, O., Meknassi, M.: A new validity index in overlapping clusters for medical images. Autom. Control. Comput. Sci. 54(3), 238–248 (2020)

    Article  Google Scholar 

  47. Liu, Y.: A new robust fuzzy clustering validity index for imbalanced datasets. Inf. Sci. 547, 579–591 (2021)

    Article  Google Scholar 

  48. Wang, L.S., Binet, D.: TRUST: a trigger-based automatic subjective weighting method for network selection. In: 2009 Fifth Advanced International Conference on Telecommunications, pp: 362–368. IEEE, (2009)

  49. Su, X.: An new fuzzy clustering algorithm based on entropy weighting. J. Comput. Inf. Syst. 6(10), 3319–3326 (2010)

    Google Scholar 

  50. Dempster, A.P.: Upper and lower probabilities induced by a multivalued mapping. In: Annals of Mathematical Statistics, Vol. 38 (1967)

  51. Yager, R.R.: On the dempster-shafer framework and new combination rules. Inf. Sci. 41(2), 93–137 (1987)

    Article  MathSciNet  Google Scholar 

  52. Wang, H.: A new method of cognitive signal recognition based on hybrid information entropy and DS evidence theory. Mob. Netw. Appl. 23(4), 677–685 (2018)

    Article  Google Scholar 

  53. Li, P., Wei, C.P.: An emergency decision-making method based on DS evidence theory for probabilistic linguistic term sets. Int. J. Disaster Risk Reduct. 37, 101–178 (2019)

    Article  Google Scholar 

  54. Lu, S., Li, P., Li, M.: An improved multi-modal data decision fusion method based on DS evidence theory. In: 2020 IEEE 4th Information Technology, Networking, Electronic and Automation Control Conference, Vol. 1, pp. 1684–1690 (2020)

  55. Ye, F., Chen, J., Li, Y.B.: Improvement of DS evidence theory for multi-sensor conflicting information. Symmetry 9(5), 69 (2017)

    Article  MathSciNet  Google Scholar 

  56. Li, Y.B.: Based on DS evidence theory of information fusion improved method. In: 2010 International Conference on Computer Application and System Modeling, Vol. 1, pp. 416–419 (2020)

  57. Li, F.J.: Multigranulation information fusion: a Dempster-Shafer evidence theory-based clustering ensemble method. Inf. Sci. 378, 389–409 (2017)

    Article  Google Scholar 

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Acknowledgements

This work was supported by the Basic Scientific Research Project of Institution of Higher Learning of Liaoning Province (Grant No. 2017FWDF10), and the Project by Liaoning Provincial Natural Science Foundation of China (Grant No. 20180550700).

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  1. School of Electronic and Information Engineering, University of Science & Technology Liaoning, Anshan, 114044, China

    Hong-Yu Wang, Jie-Sheng Wang & Guan Wang

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  1. Hong-Yu Wang
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Hong-yu Wang participated in the data collection, analysis, algorithm simulation, and draft writing. Jie-Sheng Wang participated in the concept, design, interpretation and commented on the manuscript. Guan Wang participated in the critical revision of this paper.

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Correspondence to Jie-Sheng Wang.

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Wang, HY., Wang, JS. & Wang, G. Clustering Validity Function Fusion Method of FCM Clustering Algorithm Based on Dempster–Shafer Evidence Theory. Int. J. Fuzzy Syst. 24, 650–675 (2022). https://doi.org/10.1007/s40815-021-01170-2

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