Skip to main content
SpringerLink
Log in

PSO-ECM: particle swarm optimization-based evidential C-means algorithm

  • Original Article
  • Published:
International Journal of Machine Learning and Cybernetics Aims and scope Submit manuscript

Abstract

As an extension of Fuzzy C-Means (FCM), Evidence C-Means (ECM) is proposed in the framework of Dempster–Shafer theory (DST) and has been applied to many fields. However, the objective function of ECM involves only the distortion between the object and the prototype, which relies heavily on the initial prototype. Therefore, ECM may encounter the problem of local optimization. To solve this problem, this paper introduces ECM with Particle Swarm Optimization (PSO) initialization to determine the initial clustering centroids, and proposes Particle Swarm Optimization-based Evidential C-Means (PSO-ECM), which reduces the influence of bad initial prototypes and improves the local optimality problem of ECM. PSO-ECM is compared with three other clustering algorithms in four experiments and with ECM on a noise-containing dataset. According to the experimental results, PSO-ECM performs well in terms of different clustering validity metrics compared with existing clustering algorithms, has high stability of clustering, and can effectively and stably cluster noise-containing datasets and accurately identify outlier points.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Algorithm 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

Availability of data and materials

All data and materials generated or analysed during this study are included in this article.

Code availability

The code of the current study are available from the corresponding author on reasonable request.

References

  1. Brown PO (1998) Cluster analysis and display of genome-wide expression patterns. Proc Natl Acad 95:14863–14868

    Article  Google Scholar 

  2. Bridges CC Jr (1966) Hierarchical cluster analysis. Psychol Rep 18(3):851–854

    Article  Google Scholar 

  3. Hartigan JA, Wong MA (1979) Algorithm as 136: a K-means clustering algorithm. J R Stat Soc Ser C (Appl Stat) 28(1):100–108

    Google Scholar 

  4. Jiao L, Yang H, Liu Z-G, Pan Q (2022) Interpretable fuzzy clustering using unsupervised fuzzy decision trees. Inf Sci 611:540–563

    Article  Google Scholar 

  5. Hanyu E, Cui Y, Pedrycz W, Li Z (2022) Design of distributed rule-based models in the presence of large data. IEEE Trans Fuzzy Syst 31(7):2479–2486

    Google Scholar 

  6. Cui Y, Hanyu E, Pedrycz W, Li Z (2019) Augmentation of rule-based models with a granular quantification of results. Soft Comput 23:12745–12759

    Article  Google Scholar 

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

    Article  Google Scholar 

  8. Zhou J, Pedrycz W, Yue X, Gao C, Lai Z, Wan J (2021) Projected fuzzy C-means clustering with locality preservation. Pattern Recogn 113:107748

    Article  Google Scholar 

  9. Abdellahoum H, Mokhtari N, Brahimi A, Boukra A (2021) CSFCM: An improved fuzzy C-means image segmentation algorithm using a cooperative approach. Expert Syst Appl 166:114063

    Article  Google Scholar 

  10. Wang C, Pedrycz W, Li Z, Zhou M (2020) Residual-driven fuzzy C-means clustering for image segmentation. IEEE/CAA J Autom Sin 8(4):876–889

    Article  MathSciNet  Google Scholar 

  11. Hanyu E, Cui Y, Pedrycz W, Li Z (2019) Enhancements of rule-based models through refinements of fuzzy c-means. Knowl-Based Syst 170:43–60

    Article  Google Scholar 

  12. Pang Y, Shi M, Zhang L, Song X, Sun W (2022) PR-FCM: A polynomial regression-based fuzzy C-means algorithm for attribute-associated data. Inf Sci 585:209–231

    Article  Google Scholar 

  13. Li Y-F, Huang H-Z, Mi J, Peng W, Han X (2022) Reliability analysis of multi-state systems with common cause failures based on Bayesian network and fuzzy probability. Ann Oper Res 311(1):195–209

    Article  MathSciNet  Google Scholar 

  14. Ikotun AM, Ezugwu AE, Abualigah L, Abuhaija B, Heming J (2023) K-means clustering algorithms: a comprehensive review, variants analysis, and advances in the era of big data. Inf Sci 622:178–210

    Article  Google Scholar 

  15. Zhao J, Wang Z, Cao J, Cheong KH (2023) A self-adaptive evolutionary deception framework for community structure. IEEE Trans Syst Man Cybern Syst 53(8):4954–4967

    Article  Google Scholar 

  16. Wen T, Gao Q, Chen Y-W, Cheong KH (2022) Exploring the vulnerability of transportation networks by entropy: a case study of Asia–Europe maritime transportation network. Reliab Eng Syst Saf 226:108578

    Article  Google Scholar 

  17. Arthur D, Vassilvitskii S (2006) K-means++: the advantages of careful seeding. Technical report, Stanford

  18. Whitley D (1994) A genetic algorithm tutorial. Stat Comput 4(2):65–85

    Article  Google Scholar 

  19. Van Laarhoven PJ, Aarts EH (1987) Simulated annealing. In: Simulated annealing: theory and applications. Springer, pp 7–15

  20. Eberhart R, Kennedy J (1995) Particle swarm optimization. In: Proceedings of the IEEE international conference on neural networks, vol 4. Citeseer, pp 1942–1948

  21. Robini MC, Reissman P-J (2013) From simulated annealing to stochastic continuation: a new trend in combinatorial optimization. J Glob Optim 56(1):185–215

    Article  MathSciNet  Google Scholar 

  22. Choi K, Jang D-H, Kang S-I, Lee J-H, Chung T-K, Kim H-S (2015) Hybrid algorithm combing genetic algorithm with evolution strategy for antenna design. IEEE Trans Magn 52(3):1–4

    Article  Google Scholar 

  23. Zhao J, Cheong KH (2023) Obfuscating community structure in complex network with evolutionary divide-and-conquer strategy. IEEE Trans Evol Comput 27(6):1926–1940

    Article  Google Scholar 

  24. Zhao J, Wen T, Jahanshahi H, Cheong KH (2022) The random walk-based gravity model to identify influential nodes in complex networks. Inf Sci 609:1706–1720

    Article  Google Scholar 

  25. Shi XH, Liang YC, Lee HP, Lu C, Wang Q (2007) Particle swarm optimization-based algorithms for TSP and generalized TSP. Inf Process Lett 103(5):169–176

    Article  MathSciNet  Google Scholar 

  26. Sadik NJ, Rasheed AA, Algamal ZY (2023) Tuning parameter selectors for bridge penalty based on particle swarm optimization method. Period Eng Nat Sci 11(2):221–231

    Google Scholar 

  27. Nabi S, Ahmed M (2022) PSO-RDAL: particle swarm optimization-based resource-and deadline-aware dynamic load balancer for deadline constrained cloud tasks. J Supercomput 78(2):4624–4654

    Article  Google Scholar 

  28. Dempster AP (2008) Upper and lower probabilities induced by a multivalued mapping. In: Classic works of the Dempster–Shafer theory of belief functions. Springer, Berlin, pp 57–72. https://doi.org/10.1007/978-3-540-44792-4_3

  29. Shafer G (1976) A mathematical theory of evidence. Princeton University Press, Princeton. https://doi.org/10.1515/9780691214696

    Book  Google Scholar 

  30. Liu Z-g, Fu Y-m, Pan Q, Zhang Z-w (2022) Orientational distribution learning with hierarchical spatial attention for open set recognition. IEEE Trans Pattern Anal Mach Intell 45(7):8757–8772

    Google Scholar 

  31. Huang L, Zhao W, Liu Y, Yang D, Liew AW-C, You Y (2023) An evidential multi-target domain adaptation method based on weighted fusion for cross-domain pattern classification. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2023.3275759

  32. Xiao F, Pedrycz W (2022) Negation of the quantum mass function for multisource quantum information fusion with its application to pattern classification. IEEE Trans Pattern Anal Mach Intell 45(2):2054–2070

    Article  Google Scholar 

  33. Liang Y, Ju Y, Qin J, Pedrycz W (2021) Multi-granular linguistic distribution evidential reasoning method for renewable energy project risk assessment. Inf Fus 65:147–164

    Article  Google Scholar 

  34. Deng X, Jiang W (2022) A framework for the fusion of non-exclusive and incomplete information on the basis of D number theory. Appl Intell 53(10):11861–11884

    Google Scholar 

  35. Bouhamed SA, Kallel IK, Yager RR, Bossé É, Solaiman B (2020) An intelligent quality-based approach to fusing multi-source possibilistic information. Inf Fus 55:68–90

    Article  Google Scholar 

  36. Yang J-B, Xu D-L, Xu X, Fu C (2023) Likelihood analysis of imperfect data. IEEE Trans Syst Man Cybern Syst 53(8):5046–5057

    Article  Google Scholar 

  37. Xiao F, Wen J, Pedrycz W (2022) Generalized divergence-based decision making method with an application to pattern classification. IEEE Trans Knowl Data Eng 35(7):6941–6956

    Google Scholar 

  38. Fei L, Wang Y (2022) An optimization model for rescuer assignments under an uncertain environment by using Dempster-Shafer theory. Knowl Based Syst. https://doi.org/10.1016/j.knosys.2022.109680

    Article  Google Scholar 

  39. Zhou M, Zhou Y-J, Yang J-B, Wu J (2024) A generalized belief dissimilarity measure based on weighted conflict belief and distance metric and its application in multi-source data fusion. Fuzzy Sets Syst 475:108719

    Article  MathSciNet  Google Scholar 

  40. Xiao F, Wen J, Pedrycz W (2022) Generalized divergence-based decision making method with an application to pattern classification. IEEE Trans Knowl Data Eng 35(7):6941–6956

    Google Scholar 

  41. Tao R, Liu Z, Cai R, Cheong KH (2021) A dynamic group MCDM model with intuitionistic fuzzy set: perspective of alternative queuing method. Inf Sci 555:85–103

    Article  MathSciNet  Google Scholar 

  42. Deng X, Xue S, Jiang W (2023) A novel quantum model of mass function for uncertain information fusion. Inf Fus 89:619–631

    Article  Google Scholar 

  43. Pan L, Deng Y (2022) A new complex evidence theory. Inf Sci 608:251–261

    Article  Google Scholar 

  44. Zhunga L, Jingfei D, Huang L, Dezert J, Yongqiang Z (2022) Combination of classifiers with incomplete frames of discernment. Chin J Aeronaut 35(5):145–157

    Article  Google Scholar 

  45. Zhou Q, Tian G, Deng Y (2023) BF-QC: Belief functions on quantum circuits. Expert Syst Appl 223:119885

    Article  Google Scholar 

  46. Zhou Q, Cui Y, Li Z, Deng Y (2023) Marginalization in random permutation set theory: from the cooperative game perspective. Nonlinear Dyn 111(14):13125–13141

    Article  Google Scholar 

  47. Zhou Q, Deng Y (2023) Generating Sierpinski gasket from matrix calculus in Dempster–Shafer theory. Chaos Solitons Fract 166:112962

    Article  MathSciNet  Google Scholar 

  48. Zhou Q, Cui Y, Pedrycz W, Deng Y (2024) Conjunctive and disjunctive combination rules in random permutation set theory: a layer-2 belief structure perspective. Inf Fus 102:102083

    Article  Google Scholar 

  49. Denœux T, Masson M-H (2004) EVCLUS: evidential clustering of proximity data. IEEE Trans Syst Man Cybern Part B (Cybern) 34(1):95–109

    Article  Google Scholar 

  50. Masson M-H, Denoeux T (2008) ECM: an evidential version of the fuzzy C-means algorithm. Pattern Recogn 41(4):1384–1397

    Article  Google Scholar 

  51. Jiao L, Denœux T, Liu Z-G, Pan Q (2022) EGMM: an evidential version of the Gaussian mixture model for clustering. Appl Soft Comput 129:109619

    Article  Google Scholar 

  52. Liu Z-G, Pan Q, Dezert J, Mercier G (2015) Credal C-means clustering method based on belief functions. Knowl Based Syst 74:119–132

    Article  Google Scholar 

  53. Antoine V, Quost B, Masson M-H, Denoeux T (2012) CECM: constrained evidential C-means algorithm. Comput Stat Data Anal 56(4):894–914

    Article  MathSciNet  Google Scholar 

  54. Masson M-H, Denoeux T (2009) RECM: relational evidential C-means algorithm. Pattern Recogn Lett 30(11):1015–1026

    Article  Google Scholar 

  55. Jiao L, Wang F, Liu Z-G, Pan Q (2022) TECM: Transfer learning-based evidential C-means clustering. Knowl Based Syst 257:109937

    Article  Google Scholar 

  56. Zhou K, Guo M, Martin A (2022) Evidential prototype-based clustering based on transfer learning. Int J Approx Reason 151:322–343

    Article  MathSciNet  Google Scholar 

  57. Zhang Z-W, Liu Z-G, Martin A, Zhou K (2022) BSC: belief shift clustering. IEEE Trans Syst Man Cybern Syst 53(3):1748–1760

    Article  Google Scholar 

Download references

Funding

This work was supported by the National Natural Science Foundation of China (Grant No.62373078).

Author information

Authors and Affiliations

  1. Institute of Fundamental and Frontier Science, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Yuxuan Cai, Qianli Zhou & Yong Deng

  2. Institution of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Yuxuan Cai

  3. School of Medicine, Vanderbilt University, Nashville, 37240, United States of America

    Yong Deng

Authors
  1. Yuxuan Cai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qianli Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yong Deng
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed to the study conception and design. All authors performed material preparation, data collection and analysis. YC wrote the first draft of the paper. All authors contributed to the revisions of the paper. All authors read and approved the final manuscript.

Corresponding authors

Correspondence to Qianli Zhou or Yong Deng.

Ethics declarations

Conflict of interest

All the authors certify that there is no conflict of interest with any individual or organization for this work.

Ethics approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Consent to participate

Informed consent was obtained from all individual participants included in the study.

Consent for publication

The participant has consented to the submission of the case report to the journal.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cai, Y., Zhou, Q. & Deng, Y. PSO-ECM: particle swarm optimization-based evidential C-means algorithm. Int. J. Mach. Learn. & Cyber. (2024). https://doi.org/10.1007/s13042-024-02139-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s13042-024-02139-x

Keywords

Search

Navigation