Skip to main content

Advertisement

Double fuzzy relaxation local information C-Means clustering

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

Fuzzy c-means clustering (FCM) has gained widespread application because of its ability to capture uncertain information in data effectively. However, attributed to the prior assumption of identical distribution, traditional FCM is sensitive to noise and cluster size. Modified methods incorporating local spatial information can enhance the robustness to noise. However, they tend to balance cluster sizes, resulting in poor performance when dealing with imbalanced data. Modified methods learning the statistical characteristics of data are feasible to handle imbalanced data. However, they are often sensitive to noise due to the ignorance of local information. Aiming at the lack of method that can simultaneously alleviate the sensitivity to noise and cluster size, a double fuzzy relaxation local information c-means clustering algorithm (DFRLICM) is proposed in this paper. Firstly, sample relaxation is introduced to explore potential clustering results and enhance inter-class separability. Secondly, to cooperate with the relaxation, we design fuzzy weights to record the imbalance situation of data clusters, enhancing the capability of algorithm in dealing with imbalanced data. Thirdly, we introduce fuzzy factor to account for the preservation of local structures in data and improve the robustness of algorithm. Finally, we integrate the three elements into a unified model framework to achieve the combination optimization of robustness to noise and insensitivity to cluster size simultaneously. Extensive experiments are conducted and the results demonstrate that the proposed algorithm indeed achieves a balance between robustness to noise and insensitivity to cluster size.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

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

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

Data Availability

The image data of this study are openly available in the Berkeley Segmentation Dataset [35] and the Weizmann Dataset [36]. The data that support the findings of this study are openly available in UCI datasets, at http://www.ics.uci.edu/ml.

References

  1. Li H, Wang J (2024) From soft clustering to hard clustering: A collaborative annealing fuzzy \(c\)-means algorithm. IEEE Trans Fuzzy Syst 32(3):1181–1194. https://doi.org/10.1109/TFUZZ.2023.3319663

    Article  MATH  Google Scholar 

  2. Li R, Cai Z (2023) A clustering algorithm based on density decreased chain for data with arbitrary shapes and densities. Appl Intell 53(2):2098–2109. https://doi.org/10.1007/s10489-022-03583-4

    Article  MATH  Google Scholar 

  3. Chen J (2023) Construction of data mining model of crm marketing based on big data clustering analysis. In: International conference on cognitive based information processing and applications. Springer, pp 319–330. https://doi.org/10.1007/978-981-97-1979-2_28

  4. Li Z, He X, Whitehill J (2023) Compositional clustering: Applications to multi-label object recognition and speaker identification. Pattern Recognit 144:109829. https://doi.org/10.1016/j.patcog.2023.109829

    Article  Google Scholar 

  5. Ratnakumar R, Nanda SJ (2021) A high speed roller dung beetles clustering algorithm and its architecture for real-time image segmentation. Appl Intell 51:4682–4713. https://doi.org/10.1007/s10489-020-02067-7

    Article  MATH  Google Scholar 

  6. Gong M, Liang Y, Shi J et al (2013) Fuzzy c-means clustering with local information and kernel metric for image segmentation. IEEE Trans Image Process 22(2):573–584. https://doi.org/10.1109/TIP.2012.2219547

    Article  MathSciNet  MATH  Google Scholar 

  7. Yu H, Xie S, Fan J et al (2024) Mahalanobis-kernel distance-based suppressed possibilistic c-means clustering algorithm for imbalanced image segmentation. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2024.3405497

    Article  MATH  Google Scholar 

  8. Gao Y, Li H, Li J, et al (2023) Patch-based fuzzy local weighted c-means clustering algorithm with correntropy induced metric for noise image segmentation. Int J Fuzzy Syst, pp 1–16. https://doi.org/10.1007/s40815-023-01485-2

  9. Lei L, Wu C, Tian X (2023) Robust deep kernel-based fuzzy clustering with spatial information for image segmentation. Appl Intell 53(1):23–48. https://doi.org/10.1007/s10489-022-03255-3

    Article  MATH  Google Scholar 

  10. Pan R, Zhong C, Qian J (2023) Balanced fair k-means clustering. IEEE Trans Ind Inf. https://doi.org/10.1109/TII.2023.3342888

    Article  MATH  Google Scholar 

  11. Bezdek JC, Ehrlich R, Full W (1984) Fcm: The fuzzy c-means clustering algorithm. Comput & Geosci 10(2–3):191–203. https://doi.org/10.1016/0098-3004(84)90020-7

    Article  MATH  Google Scholar 

  12. Cai H, Hu Y, Qi F et al (2024) Deep tensor spectral clustering network via ensemble of multiple affinity tensors. IEEE Trans Pattern Anal Mach Intell. https://doi.org/10.1109/TPAMI.2024.3361912

    Article  MATH  Google Scholar 

  13. Yuan W, Li X, Guan D (2023) Multi-view attributed network embedding using manifold regularization preserving non-negative matrix factorization. IEEE Trans Knowl Data Eng. https://doi.org/10.1109/TKDE.2023.3325461

    Article  MATH  Google Scholar 

  14. Ahmed MN, Yamany SM, Mohamed N et al (2002) A modified fuzzy c-means algorithm for bias field estimation and segmentation of mri data. IEEE Trans Med Imaging 21(3):193–199. https://doi.org/10.1109/42.996338

    Article  MATH  Google Scholar 

  15. Chen S, Zhang D (2004) Robust image segmentation using fcm with spatial constraints based on new kernel-induced distance measure. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics) 34(4):1907–1916. https://doi.org/10.1109/TSMCB.2004.831165

  16. Szilagyi L, Benyo Z, Szilagyi S, et al (2003) Mr brain image segmentation using an enhanced fuzzy c-means algorithm. In: Proceedings of the 25th annual international conference of the ieee engineering in medicine and biology society (IEEE Cat. No.03CH37439), pp 724–726 Vol.1, https://doi.org/10.1109/IEMBS.2003.1279866

  17. Cai W, Chen S, Zhang D (2007) Fast and robust fuzzy c-means clustering algorithms incorporating local information for image segmentation. Pattern Recognit 40(3):825–838. https://doi.org/10.1016/j.patcog.2006.07.011

    Article  MATH  Google Scholar 

  18. Krinidis S, Chatzis V (2010) A robust fuzzy local information c-means clustering algorithm. IEEE Trans Image Process 19(5):1328–1337. https://doi.org/10.1109/TIP.2010.2040763

    Article  MathSciNet  MATH  Google Scholar 

  19. Li F, Qin J (2017) Robust fuzzy local information and-norm distance-based image segmentation method. IET Image Processing 11(4):217–226. https://doi.org/10.1049/iet-ipr.2016.0539

    Article  MathSciNet  MATH  Google Scholar 

  20. Zhang H, Wang Q, Shi W et al (2017) A novel adaptive fuzzy local information \( c \)-means clustering algorithm for remotely sensed imagery classification. IEEE Trans Geosci Remote Sens 55(9):5057–5068. https://doi.org/10.1109/TGRS.2017.2702061

    Article  MATH  Google Scholar 

  21. Zhang Y, Bai X, Fan R et al (2019) Deviation-sparse fuzzy c-means with neighbor information constraint. IEEE Trans Fuzzy Syst 27(1):185–199. https://doi.org/10.1109/TFUZZ.2018.2883033

    Article  MATH  Google Scholar 

  22. Lei T, Jia X, Zhang Y et al (2018) Significantly fast and robust fuzzy c-means clustering algorithm based on morphological reconstruction and membership filtering. IEEE Trans Fuzzy Syst 26(5):3027–3041. https://doi.org/10.1109/TFUZZ.2018.2796074

    Article  MATH  Google Scholar 

  23. Jiao J, Wang X, Wei T et al (2023) An adaptive fuzzy c-means noise image segmentation algorithm combining local and regional information. IEEE Trans Fuzzy Syst 31(8):2645–2657. https://doi.org/10.1109/TFUZZ.2023.3235392

    Article  MATH  Google Scholar 

  24. Gao X, Zhang Y, Wang H et al (2023) A modified fuzzy clustering algorithm based on dynamic relatedness model for image segmentation. The Vis Comput 39(4):1583–1596. https://doi.org/10.1007/s00371-022-02430-4

    Article  MATH  Google Scholar 

  25. Wu KL, Yu J, Yang MS (2005) A novel fuzzy clustering algorithm based on a fuzzy scatter matrix with optimality tests. Pattern Recogn Lett 26(5):639–652. https://doi.org/10.1016/j.patrec.2004.09.016

    Article  MATH  Google Scholar 

  26. Ji J, Wang KL (2014) A robust nonlocal fuzzy clustering algorithm with between-cluster separation measure for sar image segmentation. IEEE J Sel Top Appl Earth Obs Remote Sens 7(12):4929–4936. https://doi.org/10.1109/JSTARS.2014.2308531

    Article  MATH  Google Scholar 

  27. Zhao X, Nie F, Wang R et al (2023) Robust fuzzy k-means clustering with shrunk patterns learning. IEEE Trans Knowl Data Eng 35(3):3001–3013. https://doi.org/10.1109/TKDE.2021.3116257

    Article  MATH  Google Scholar 

  28. Xu J, Han J, Xiong K, et al (2016) Robust and sparse fuzzy k-means clustering. In: IJCAI, pp 2224–2230

  29. Gao Y, Lin T, Pan J et al (2022) Fuzzy sparse deviation regularized robust principal component analysis. IEEE Trans Image Process 31:5645–5660. https://doi.org/10.1109/TIP.2022.3199086

    Article  MATH  Google Scholar 

  30. Lin PL, Huang PW, Kuo CH et al (2014) A size-insensitive integrity-based fuzzy c-means method for data clustering. Pattern Recognit 47(5):2042–2056. https://doi.org/10.1016/j.patcog.2013.11.031

  31. Bensaid AM, Hall LO, Bezdek JC et al (1996) Partially supervised clustering for image segmentation. Pattern Recognit 29(5):859–871. https://doi.org/10.1016/0031-3203(95)00120-4

    Article  MATH  Google Scholar 

  32. Noordam J, Van Den Broek W, Buydens L (2002) Multivariate image segmentation with cluster size insensitive fuzzy c-means. Chemometr Intell Lab Syst 64(1):65–78. https://doi.org/10.1016/S0169-7439(02)00052-7

    Article  Google Scholar 

  33. Dunn JC (1973) A fuzzy relative of the isodata process and its use in detecting compact well-separated clusters. J Cybern 3(3):32–57. https://doi.org/10.1080/01969727308546046

    Article  MathSciNet  MATH  Google Scholar 

  34. Nie F, Wang X, Huang H (2014) Clustering and projected clustering with adaptive neighbors. In: Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining, pp 977–986, https://doi.org/10.1145/2623330.2623726

  35. Arbeláez P, Maire M, Fowlkes C et al (2011) Contour detection and hierarchical image segmentation. IEEE Trans Pattern Anal Mach Intell 33(5):898–916. https://doi.org/10.1109/TPAMI.2010.161

    Article  MATH  Google Scholar 

  36. Alpert S, Galun M, Brandt A et al (2012) Image segmentation by probabilistic bottom-up aggregation and cue integration. IEEE Trans Pattern Anal Mach Intell 34(2):315–327. https://doi.org/10.1109/TPAMI.2011.130

    Article  MATH  Google Scholar 

  37. Fränti P, Sieranoja S (2024) Clustering accuracy. Appl. Comput Intell 4(1):24–44. https://doi.org/10.3934/aci.2024003

    Article  MATH  Google Scholar 

  38. Kvålseth TO (2017) On normalized mutual information: measure derivations and properties. Entropy 19(11):631. https://doi.org/10.3390/e19110631

    Article  MATH  Google Scholar 

  39. Wilcoxon F (1992) Individual comparisons by ranking methods. In: Breakthroughs in statistics: Methodology and distribution. Springer, pp 196–202. https://doi.org/10.1007/978-1-4612-4380-9_16

  40. Wang X, Jiang H, Wu Z et al (2023) Adaptive variational autoencoding generative adversarial networks for rolling bearing fault diagnosis. Adv Eng Inf 56:102027. https://doi.org/10.1016/j.aei.2023.102027

    Article  MATH  Google Scholar 

  41. Dong Y, Jiang H, Jiang W et al (2024) Dynamic normalization supervised contrastive network with multiscale compound attention mechanism for gearbox imbalanced fault diagnosis. Eng Appl Artif Intell 133:108098. https://doi.org/10.1016/j.engappai.2024.108098

    Article  MATH  Google Scholar 

  42. Liu Y, Jiang H, Yao R et al (2024) Counterfactual-augmented few-shot contrastive learning for machinery intelligent fault diagnosis with limited samples. Mech Syst Signal Process 216:111507. https://doi.org/10.1016/j.ymssp.2024.111507

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant 42076058, Special Foundation of Fujian Province to Promote High-quality Development of Marine and Fishery Industries, under Grant FJHYF-ZH-2023-05, the Natural Science Foundation of Fujian Province of China under Grant 2020J01713 and Grant 2022J01061.

Author information

Authors and Affiliations

Authors

Contributions

Yunlong Gao: Methodology, Conceptualization, Formal analysis, Supervision, Writing - Review & Editing, Resources, Approving the final version of the article for submission. Xingshen Zheng: Investigation, Software, Validation, Visualization, Writing - original draft, Writing - Review & Editing, Approving the final version of the article for submission. Qinting Wu: Data curation, Writing - Review & Editing, Approving the final version of the article for submission. Jiahao Zhang: Investigation, Writing - Review & Editing, Approving the final version of the article for submission. Chao Cao: Supervision, Funding acquisition, Writing - Review & Editing, Approving the final version of the article for submission. Jinyan Pan: Supervision, Resources, Project administration, Writing - Review & Editing, Approving the final version of the article for submission.

Corresponding author

Correspondence to Yunlong Gao.

Ethics declarations

Competing interests

No conflict of interest exists in the manuscript, and the manuscript has been approved by all authors for publication.

Ethical and informed consent for data used

This manuscript does not involve any studies with human participants or animals performed by any of the authors. The data used in the study are openly available and the relevant references have been cited.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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

Gao, Y., Zheng, X., Wu, Q. et al. Double fuzzy relaxation local information C-Means clustering. Appl Intell 55, 162 (2025). https://doi.org/10.1007/s10489-024-06078-6

Download citation

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10489-024-06078-6

Keywords