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.
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
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
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
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
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
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
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
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
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
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
Pan R, Zhong C, Qian J (2023) Balanced fair k-means clustering. IEEE Trans Ind Inf. https://doi.org/10.1109/TII.2023.3342888
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Xu J, Han J, Xiong K, et al (2016) Robust and sparse fuzzy k-means clustering. In: IJCAI, pp 2224–2230
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
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
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
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
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
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
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
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
Fränti P, Sieranoja S (2024) Clustering accuracy. Appl. Comput Intell 4(1):24–44. https://doi.org/10.3934/aci.2024003
Kvålseth TO (2017) On normalized mutual information: measure derivations and properties. Entropy 19(11):631. https://doi.org/10.3390/e19110631
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
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
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
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
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
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
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.
About this article
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
Accepted:
Published:
DOI: https://doi.org/10.1007/s10489-024-06078-6