Skip to main content
SpringerLink
Log in

Kernel intuitionistic fuzzy c-means and state transition algorithm for clustering problem

  • Methodologies and Application
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

Clustering problems widely exist in machine learning, pattern recognition, image analysis and information sciences, etc. Although many clustering algorithms have been proposed, it is unpractical to find a clustering algorithm suitable for all types of datasets. Fuzzy c-means (FCM) is one of the most frequently-used fuzzy clustering algorithm for the reason that it is efficient, straightforward, and easy to implement. However, the traditional FCM taking Euclidean distance as similarity measurement can not distinguish the intersection between two clusters. Therefore, kernel function has been taken as similarity measurement to solve this issue. As a comprehensive partition criterion, intuitionistic fuzzy set which consider both membership degree and non-membership degree has been used to replace traditional fuzzy set to describe the natural attributes of objective phenomena more delicately. Thus, Kernel intuitionistic fuzzy c-means (KIFCM) has been proposed in this paper to settle clustering problem. Considering FCM is easily getting trapped in local optima due to its high sensitivity to initial centroid. State Transition Algorithm (STA) has been adopted in this study to obtain the initial centroid to enhance its stability. The proposed STA-KIFCM compared with some other clustering algorithms are implemented using five benchmark datasets. Experimental results not only show that the proposed method is efficient and can reveal encouraging results, but also indicate that the proposed method can achieve high accuracy.

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
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  • Askari S, Montazerin N, Zarandi MH et al (2017) Generalized entropy based possibilistic fuzzy C-Means for clustering noisy data and its convergence proof. Neurocomputing 219:186–202

    Article  Google Scholar 

  • Atanassov KT, Rangasamy P (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96

    Article  MATH  Google Scholar 

  • Babu GP, Murty MN (1993) A near-optimal initial seed value selection in K-means algorithm using a genetic algorithm. Pattern Recognit Lett 14(10):763–769

    Article  MATH  Google Scholar 

  • Bastanlar Y, Ozuysal M (2014) Introduction to machine learning. Methods Mol Biol 1107:105–128

    Article  Google Scholar 

  • Bezdek JC, Ehrlich R, Full WE et al (1984) FCM: the fuzzy c-means clustering algorithm. Comput Geosci 10:191–203

    Article  Google Scholar 

  • Chaira T (2011) A novel intuitionistic fuzzy C means clustering algorithm and its application to medical images. Appl Soft Comput 11(2):1711–1717

    Article  Google Scholar 

  • Davies DL, Bouldin DW (1979) A cluster separation measure. IEEE Trans Pattern Analysis and Mach Intell 1(2):224–227

    Article  Google Scholar 

  • Deng W, Yao R, Zhao H et al (2019) A novel intelligent diagnosis method using optimal LS-SVM with improved PSO algorithm. Soft Comput 23(7):2445–2462

    Article  Google Scholar 

  • Fan J, Han M, Wang J et al (2009) Single point iterative weighted fuzzy C-means clustering algorithm for remote sensing image segmentation. Pattern Recognit 42(11):2527–2540

    Article  MATH  Google Scholar 

  • Filho TD, Pimentel BA, De Souza RM et al (2015) Hybrid methods for fuzzy clustering based on fuzzy c-means and improved particle swarm optimization. Expert Syst Appl 42(17):6315–6328

    Article  Google Scholar 

  • Fisher RA (1936) The use of multiple measurements in taxonomic problems. Ann Human Genet 7(2):179–188

    Google Scholar 

  • Fouche G, Langit L (2011) Introduction to data mining. Scalable Comput Pract Exp 9(4):369–402

    Google Scholar 

  • Ghosh S, Dubey SK (2013) Comparative analysis of K-means and fuzzy C-means algorithms. Int J Adv Comput Sci Appl 4:4

    Google Scholar 

  • Han J, Yang C, Zhou X et al (2018) A two-stage state transition algorithm for constrained engineering optimization problems. Int J Control Autom Syst 16(2):522–534

    Article  Google Scholar 

  • Hathaway RJ, Bezdek JC (1995) Optimization of clustering criteria by reformulation. IEEE Trans Fuzzy Syst 3(2):241–245

    Article  Google Scholar 

  • Hosseinabadi AAR, Vahidi J, Saemi B et al (2019) Extended genetic algorithm for solving open-shop scheduling problem. Soft Comput 23(13):5099–5116

    Article  Google Scholar 

  • Huang Z, Yang C, Zhou X et al (2018) A novel cognitively inspired state transition algorithm for solving the linear bi-level programming problem. Cogn Comput. 1:1–11

    Article  Google Scholar 

  • Huang Z, Yang C, Zhou X et al (2018) A hybrid feature selection method based on binary state transition algorithm and relieff. IEEE J Biomed Health Inf 23(5):1888–1898

    Article  Google Scholar 

  • Huang M, Zhou X, Huang T et al (2019) Dynamic optimization based on state transition algorithm for copper removal process. Neural Comput Appl 31(7):2827–2839

    Article  Google Scholar 

  • Hutchinson RA, Westphal JA, Kieffer SW (1997) In situ observations of old faithful geyser. Geology 25(10):875–878

    Article  Google Scholar 

  • Kuo RJ, Mei CH, Zulvia FE et al (2016) An application of a metaheuristic algorithm-based clustering ensemble method to APP customer segmentation. Neurocomputing 205:116–129

    Article  Google Scholar 

  • Kuo RJ, Lin TC, Zulvia FE et al (2018) A hybrid metaheuristic and kernel intuitionistic fuzzy c-means algorithm for cluster analysis. Appl Soft Comput 67:299–308

    Article  Google Scholar 

  • Li C, Zhou J, Kou P et al (2012) A novel chaotic particle swarm optimization based fuzzy clustering algorithm. Neurocomputing 83:98–109

    Article  Google Scholar 

  • Lin K (2014) A novel evolutionary kernel intuitionistic fuzzy C-means clustering algorithm. IEEE Trans Fuzzy Syst 22(5):1074–1087

    Article  Google Scholar 

  • Liu J, Xu M (2008) Kernelized fuzzy attribute C-means clustering algorithm. Fuzzy Sets Syst 159(18):2428–2445

    Article  MathSciNet  MATH  Google Scholar 

  • Michielssen E, Ranjithan S, Mittra R (1992) Optimal multilayer filter design using real coded genetic algorithms. IEE Proc J (Optoelectronics) 139(6):413–420

    Article  Google Scholar 

  • Papageorgiou EI, Iakovidis DK (2013) Intuitionistic fuzzy cognitive maps. IEEE Trans Fuzzy Syst 21(2):342–354

    Article  Google Scholar 

  • Pedrycz W, Rai P (2008) Collaborative clustering with the use of fuzzy C-means and its quantification. Fuzzy Sets Syst 159(18):2399–2427

    Article  MathSciNet  MATH  Google Scholar 

  • Pena JM, Lozano JA, Larranaga P et al (1999) An empirical comparison of four initialization methods for the K-means algorithm. Pattern Recognit Lett 20(10):1027–1040

    Article  Google Scholar 

  • Sipe MA (2001) Statistical pattern recognition. Pattern Anal Appl 4(1):71–72

    Article  Google Scholar 

  • Wang P (1983) Pattern recognition with fuzzy objective function algorithms (James C. Bezdek). Siam Rev 25(3):442–442

    Google Scholar 

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

    Article  Google Scholar 

  • Zadeh LA (1999) Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst 100(1):9–34

    Article  MathSciNet  Google Scholar 

  • Zhang DQ, Chen SC (2003) Clustering incomplete data using kernel-based fuzzy C-means algorithm. Neural Process Lett 18(3):155–162

    Article  Google Scholar 

  • Zhang DQ, Chen SC (2004) A novel kernelized fuzzy C-means algorithm with application in medical image segmentation. Artif Intell Med 32(1):37–50

    Article  Google Scholar 

  • Zhao H, Xu Z, Ni M et al (2010) Generalized aggregation operators for intuitionistic fuzzy sets. Int J Intell Syst 25(1):1–30

    Article  MATH  Google Scholar 

  • Zhou X, Yang C, Gui W et al (2012) State transition algorithm. J Ind Manag Optim 8(4):1039–1056

    MathSciNet  MATH  Google Scholar 

  • Zhou KL, Chao F, Yang SL (2014) Fuzziness parameter selection in fuzzy c-means: the perspective of cluster validation. Sci China Inf Sci 57(11):1–8

    Google Scholar 

  • Zhou X, Gao DY, Yang C et al (2016) Discrete state transition algorithm for unconstrained integer optimization problems. Neurocomputing 173:864–874

    Article  Google Scholar 

  • Zhou X, Shi P, Lim CC et al (2018) A dynamic state transition algorithm with application to sensor network localization. Neurocomputing 273:237–250

    Article  Google Scholar 

  • Zhou X, Yang C, Gui W (2018) A statistical study on parameter selection of operators in continuous state transition algorithm. IEEE Trans Cybern 49(10):3722–3730

    Article  Google Scholar 

  • Zhou X, Zhou J, Yang C et al (2018) Set-point tracking and multi-objective optimization-based PID control for the goethite process. IEEE Access 6:36683–36698

    Article  Google Scholar 

  • Zhou X, Huang M, Huang T et al (2019) Dynamic optimization for copper removal process with continuous production constraints. IEEE Trans Ind Inf. https://doi.org/10.1109/TII.2019.2943500

    Article  Google Scholar 

  • Zhou X, Yang K, Xie Y et al (2019a) A novel modularity-based discrete state transition algorithm for community detection in networks. Neurocomputing 334:89–99

    Article  Google Scholar 

  • Zhou X, Long J, Xu C et al (2019) An external archive-based constrained state transition algorithm for optimal power dispatch. Complexity. https://doi.org/10.1155/2019/4727168

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Automation, Central South University, Changsha, 410083, China

    Xiaojun Zhou, Rundong Zhang, Xiangyue Wang & Chunhua Yang

  2. The Peng Cheng Laboratory, Shenzhen, Changsha, 51800, China

    Xiaojun Zhou

  3. Texas A&M University at Qatar, PO Box 23874, Doha, Qatar

    Tingwen Huang

Authors
  1. Xiaojun Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rundong Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xiangyue Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Tingwen Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Chunhua Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rundong Zhang.

Ethics declarations

Conflit of interest

The authors declare that they have no conflict of interest.

Ethical approval

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

Funding

This work was funded by the National Natural Science Foundation of China (Grant Nos. 61860206014, 61873285), the Innovation-Driven Plan in Central South University (Grant No. 2018CX012), the 111 Project (Grant No. B17048) and Hunan Provincial Natural Science Foundation of China (Grant No. 2018JJ3683) and the Fundamental Research Funds for the Central Universities of Central South University (Grant No. 2019zzts577).

Informed consent

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

Additional information

Communicated by V. Loia.

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhou, X., Zhang, R., Wang, X. et al. Kernel intuitionistic fuzzy c-means and state transition algorithm for clustering problem. Soft Comput 24, 15507–15518 (2020). https://doi.org/10.1007/s00500-020-04879-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-020-04879-8

Keywords

Search

Navigation