Skip to main content
SpringerLink
Log in

Fuzzy least squares twin support vector clustering

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

In this paper, we have formulated a fuzzy least squares version of recently proposed clustering method, namely twin support vector clustering (TWSVC). Here, a fuzzy membership value of each data pattern to different cluster is optimized and is further used for assigning each data pattern to one or other cluster. The formulation leads to finding k cluster center planes by solving modified primal problem of TWSVC, instead of the dual problem usually solved. We show that the solution of the proposed algorithm reduces to solving a series of system of linear equations as opposed to solving series of quadratic programming problems along with system of linear equations as in TWSVC. The experimental results on several publicly available datasets show that the proposed fuzzy least squares twin support vector clustering (F-LS-TWSVC) achieves comparable clustering accuracy to that of TWSVC with comparatively lesser computational time. Further, we have given an application of F-LS-TWSVC for segmentation of color images.

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
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Anderberg M (1973) Cluster analysis for applications. Academic Press, New York

    MATH  Google Scholar 

  2. Jain A, Murty M, Flynn P (1999) Data clustering: a review. ACM Comput Surv CSUR 31(3):264–323

    Article  Google Scholar 

  3. Qimin C, Qiao G, Yongliang W, Xianghua W (2015) Text clustering using VSM with feature clusters. Neural Comput Appl 26(4):995–1003

    Article  Google Scholar 

  4. Zhan Y, Yin J, Liu X (2013) Nonlinear discriminant clustering based on spectral regularization. Neural Comput Appl 22(7–8):1599–1608

    Article  Google Scholar 

  5. Tu E, Cao L, Yang J, Kasabov N (2014) A novel graph-based k-means for nonlinear manifold clustering and representative selection. Neurocomputing 143:109–122

    Article  Google Scholar 

  6. Liu X, Li M (2014) Integrated constraint based clustering algorithm for high dimensional data. Neurocomputing 142:478–485

    Article  Google Scholar 

  7. Bradley P, Mangasarian O (1997) Clustering via concave minimization. Adv Neural Inf Process Syst 9:368–374

    Google Scholar 

  8. Bradley P, Mangasarian O (2000) k-Plane clustering. J Glob Optim 16(1):23–32

    Article  MathSciNet  MATH  Google Scholar 

  9. Shao Y, Bai L, Wang Z, Hua X, Deng N (2013) Proximal plane clustering via eigenvalues. Procedia Comput Sci 17:41–47

    Article  Google Scholar 

  10. Yang Z, Guo Y, Li C, Shao Y (2014) Local k-proximal plane clustering. Neural Comput Appl 26(1):199–211

    Article  Google Scholar 

  11. Jayadeva KR, Chandra S (2007) Twin support vector machines for pattern classification. IEEE Trans Pattern Anal Mach Intell 29:905–910

    Article  MATH  Google Scholar 

  12. Mehrkanoon S, Huang X, Suykens JA (2014) Non-parallel support vector classifiers with different loss functions. Neurocomputing 143:294–301

    Article  Google Scholar 

  13. Xie X, Sun S (2014) Multi-view Laplacian twin support vector machines. Appl Intell 41:1059–1068

    Article  Google Scholar 

  14. Xie X, Sun S (2015) Multitask centroid twin support vector machines. Neurocomputing 149:1085–1091

    Article  Google Scholar 

  15. Ding S, Zhang N, Zhang X, Wu F (2016) Twin support vector machine: theory, algorithm and applications. Neural Comput Appl. doi:10.1007/s00521-016-2245-4

    Google Scholar 

  16. Tian Y, Qi Z (2014) Review on: twin support vector machines. Ann Data Sci 1:253–277

    Article  Google Scholar 

  17. Wang Z, Shao Y, Bai L, Deng N (2014) Twin support vector machine for clustering. IEEE Tran Neural Netw Learn Syst. doi:10.1109/TNNLS.2014.2379930

    Google Scholar 

  18. Fung G, Mangasarian OL (2001) Proximal support vector machine classifiers. In: Proceedings of seventh international conference on knowledge and data discovery, pp 77–86

  19. Keller JM, Gray MR, Givens JA (1985) A fuzzy k-nearest neighbor algorithm. IEEE Trans Syst Man Cybern 4:580–585

    Article  Google Scholar 

  20. Yuille AL, Rangarajan A (2002) The concave-convex procedure (CCCP). Adv Neural Inf Process Syst 2:1033–1040

    Google Scholar 

  21. Kumar A, Gopal M (2009) Least squares twin support vector machines for pattern classification. Exp Syst Appl 36:7535–7543

    Article  Google Scholar 

  22. Golub GH, Van Loan CF (1996) Matrix Computations. The John Hopkins University Press, Baltimore

    MATH  Google Scholar 

  23. MATLAB (1994–2001) User’s guide. The MathsWorks, Inc. http://www.mathworks.com

  24. Blake CL, Merz CJ (1998) UCI Repository for machine learning databases. University of California, Department of Information and Computer Sciences, Irvine. http://www.ics.uci.edu/~mlearn/MLRepository.html

  25. Arbelaez P, Fowlkes C, Martin D (2007) The berkeley segmentation dataset and benchmark. http://www.eecs.berkeley.edu/Research/Projects/CS/vision/bsds

  26. Mehrkanoon S, Alzate C, Mall R, Langone R, Suykens J (2015) Multiclass semisupervised learning based upon kernel spectral clustering. IEEE Trans Neural Netw Learn Syst 26(4):720–733

    Article  MathSciNet  Google Scholar 

  27. Wang XY, Wang T, Bu J (2011) Color image segmentation using pixel wise support vector machine classification. Pattern Recognit 44(4):777–787

    Article  MATH  Google Scholar 

  28. Duda RO, Hart PE, Stork DG (2001) Pattern classification, 2nd edn. Wiley, New York

  29. Huttenlocher DP, Klanderman GA, Rucklidge WJ (1993) Comparing images using the Hausdorff distance. IEEE Trans Pattern Anal Mach Intell 15(9):850–863

    Article  Google Scholar 

  30. Sartakhti JS, Ghadiri N, Afrabandpey H (2015) Fuzzy Least squares twin support vector machines. arXiv:1505.05451

  31. Wang X, Wang Y, Wang L (2004) Improving fuzzy c-means clustering based on feature-weight learning. Pattern Recognit Lett 25:1123–1132

    Article  Google Scholar 

  32. Manjunath BS, Ma WY (1996) Texture features for browsing and retrieval of image data. IEEE Trans Pattern Anal Mach Intell 18(8):837–842

    Article  Google Scholar 

Download references

Acknowledgments

We are very thankful to Mr. Keshav Goyal for his initial contribution to the analysis of the draft. We are also extremely grateful to the anonymous reviewers and Editor for their valuable comments that helped us to enormously improve the quality of the paper.

Author information

Authors and Affiliations

  1. South Asian University, New Delhi, India

    Reshma Khemchandani & Aman Pal

  2. Indian Institute of Technology, New Delhi, India

    Suresh Chandra

Authors
  1. Reshma Khemchandani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Aman Pal
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Suresh Chandra
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Reshma Khemchandani.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khemchandani, R., Pal, A. & Chandra, S. Fuzzy least squares twin support vector clustering. Neural Comput & Applic 29, 553–563 (2018). https://doi.org/10.1007/s00521-016-2468-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-016-2468-4

Keywords

Search

Navigation