Soft Computing

, Volume 21, Issue 19, pp 5859–5865 | Cite as

Clustering via fuzzy one-class quadratic surface support vector machine

Methodologies and Application
  • 101 Downloads

Abstract

This paper proposes a soft clustering algorithm based on a fuzzy one-class kernel-free quadratic surface support vector machine model. One main advantage of our new model is that it directly uses a quadratic function for clustering instead of the kernel function. Thus, we can avoid the difficult task of finding a proper kernel function and corresponding parameters. Besides, for handling data sets with a large amount of outliers and noise, we introduce the Fisher discriminant analysis to consider minimizing the within-class scatter. Our experimental results on some artificial and real-world data sets demonstrate that the proposed algorithm outperforms Bicego’s benchmark algorithm in terms of the clustering accuracy and efficiency. Moreover, this proposed algorithm is also shown to be very competitive with several state-of-the-art clustering methods.

Keywords

Clustering Kernel-free One-class support vector machine Within-class scatter Quadratic surface 

Notes

Acknowledgements

Tian’s research has been supported by the Chinese National Science Foundation #11401485 and #71331004.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. An W, Liang M (2013) Fuzzy support vector machine based on within-class scatter for classification problems with outliers or noises. Neurocomputing 110:101–110CrossRefGoogle Scholar
  2. Bache K, Lichman M (2013) UCI machine learning repository. http://archive.ics.uci.edu/ml
  3. Bai Y, Han X, Chen T, Yu H (2015) Quadratic kernel-free least squares support vector machine for target diseases classification. J Comb Optim 30:850–870MathSciNetCrossRefMATHGoogle Scholar
  4. Baudat G, Anouar F (2000) Generalized discriminant analysis using a kernel approach. Neural Comput 12:2385–2404CrossRefGoogle Scholar
  5. Bicego M, Figueiredo M (2009) Soft clustering using weighted one-class support vector machines. Pattern Recogn 42:27–32CrossRefMATHGoogle Scholar
  6. Camastra F, Verri A (2005) A novel kernel method for clustering. IEEE Trans Pattern Anal 27:801–805CrossRefGoogle Scholar
  7. Cortes C, Vapnik V (1995) Support-vector networks. Mach Learn 20:273–297MATHGoogle Scholar
  8. Dagher I (2008) Quadratic kernel-free non-linear support vector machine. J Glob Optim 41:15–30MathSciNetCrossRefMATHGoogle Scholar
  9. Figueiredo M, Jain A (2002) Unsupervised learning of finite mixture models. IEEE Trans Pattern Anal 24:381–396CrossRefGoogle Scholar
  10. Fisher R (1936) The use of multiple measurements in taxonomic problems. Ann Hum Genet 7:179–188Google Scholar
  11. Fukunaga K (1990) Introduction to statistical pattern recognition. Academic, San DiegoMATHGoogle Scholar
  12. Jain A, Dubes R (1988) Algorithms for clustering data. Prentice-Hall, Englewood CliffsMATHGoogle Scholar
  13. Kohonen T (1982) Self-organized formation of topologically correct feature maps. Biol Cybern 43:59–69MathSciNetCrossRefMATHGoogle Scholar
  14. Krawczyk B, Wozniak M (2015) One-class classifiers with incremental learning and forgetting for data streams with concept drift. Soft Comput 19:3387–3400CrossRefGoogle Scholar
  15. Krawczyk B, Wozniak M, Cyganek B (2014) Clustering-based ensembles for one-class classification. Inf Sci 264:182–195MathSciNetCrossRefMATHGoogle Scholar
  16. Lin C, Wang S (2002) Fuzzy support vector machines. IEEE Trans Neural Netw 13:464–471Google Scholar
  17. Livi L, Sadeghian A, Pedrycz W (2015) Entropic one-class classifiers. IEEE Trans Neural Netw 26:3187–3200Google Scholar
  18. Luo J, Fang S-C, Deng Z, Guo X (2016a) Quadratic surface support vector machine for binary classification. Asia Pac J Oper Res 33:1650046. doi:10.1142/S0217595916500469 MathSciNetCrossRefMATHGoogle Scholar
  19. Luo J, Fang S-C, Bai Y, Deng Z (2016b) Fuzzy quadratic surface support vector machine based on Fisher discriminant analysis. J Ind Manag Optim 12:357–373MathSciNetCrossRefMATHGoogle Scholar
  20. Martinetz T, Schulten K (1993) Neural-gas network for vector quantization and its application to time-series prediction. IEEE Trans Neural Netw 4:558–569CrossRefGoogle Scholar
  21. Ng A, Jordan M, Weiss Y (2001) On spectral clustering: analysis and an algorithm. Adv Neural Inf Process Syst 2:558–569Google Scholar
  22. Sartakhti JS, Afrabandpey H, Saraee M (2016) Simulated annealing least squares twin support vector machine (SA-LSTSVM) for pattern classification. Soft Comput. doi:10.1007/s00500-016-2067-4 Google Scholar
  23. Schölkopf B, Smola A (2002) Learning with kernels: support vector machines, regularization, optimization, and beyond. MIT Press, CambridgeGoogle Scholar
  24. Shawe-Taylor J, Cristianini N (2004) Kernel methods for pattern analysis. University Press, CambridgeCrossRefMATHGoogle Scholar
  25. Tax D, Duin R (1999) On spectral clustering: analysis and an algorithm. IEEE Trans Neural Netw 20:1191–1199Google Scholar
  26. Tay F, Cao I (2001) Application of support vector machines in financial time series forecasting. Omega 29:309–317CrossRefGoogle Scholar
  27. Yang J, Deng J, Li S, Hao Y (2015) Improved traffic detection with support vector machine based on restricted Boltzmann machine. Soft Comput. doi:10.1007/s00500-015-1994-9 Google Scholar
  28. Zhou L, Lai K, Yen J (2009) Credit scoring models with AUC maximization based on weighted SVM. Int J Inf Technol Decis Making 4:677–696CrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.School of Management Science and EngineeringDongbei University of Finance and EconomicsDalianChina
  2. 2.School of Business Administration and Research Center for Big DataSouthwestern University of Finance and EconomicsChengduChina
  3. 3.Department of MathematicsShanghai UniversityShanghaiChina

Personalised recommendations