DOI QR코드

DOI QR Code

Multi-Radial Basis Function SVM Classifier: Design and Analysis

  • Wang, Zheng ;
  • Yang, Cheng ;
  • Oh, Sung-Kwun ;
  • Fu, Zunwei
  • Received : 2018.04.30
  • Accepted : 2018.07.19
  • Published : 2018.11.01

Abstract

In this study, Multi-Radial Basis Function Support Vector Machine (Multi-RBF SVM) classifier is introduced based on a composite kernel function. In the proposed multi-RBF support vector machine classifier, the input space is divided into several local subsets considered for extremely nonlinear classification tasks. Each local subset is expressed as nonlinear classification subspace and mapped into feature space by using kernel function. The composite kernel function employs the dual RBF structure. By capturing the nonlinear distribution knowledge of local subsets, the training data is mapped into higher feature space, then Multi-SVM classifier is realized by using the composite kernel function through optimization procedure similar to conventional SVM classifier. The original training data set is partitioned by using some unsupervised learning methods such as clustering methods. In this study, three types of clustering method are considered such as Affinity propagation (AP), Hard C-Mean (HCM) and Iterative Self-Organizing Data Analysis Technique Algorithm (ISODATA). Experimental results on benchmark machine learning datasets show that the proposed method improves the classification performance efficiently.

Keywords

Multi-RBF SVM;Composite kernel;Dual RBF structure;Clustering method;Particle Swam optimization

References

  1. N. Cristianini, J. Shawe-Taylor, "An Introduction to Support Vector Machines," Cambridge, UK: Cambridge Univ. Press, 2000.
  2. Brodley CE, Friedl MA (1999) "Identifying mislabeled training data," J Artif Intell Res, 11:131-167. https://doi.org/10.1613/jair.606
  3. E. Osuna, R. Freund, F. Girosi. "Support Vector Machines: Training and Applications," In A.I. Memo 1602, MIT A.I.Lab., 1997.
  4. Cormen T T, Leiserson C E, Rivest R L. Introduction to algorithms =[M]. MIT Press, 2002.
  5. Li B, Wang Q, Hu J., "Multi-SVM classifier system with piecewise interpolation[J]." Ieej Transactions on Electrical & Electronic Engineering, 2013, vol. 8, no. 2, pp. 132-138. https://doi.org/10.1002/tee.21832
  6. H. Cheng, P. Tan, and R. Jin, "Efficient algorithm for localized support vector machine," IEEE Transactions on Knowledge and Data Engineering, vol. 22, no. 4, pp. 537-549, 2010. https://doi.org/10.1109/TKDE.2009.116
  7. Z. Fu and A. Robles-Kelly, "On mixtures of linear SVMs for nonlinear classification," Lecture Notes in Computer Science, vol. 5342, pp. 489-499, 2010.
  8. D. S. Frossyniotis, and A. Stafylopatis, "A Multi-SVM Classification System," Lecture Notes in Computer Science, vol.2096/2001, pp. 198-207, 2001.
  9. B. Chen, F. Sun, and J. Hu, "Local linear multi-SVM method for gene function classification," in Proc of the World Congress on Nature and Biologically Inspired Computing (NaBIC'10) (Kitakyushu), Dec. 2010, pp. 183-188.
  10. C. Lin and S. Wang, "Fuzzy support vector machine," IEEE Trans. Neural Netw., vol. 13, no. 2, pp. 464-471, Mar. 2002. https://doi.org/10.1109/72.991432
  11. Y. Chen and J. Wang, "Support vector learning for fuzzy rule-based classification systems," IEEE Trans. Fuzzy Syst., vol. 11, no. 6, pp. 716-728, Dec. 2003. https://doi.org/10.1109/TFUZZ.2003.819843
  12. J. Chiang and P. Hao, "Support vector learning mechanism for fuzzy rulebased modeling: A new approach," IEEE Trans. Fuzzy Syst., vol. 12, no. 1, pp. 1-12, Feb. 2004. https://doi.org/10.1109/TFUZZ.2003.817839
  13. Y. Wang, S. Wang, and K. Lai, "A new fuzzy support vector machine to evaluate credit risk," IEEE Trans. Fuzzy Syst., vol. 13, no. 6, pp. 820-831, Dec. 2005. https://doi.org/10.1109/TFUZZ.2005.859320
  14. Q. Fan, Z. Wang, D. Li, D. Gao, and H. Zha, "Entropy-based fuzzy support vector machine for imbalanced data sets," Knowl.-Based Syst., vol. 115, pp. 87-99, 2017. https://doi.org/10.1016/j.knosys.2016.09.032
  15. X. Yang, L. Han, L. Yan, and L. He, "A bilateral-truncated-loss based robust support vector machine for classification problems," Soft Comput., vol. 19, no. 10, pp. 2871-2882, 2015. https://doi.org/10.1007/s00500-014-1448-9
  16. S. Chen and X. Wu, "A new fuzzy twin support vector machine for pattern classification," Int. J. Mach. Learn. Cybern., vol. 3, pp. 1-12, 2017.
  17. S. Abe, T. Inoue, "Fuzzy Support Vector Machines for Multiclass Problems," Proc. of ESANN'2002, Belgium, pp. 113-118, 2002.
  18. Y. Zhung, S. W. Wu, Y. L. Wang, W. X. Wu, and Y. L. Chen, "Source separation of household waste: A case study in China," Waste Management, vol. 28, pp. 2022-2030, 2008. https://doi.org/10.1016/j.wasman.2007.08.012
  19. S.-B. Roh, S.-K. Oh, "Identification of plastic wastes by using fuzzy radial basis function neural networks classifier with conditional fuzzy C-means clustering," Journal of Electrical Engineering and Technology, vol. 11, no. 6, pp. 1872-1879, 2016. https://doi.org/10.5370/JEET.2016.11.6.1872
  20. J. Kuiligowski, G. Quintas, S. Garrigues, and M. de la Guardia, "New background correction approach based on polynomial regressions for on-line liquid chromatography-Fouirer transform infrared spectroscopy," Journal of Chromatography A, vol. 1216, pp. 3122-3130, 2009. https://doi.org/10.1016/j.chroma.2009.01.110
  21. J. Peng, S. Peng, A. Jiang, J. Wei, C. Li, and J. Tan, "Asymmetric least squares for multiple spectra baseline correction," Analytica Chimica Acta., vol. 683, pp. 63-68, 2010. https://doi.org/10.1016/j.aca.2010.08.033
  22. C. Liu, S. X. Yang, L. Dong, "A comparative study for least angle regression on NIR spectra analysis to determine internal qualities of novel oranges," Expert Systems with Applications, vol. 42, pp. 8497-8503, 2015. https://doi.org/10.1016/j.eswa.2015.07.005
  23. Yang X, Zhang G, Lu J, et al. "A Kernel Fuzzy c-Means Clustering-Based Fuzzy Support Vector Machine Algorithm for Classification Problems With Outliers or Noises[J]," IEEE Transactions on Fuzzy Systems, vol. 19, no. 1, pp. 105-115, 2011. https://doi.org/10.1109/TFUZZ.2010.2087382
  24. V. Vapnik, The Nature of Statistical Learning Theory. Springer, Verlag Berlin, 1999.
  25. O. Chapelle and V. Vapnik, "Model selection for Support Vector Machines," Adv. Neural Inf. Proc. Syst. 12, Cambridge, MA, MIT Press,2000.
  26. B. Li, Q. Wang and J. Hu, "A fast SVM training method for very large datasets," IJCNN, 2009 International Joint Conference on Neural Networks, pp. 1784-1789, 2009.
  27. E. Osuna, R. Freund and F. Girosi., "Support Vector Machines: Training and Applications," A.I. Memo 1602, MIT A.I.Lab., 1997.
  28. Christian Platzer, Florian Rosenberg, and Schahram Dustdar, "Web Service Clustering using Multidimensional Angles as Proximity Measures Vienna University of Technology," ACM Transactions on Internet Technology, vol. 9, no. 3, Article 11, Publication date: July 2009.
  29. J. Suykens: Least Squares Support Vector Machines. Tutorial IJCNN, 2003.
  30. A. J. Smola and B. Schokopf, "On a kernelbased method for pattern recognition, regression, approximation and operator inversion," Algorithmica, 1998. emTechnical Report 1064, GMD FIRST, April 1997.
  31. S. R. Gunn., "Support Vector Machines for Classification and Regression," Technical Report, Faculty of Engineering, Science and Mathematics School of Electronics and Computer Science, 10 May, 1998.
  32. Chen B, Sun F, Hu J., "Local linear multi-SVM method for gene function classification[C]," Nature and Biologically Inspired Computing. IEEE, 2011: 183-188.
  33. Liu Y, Parhi K K., "Computing RBF Kernel for SVM Classification Using Stochastic Logic[C]," IEEE International Workshop on Signal Processing Systems. IEEE, pp. 327-332, 2016.
  34. Zhou B, Yang C, Guo H, et al. "A quasi-linear SVM combined with assembled SMOTE for imbalanced data classification[C]," International Joint Conference on Neural Networks. IEEE, pp. 1-7, 2013.
  35. [Online] Available weka platform: https://www.cs.waikato.ac.nz/ml/weka/.
  36. [Online] Available UCI dataset: http://archive.ics.uci.edu/ml/datasets.html.

Acknowledgement

Supported by : National Research Foundation of Korea(NRF)