A novel sparse least squares support vector machines

Mathematical Problems in Engineering

Volumn 2013, Issue , 2013, Pages

  Xia, Xiao Lei ^a   Jiao, Weidong ^a,b   Li, Kang ^c   Irwin, George ^c  

^a JIAXING UNIVERSITY   (China)

^b ZHEJIANG NORMAL UNIVERSITY   (China)

^c QUEEN'S UNIVERSITY BELFAST   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BENCHMARK DATASETS; GENERALIZATION ABILITY; GRAMIANS; GREEDY APPROXIMATION ALGORITHMS; LEAST SQUARE; LEAST SQUARES SUPPORT VECTOR MACHINES; LINEAR DEPENDENCY; LOSS FUNCTIONS; REGULARIZATION PARAMETERS; SUPPORT VECTOR; SVM ALGORITHM; TRAINING COSTS;

APPROXIMATION ALGORITHMS; LEAST SQUARES APPROXIMATIONS;

SUPPORT VECTOR MACHINES;

EID: 84874145659     PISSN: 1024123X     EISSN: 15635147     Source Type: Journal    
DOI: 10.1155/2013/602341     Document Type: Article

References (32)

1. J. A. K. Suykens, T. V. Gestel, J. Vandewalle, and B. D. Moor, "A support vector machine formulation to PCA analysis and its kernel version, " IEEE Transactions on Neural Networks, vol. 14, no. 2, pp. 447-450, 2003.
2. J. A. K. Suykens and J. Vandewalle, "Least squares support vector machine classifers, " Neural Processing Letters, vol. 9, no. 3, pp. 293-300, 1999.
3. V. Vapnik, The Nature of Statistical Learning Theory, Springer, New York, NY, USA, 1995.
4. V. Vapnik, Statistical Learning Theory, John Wiley & Sons, New York, NY, USA, 1998.
5. J. A. K. Suykens, L. Lukas, P. V. Dooren, B. D. Moor, and J. Vandewalle, "Least squares support vector machine classifers: a large scale algorithm, " in Proceedings of the European Conference on Circuit Theory and Design (ECCTD '99), pp. 839-842, Stresa, Italy, September 1999.
6. T. V. Gestel, J. A. K. Suykens, B. Baesens et al., "Benchmarking least squares support vector machine classifers, " Machine Learning, vol. 54, no. 1, pp. 5-32, 2004.
7. W. Chu, C. J. Ong, and S. S. Keerthi, "An improved conjugate gradient scheme to the solution of least squares SVM, " IEEE Transactions on Neural Networks, vol. 16, no. 2, pp. 498-501, 2005.
8. S. S. Keerthi, S. K. Shevade, C. Bhattacharyya, and K. R. K. Murthy, "Improvements to Platt's SMO algorithm for SVM classifer design, " Neural Computation, vol. 13, no. 3, pp. 637-649, 2001.
9. J. A. K. Suykens, J. de Brabanter, L. Lukas, and J. Vandewalle, "Weighted least squares support vector machines: robustness and sparce approximation, " Neurocomputing, vol. 48, no. 1, pp. 85-105, 2002.
10. B. J. de Kruif and T. J. A. de Vries, "Pruning error minimization in least squares support vector machines, " IEEE Transactions on Neural Networks, vol. 14, no. 3, pp. 696-702, 2003.
11. X. Zeng and X. W. Chen, "SMO-based pruning methods for sparse least squares support vector machines, " IEEE Transactions on Neural Networks, vol. 16, no. 6, pp. 1541-1546, 2005.
12. L. Jiao, L. Bo, and L. Wang, "Fast sparse approximation for least squares support vector machine, " IEEE Transactions on Neural Networks, vol. 18, no. 3, pp. 685-697, 2007.
13. K. Li, J. X. Peng, and G. W. Irwin, "A fast nonlinear model identi-fcation method, " IEEE Transactions on Automatic Control, vol. 50, no. 8, pp. 1211-1216, 2005.
14. C. J. C. Burges, "A tutorial on support vector machines for pattern recognition, " Data Mining and Knowledge Discovery, vol. 2, no. 2, pp. 121-167, 1998.
15. N. Cristianini and J. Shawe-Taylor, An Introduction to Support Vector Machines and Other Kernel-Based Learning Methods, Cambridge University Press, New York, NY, USA, 2000.
16. R. Fletcher, Practical Methods of Optimization, John Wiley & Sons, New York, NY, USA, 1987.
17. C. Saunders, A. Gammerman, and V. Vovk, "Ridge regression learning algorithm in dual variables, " in Proceedings of the 15th International Conference on Machine Learning (ICML '98), pp. 515-521, Morgan Kaufmann, 1998.
18. S. Mika, G. Ratsch, and K. Muller, "A mathematical programming approach to the kernel fsher algorithm, " in Advances in Neural Information Processing Systems, pp. 591-597, 2001.
19. T. Gestel, J. A. K. Suykens, G. Lanckriet, A. Lambrechts, B. Moor, and J. Vandewalle, "Bayesian framework for least-squares support vector machine classifers, gaussian processes, and kernel fsher discriminant analysis, " Neural Computation, vol. 14, no. 5, pp. 1115-1147, 2002.
20. X. Xia, K. Li, and G. Irwin, "Improved training of an optimal sparse least squares support vector machine, " in Proceedings of the 17th World Congress The International Federation of Automatic Control (IFAC '08), Seoul, Korea, July 2008.
21. C. Lawson and R. Hanson, "Solving least squares problems, " in Prentice-Hall Series in Automatic Computation, Prentice Hall, Englewood Clifs, NJ, USA, 1974.
22. S. Chen, S. Billings, and W. Luo, "Orthogonal least squares methods and their application to non-linear system identifca-tion, " International Journal of Control, vol. 50, no. 5, pp. 1873-1896, 1989.
23. S. Chen, C. F. N. Cowan, and P. M. Grant, "Orthogonal least squares learning algorithm for radial basis function networks, " IEEE Transactions on Neural Networks, vol. 2, no. 2, pp. 302-309, 1991.
24. S. Chen and J. Wigger, "Fast orthogonal least squares algorithm for efcient subset model selection, " IEEE Transactions on Signal Processing, vol. 43, no. 7, pp. 1713-1715, 1995.
25. O. L. Mangasarian and D. R. Musicant, "Successive overrelax-ation for support vector machines, " IEEE Transactions on Neural Networks, vol. 10, no. 5, pp. 1032-1037, 1999.
26. K. Li, J. X. Peng, and E. Bai, "A two-stage algorithm for identifcation of nonlinear dynamic systems, " Automatica, vol. 42, no. 7, pp. 1189-1197, 2006.
27. S. Fahlman and C. Lebiere, "The cascade-correlation learning architecture, " in Advances in Neural Information Processing Systems 2, D. S. Touretzky, Ed., 1990.
28. C. Chang and C. Lin, "LIBSVM: a library for support vector machines, " Sofware, vol. 80, pp. 604-611, 2001, http://www.csie.ntu.edu.tw/ ∼cjlin/libsvm/.
29. K. Pelckmans, J. Suykens, T. van Gestel et al., "LSSVMlab: a matlab/C toolbox for least squares support vector machines, " in Tutorial, KULeuven-ESAT, Leuven, Belgium, 2002.
30. J. Garcke, M. Griebel, and M. Tess, "Data mining with sparse grids, " Computing, vol. 67, no. 3, pp. 225-253, 2001.
31. L. Breiman, "Arcing classifer (with discussion and a rejoinder by the author), " The Annals of Statistics, vol. 26, no. 3, pp. 801-849, 1998.
32. S. Chen, X. Hong, and C. J. Harris, "Regression based D-optimality experimental design for sparse kernel density estimation, " Neurocomputing, vol. 73, no. 4-6, pp. 727-739, 2010.