A Support Vector Machine with a Hybrid Kernel and Minimal Vapnik-Chervonenkis Dimension

IEEE Transactions on Knowledge and Data Engineering

Volumn 16, Issue 4, 2004, Pages 385-395

  Tan, Ying ^a   Wang, Jun ^b  

^a UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA   (China)

^b CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Hybrid kernel function; Hyperplane; Structural risk minimization; Support vector machines; VC dimension

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; NEURAL NETWORKS; PATTERN RECOGNITION; POLYNOMIALS; PROBLEM SOLVING; QUADRATIC PROGRAMMING; RADIAL BASIS FUNCTION NETWORKS; REAL TIME SYSTEMS; REGRESSION ANALYSIS;

HYBRID KERNEL FUNCTION; HYPERPLANE; STRUCTURAL RISK MINIMIZATION; SUPPORT VECTOR MACHINES; VC DIMENSION;

LEARNING SYSTEMS;

EID: 2142643698     PISSN: 10414347     EISSN: None     Source Type: Journal    
DOI: 10.1109/TKDE.2004.1269664     Document Type: Article

References (31)

1. V.N. Vapnik, The Nature of Statistical Learning Theory. New York: Springer Verlag, 1995.
2. B.E. Boser, I.M. Guyon, and V.N. Vapnik, "A Training Algorithm for Optimal Margin Classifiers," Proc. Fifth Ann. Workshop Computing Learning Theory, pp. 144-152, 1995.
3. V.N. Vapnik, "An Overview of Statistical Learning Theory," IEEE Trans. Neural Networks, vol. 10, no. 5, pp. 988-999, 1999.
4. C. Cortes and V.N. Vapnik, "Support-Vector Networks," Machine Learning, vol. 20, pp. 273-297, 1995.
5. B. Scholkopf, "Support Vector Learning," PhD dissertation, Technische Universitat Berlin, Germany, 1997.
6. V. Vapnik, S. Golowich, and A. Smola, "Support Vector Method for Function Approximation, Regression Estimation and Signal Processing," Advances in Neural Information Processing Systems, vol. 9, Cambridge, Mass.: MIT Press, 1997.
7. E. Osuna, R. Freund, and F. Girosi, "Training Support Vector Machines: An Application to Face Detection," Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 17-19, 1997.
8. M. Pontil and A. Verri, "Support Vector Machines for 3D Object Recognition," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 20, no. 6, pp. 637-646, 1998.
9. O.L. Mangasarian and D.R. Musicant, "Successive Overtaxation for Support Vector Machines," IEEE Trans. Neural Networks, vol. 10, no. 5, pp. 1032-1037, 1999.
10. B. Scholkopf, A. Smola, and K.-R. Muler, "Nonlinear Component Analysis as a Kernel Eigenvalue Problem," Neural Computation, vol. 10, pp. 1299-1319, 1998.
11. N. Aronszajn, "Theory of Reproducing Kernels," Trans. Am. Math. Soc., vol. 68, pp. 337-404, 1950.
12. J. Shawe-Taylor, P.L. Bartlett, R.C. Willianmson, and M. Anthony, "Structural Risk Minimization over Data-Dependent Hierarchies," IEEE Trans. Information Theory, vol. 44, no. 5, pp. 1926-1940, 1998.
13. B. Scholkopf, K. Sung, C.J.C. Burges, and F. Girosi, "Comparing Support Vector Machines with Gaussian Kernels to Radial Basis Function Classifiers," IEEE Trans. Signal Processing, vol. 45, no. 11, pp. 2758-2765, 1999.
14. B. Carl and I. Stephani, Entropy, Compactness, and the Approximation of Operators. Cambridge, UK: Cambridge Univ. Press, 1990.
15. C.J.C. Burges, "Simplified Support Vector Decision Rules," Proc. 13th Int'l Conf. Machine Learning, L. Saitta, ed., 1996.
16. C.J.C. Burges and B. Scholkopf, "Improving the Accuracy and Speed of Support Vector Machines," Proc. Neural Information Processing Systems, vol. 9, M. Mozer, M. Jordan, T. Petsche, eds., 1997.
17. J.A.K. Suykens and J. Vandewalle, "Training Multilayer Perceptron Classifiers Based on a Modified Support Vector Method," IEEE Trans. Neural Networks, vol. 10, no. 4, pp. 907-911, 1999.
18. T. Joachims, "Making Large-Scale SVM Learning Practical," Advances in Kernel Methods - Support Vector Learning, B. Scholkopf, C.J.C. Burges, and A.J. Smola, eds., Cambridge, Mass.: MIT Press, 1999.
19. J. Platt, "Sequential Minimal Optimization: A Fast Algorithm for Training Support Vector Machines," Advances in Kernel Methods - Support Vector Learning, B. Scholkopf, C.J.C. Burges, and A.J. Smola, eds., Cambridge, Mass.: MIT Press, pp. 185-208, 1999.
20. Y. Tan, Y. Xia, and J. Wang, "Neural Network Realization of Support Vector Machines for Pattern Classification," Proc. IEEE Int'l Joint Conf. Neural Networks, vol. 5, pp. 411-416, 2000.
21. D. Haussler, "Convolution Kernels over Discrete Structures," Technical Report, UCSC-CRL-99-10, Univ. of California in Santa Cruz, 2000. http://www.cse.ucsc.edu/haussler/convolutions.ps.
22. M. Cristianini, J. Shawe-Taylor, and C. Campbell, "Dynamically Adapting Kernels in Support Vector Machines," NIPS-98 or NeuroCOLT2 Technical Report Series NC2-TR-1998-017, Dept. of Engineering Mathematics, Univ. of Bristol, U.K., 1998. ftp://www.neurocolt.com/pub/neurocolt/tech_reports/ 1998/98017.ps.Z.
23. N. Cristianini and J. Shawe-Taylor, An Introduction to Support Vector Machines. Cambridge Univ. Press, 2000. http://www.suppor-vector.net.
24. T. Evgeniou, M. Pontil, and T. Poggio, "Regularization Networks and Support Vector Machines," Advances in Computational Mathematics, 2003. http://www.ai.mit.edu/people/theos/publications/reviewall.ps.
25. B. Scholkopf, C. Burges, and V. Vapnik, "Extracting Support Data for a Given Task," Proc. First Int'l Conf. Knowledge Discovery and Data Mining, U.M. Fayyad and R. Uthurusamy, eds., 1995.
26. S. Amari and S. Wu, "Improving Support Vector Machine Classifier by Modifying Kernel Functions," Neural Networks, vol. 12, pp. 783-789, 1999.
27. T. Mercer, "Functions of Positive and Negative Type and Their Connection with the Theory of Integral Equations," Philosophical Trans. of the Royal Soc. of London, Series A, pp. 415-446, 1909.
28. R.C. Williamson, A.J. Smola, and B. Scholkopf, "Generalization Performance of Regularization Networks and Support Vector Machines via Entropy Numbers of Compact Operators," Technical Report 19, NeuroCOLT, 1998. http://www.neurocolt.com.
29. C.A. Micchelli, "Interpolation of Scattered Data: Distance Matrices and Conditionally Positive Definite Functions," Constructive Approximation, vol. 2, pp. 11-22, 1986.
30. Y. LeCun et al., "Comparison of Learning Algorithms for Handwritten Digit Recognition," Proc. Int'l Conf. Artificial Neural Networks, pp. 53-60, 1995.
31. K. Duan, S. Sathiya Keerthi, and A. Neow Poo, "Evaluation of Simple Performance Measures for Tuning SVM Hyperparameters," http://guppy.mpe.nus. edu.sg/mpessk/comparison.shtml, 2002.