Feature scaling for kernel fisher discriminant analysis using leave-one-out cross validation

Neural Computation

Volumn 18, Issue 4, 2006, Pages 961-978

  Bo, Liefeng ^a   Wang, Ling ^a   Jiao, Licheng ^a  

^a XIDIAN UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33645727457     PISSN: 08997667     EISSN: 1530888X     Source Type: Journal    
DOI: 10.1162/neco.2006.18.4.961     Document Type: Article

References (28)

1. Aronszajn, N. (1950). Theory of reproducing kernels. Transactions of the American Mathematical Society, 68, 337-404.
2. Bengio, Y. (2000). Gradient-based optimization of hyper-parameters. Neural Computation, 12, 1889-1900.
3. Blake, C. L., & Merz, C. J. (1998). UCI repository of machine learning databases. Irvine, CA: University of California, Department of Information and Computer Science. Available online at http://www.ics.uci.edu/ ~mlearn/MLRepository.html.
4. Cawley, G. C., & Talbot, N. L. C. (2003). Efficient leave-one-out cross validation of kernel Fisher discriminant classifiers. Pattern Recognition, 36, 2585-2592.
5. Chapelle, O., Vapnik, V., Bousquet, O., & Mukherjee, S. (2002). Choosing multiple parameters for support vector machines. Machine Learning, 46, 131-159.
6. Figueiredo, M. A. T. (2003). Adaptive sparseness for supervised learning. IEEE Transactions on Pattern Analysis and Machine. Intelligence, 25, 1150-1159.
7. Fisher, R. A. (1936). The use of multiple measurements in taxonomic problems. Annual of Eugenics, 7, 179-188.
8. Fukunaga, K. (1990). Introduction to statistical pattern recognition (2nd ed.). Orlando, FL. Academic Press.
9. Gestel, T. V., Suykens, J., Lanckriet, C., Lambrechts, A., Moor, B. D., & Vandewalle, J. (2002). Bayesian framework for least squares support vector machine classifiers, gaussian processes and kernel Fisher discriminant analysis. Neural Computation, 15, 1115-1148.
10. Hsu, C. W., & Lin, C. J. (2002). A comparison of methods for multiclass support vector machines. IEEE Transactions on Neural Networks, 13, 415-425.
11. Krishnapuram, B., Hartemink, A., Carin, L., & Figueiredo, M. (2004). A Bayesian approach to joint feature selection and classifier design. IEEE Transactions on Pattern Analysis and Machine Intelligence, 26, 1105-1111.
12. Lanckriet, G. R. G., Cristianini, N., Bartlett, P., Ghaoui, L. E., & Jordan, M. I. (2004). Learning the kernel matrix with semidefinite programming, Journal of Machine Learning Research, 5, 27-72.
13. Lowe, D. (1995). Similarity metric learning for a variable-kernel classifier, Neural Computation, 7, 72-85.
14. Luntz, A., & Brailovsky, V. (1969). On estimation of characters obtained in statistical procedure of recognition. (In Russian). Techicheskaya Kibernetica, 3.
15. Mika, S. (2002). Kernel fisher discriminants. Unpublished doctoral dissertation, University of Technology, Berlin.
16. Mika, S., Ratsch, G., & Weston, J. (1999). Fisher discriminant analysis with kernels. In Proceedings of the IEEE Workshop on Neural Networks for Signal Processing (pp. 41-48). Piscataway, NJ: IEEE Press.
17. Ong, C. S., & Smola, A. J. (2003). Machine learning with hyperkernels. In Proceedings of the Twentieth International Conference on Machine Learning (pp. 568-575). Menlo Park, CA: AAAI Press.
18. Rätsch, G. (2001). Robust boosting via convex optimization. Unpublished doctoral dissertation, University of Potsdam, Potsdam, Germany.
19. Rifkin, R., & Klautau, A. (2004). In defense of one-vs-all classification. Journal of Machine Learning Research, 5, 101-141.
20. Schölkopf, B., & Smola, A. J. (2002). Learning with kernels. Cambridge, MA: MIT Press.
21. Suykens, J. A. K., & Vandewalle, J. (1999). Least squares support vector machine classifiers, Neural Processing Letters, 9, 293-300.
22. Tipping, M. E. (2001). Sparse Bayesian learning and the relevance vector machine. Journal Machine Learning Research, 1, 211-244.
23. Vapnik, V. (1995). The nature, of statistical learning theory. New York: Springer-Verlag.
24. Vapnik, V. (1998). Statistical learning theory, New York: Wiley.
25. Vapnik, V., & O. Chapelle. (2000). Bounds on error expectation for support vector machines. Neural Computation, 12, 2013-2036.
26. Weston, J., Mukherjee, M., Chapelle, O., Pontil, M., Poggio, T., & Vapnik, V. (2001). Feature selection for SVMs. In T. K. Leen, T. G. Dietterich, & V. Tresp (Eds.), Advances in neural information processing systems, 13 (pp. 668-674), Cambridge, MA: MIT Press.
27. Williams, C. K. I., & Barber, D. (1998). Bayesian classification with gaussian processes. IEEE Transactions on Pattern Analysis and Machine Intelligence, 20, 1342-1351.
28. Xu, J., Zhang, X., & Li, Y. (2001). Kernel MSE algorithm: A unified framework for KFD, LS-SVM and KRR. In Proceedings of the International Joint Conference on Neural Networks (pp. 1486-1491). Piscataway, NJ: IEEE Press.