An efficient kernel matrix evaluation measure

Pattern Recognition

Volumn 41, Issue 11, 2008, Pages 3366-3372

  Nguyen, Canh Hao ^a   Ho, Tu Bao ^a  

^a JAPAN ADVANCED INSTITUTE OF SCIENCE AND TECHNOLOGY   (Japan)

Author keywords

Class separability measure; Classification; Kernel matrix quality measure; Kernel methods; Kernel target alignment

Indexed keywords

KERNEL MATRICES; MODEL SELECTIONS;

MATRIX ALGEBRA;

EID: 48149084956     PISSN: 00313203     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.patcog.2008.04.005     Document Type: Article

References (27)

1. Schölkopf B., and Smola A.J. Learning with Kernels (2002), MIT Press, Cambridge, MA
2. Shawe-Taylor J., and Cristianini N. Kernel Methods for Pattern Analysis (2004), Cambridge University Press, New York, NY, USA
3. Vapnik N.V. The Nature of Statistical Learning Theory (2000), Springer, New York, NY
4. Schölkopf B., Smola A.J., and Müller K.-R. Kernel principal component analysis. Advances in kernel methods: support vector learning (1999) 327-352
5. Wahba G. Spline Models for Observational Data. CBMS-NSF Regional Conference Series in Applied Mathematics vol. 59 (1990), SIAM, Philadelphia
6. Fine S., and Scheinberg K. Efficient SVM training using low-rank kernel representations. J. Mach. Learn. Res. 2 (2002) 243-264
7. Ong C.S., Smola A.J., and Williamson R.C. Learning the kernel with hyperkernels. J. Mach. Learn. Res. 6 (2005) 1043-1071
8. Cristianini N., Shawe-Taylor J., Elisseeff A., and Kandola J. On kernel-target alignment. In: Dietterich T.G., Becker S., and Ghahramani Z. (Eds). Advances in Neural Information Processing Systems (2001), MIT Press, Cambridge, MA
9. Lanckriet G.R.G., Cristianini N., Bartlett P., Ghaoui L.E., and Jordan M.I. Learning the kernel matrix with semidefinite programming. J. Mach. Learn. Res. 5 (2004) 27-72
10. Neumann J., Schnorr C., and Steidl G. Combined SVM-based feature selection and classification. Mach. Learn. 61 1-3 (2005) 129-150
11. Wu M., and Farquhar J. A subspace kernel for nonlinear feature extraction. In: Veloso M.M. (Ed). International Conference on Artificial Intelligence (2007) 1125-1130
12. Kwok J.T., and Tsang I.W. Learning with idealized kernels. International Conference on Machine Learning (2003) 400-407
13. Crammer K., Keshet J., and Singer Y. Kernel design using boosting. Advances in Neural Information Processing Systems (2002) 537-544
14. Kandola J., Cristianini N., and Shawe-Taylor J. Learning semantic similarity. Advances in Neural Information Processing Systems vol. 15 (2003)
15. Kandola J., and Shawe-Taylor J. Refining kernels for regression and uneven classification problems. In: Bishop C., and Frey B. (Eds). Proceedings of the Ninth International Workshop on Artificial Intelligence and Statistics (2003)
16. Boyd S., and Vandenberghe L. Convex Optimization (2004), Cambridge University Press, New York, NY, USA
17. Meila M. Data centering in feature space. In: Bishop C.M., and Frey B.J. (Eds). Ninth International Workshop on Artificial Intelligence and Statistics (2003)
18. Gradshteyn I.S., and Ryzhik I.M. Table of Integrals, Series, and Products (2000), Academic Press, San Diego, CA
19. Gartner T., Lloyd J.W., and Flach P.A. Kernels and distances for structured data. Mach. Learn. J. 57 3 (2004) 205-232
20. Jebara T., Kondor R., and Howard A. Probability product kernels. J. Mach. Learn. Res. 5 (2004) 819-844
21. Feller W. An Introduction to Probability Theory and its Applications vol. 2 (1971), Wiley, New York
22. Japkowicz N., and Stephen S. The class imbalance problem: a systematic study. Intell. Data Anal. 6 5 (2002) 429-449
23. Lanckriet G.R.G., Ghaoui L.E., Bhattacharyya C., and Jordan M.I. A robust minimax approach to classification. J. Mach. Learn. Res. 3 (2002) 555-582
24. L. Wang, K.L. Chan, Learning kernel parameters by using class separability measure, in: Advances in Neural Information Processing Systems, Sixth workshop on Kernel Machines, Canada, 2002.
25. Fukunaga K. Introduction to Statistical Pattern Recognition. second ed. (1990), Academic Press, New York
26. Globerson A., and Roweis S. Metric learning by collapsing classes. In: Weiss Y., Schölkopf B., and Platt J. (Eds). Advances in Neural Information Processing Systems vol. 18 (2006), MIT Press, Cambridge, MA 451-458
27. Mika S., Rätsch G., Weston J., Schölkopf B., and Müller K.-R. Fisher discriminant analysis with kernels. In: Hu Y.-H., Larsen J., Wilson E., and Douglas S. (Eds). Neural Networks for Signal Processing IX (1999), IEEE 41-48