Efficient regularized least squares classification

IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops

Volumn 2004-January, Issue January, 2004, Pages

  Zhang, Peng ^a   Peng, Jing ^a  

^a TULANE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

KERNEL TRICK; LEASTSQUARE ALGORITHM; MATHEMATICAL FOUNDATIONS; PERFORMANCE; REGULARIZED LEAST SQUARES; REPRODUCING KERNEL HILBERT SPACES; SIMPLE++; SPARSE REPRESENTATION; STRUCTURE RISK MINIMIZATION PRINCIPLES; SUPPORT VECTORS MACHINE;

SUPPORT VECTOR MACHINES;

EID: 84932622260     PISSN: 21607508     EISSN: 21607516     Source Type: Conference Proceeding    
DOI: 10.1109/CVPR.2004.331     Document Type: Conference Paper

References (36)

1. I. M. Author, 'Some Related Article I Wrote, ' Some Fine Journal, Vol. 17, pp. 1-100, 1987.
2. A. N. Expert, A Book He Wrote, His Publisher, 1989.
3. G. Baudat and F. Anouar. Generalized discriminant analysis using akernel approach. Neural Computation, Vol. 12, pp. 2385-2404, 2000.
4. M. Bertero, T. Poggio, and T. Torre. Ill-posed problems in early vision. Proceedings of the IEEE, 76(8):869-889, 1988.
5. C. Bishop. Neural Networks for Patt ern Recognition. Oxford University Press, 1995.
6. C. J. C. Burges. A tutorial on support vector machines for pattern recognition. Data Mining and Knowledge Discovery, 2(2):121-167, 1998.
7. P. Burman. A comparative study of ordinary cross-validation, v-fold cross-validation and the repeated learning-testing methods. Biometrika, 76(3):503-514, 1989.
8. C.-C. Chang and C.-J. Lin. LIBSVM : a library for support vector machines, 2001.
9. O. Chapelle and V. Vapnik. Model selection for support vector machines. In Advances in Neural Information Processing Systems, 2000.
10. S. Coppersmith and S. Winograd. On the asymptotic complexity of matrix multiplocation. SIAM Journal on Computing, 11(3):472-492, Aug. 1982.
11. N. Cristianini and J. Shawe-Taylor. An Introduction to Support Vector Machines and other kernel-based learning methods. Cambridge University Press, Cambridge, UK, 2000.
12. F. Cucker and S. Smale . On the mathematical foundations of learning. Bulletin of the American Mathematical society, pages 1-49, October 2001.
13. G. Fung and O. L. Mangasarian. Proximal support vector machine class ifiers. In Knowledge Discovery in Databases, pages 77-86, 2001.
14. G. Golub and C. V. Loan. Matrix Computations. John Hopkins University Press, 1989.
15. T. Hastie, R. Tibshirani, and J. Friedman. The Elements of Statistical Learning. Springer-Verlag, Basel, 2001.
16. A. Hoerl and R. Kennard. Ridge regression: biased estimation for non orthogonal problems. Technometrics, 12(1):55-82, 1970.
17. V. Ivanov. The Theory of Approximate Methods and Their Application to the Numerical Solution of Singular Integral Equations. Nordhoff International, 1976.
18. M. Kearns. A bound on the error of cross validation using the approximation and estimation rates, with consequences for the training-te st split. Neural Computation, 9(5):43-1161, 1997.
19. D. MacKay. The evidence framework applied to classification networks. Neural Computation, 4:698-714, 1992.
20. V. Morozov. Methods for Solving Incorrectly Posed Problems. Springer-Verlag, 1984.
21. T. Poggio and F. Girosi. Networks for approximation and learning. Proceedings of the IEEE, 78:1481-1497, 1988.
22. T. Poggio and S. Smale. The mathematics of learning: Dealing with data. Notices of the AMS, 50(5):537-544, May 2003.
23. R. Rifkin. Everything Old is New Again: A Fresh Look at Historical Approaches to Machine Learning. Ph.D. Thesis, MIT, 2002.
24. J. Rissanen. Modelling by shortest data description. Automatica, 14:465-471, 1978.
25. B. Schölkopf. The kernel trick for distances. In T. K. Leen, T. G. Dietterich, and V. Tresp, editors, Advanc es in Neural Information Processing Systems, volume 13, pages 301-307. The MIT Press, 2001.
26. B. Scholkopf, C. J. C. Burges, and A. J. Smola, editors. Advances in kernel methods: support vector learning. MIT Press, Cambridge, MA, 1999.
27. B. Scholkopf and etal. Input space versus feature space in kernel-based methods. IEEE Transactions on Neural Networks, 10(5):1000-1017, September 1999.
28. B. Scholkopf and A. Smola. Learning with Kernels. MIT Press, Cambridge, MA., 2002.
29. L. Schumaker. Spline Functions: Basic Theory. NewYork: Wiley, 1981.
30. G. Stewart. Introduction to Matrix Computations. Academic Press, INC, 1973.
31. M. Stone. Cross-validatory choice and assessment of statistical predictions. J. Royal Statist. Soc. Ser. B, 36:111-147, 1974.
32. V. Strassen. Gaussian elimination is not optimal. Numerical Mathematics, 13:354-356, 1969.
33. J. Suykens and et al. Least Squares Support Vecto r Machines. World Scientific, Singapore, 2002.
34. A. N. Tikhonov and V. Y. Arsenin. Solutions of Ill-posed problems. John Wiley and Sons, Washington D.C., 1977.
35. V. N. Vapnik. Statistical Learning Theory. John Wiley and Sons, New York, 1998.
36. G. Wahba. Splines models for observational data. Series in Applied Mathematics, 59, 1990.