Minimal kernel classifiers

Journal of Machine Learning Research

Volumn 3, Issue 2, 2003, Pages 303-321

  Fung, Glenn M ^a   Mangasarian, Olvi L ^a   Smola, Alexander J ^b  

^a University of Wisconsin Madison   (United States)

^b AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

Concave Minimization; Data Reduction; Sparse Kernels; Support Vector Machines

Indexed keywords

COMPUTER SCIENCE; DATA REDUCTION; LEARNING ALGORITHMS; LINEAR PROGRAMMING;

SUPPORT VECTOR MACHINES;

LEARNING SYSTEMS;

EID: 0042466486     PISSN: 15324435     EISSN: None     Source Type: Journal    
DOI: 10.1162/153244303765208403     Document Type: Article

References (44)

1. A. Blumer, A. Ehrenfeucht, D. Haussler, and M. K. Warmuth. Occam's razor. Information Processing Letters, 24:377-380, 1987
2. L. Bottou, C. Cortes, J. Denker, H. Drucker, I. Guyon, L. Jackel, Y. LeCun, U. Muller, E. Sackinger, P. Simard, and V. Vapnik. Comparison of classifier methods: A case study in handwriting digit recognition. In International Conference on Pattern Recognition, pages 77-87. IEEE Computer Society Press, 1994.
3. P. S. Bradley and O. L. Mangasarian. Feature selection via concave minimization and support vector machines. In J. Shavlik, editor, Machine Learning Proceedings of the Fifteenth International Conference(ICML '98), pages 82-90, San Francisco, California, 1998. Morgan Kaufmann, ftp://ftp.cs.wisc.edu/math-prog/tech-reports/98-03.ps.
4. P. S. Bradley and O. L. Mangasarian. Massive data discrimination via linear support vector machines. Optimization Methods and Software, 13:1-10, 2000. ftp://ftp.cs.wisc.edu/math-prog/tech-reports/98-03.ps.
5. P. S. Bradley, O. L. Mangasarian, and J. B. Rosen. Parsimonious least norm approximation. Computational Optimization and Applications, 11(1):5-21, October 1998a. ftp://ftp.cs.wisc.edu/math-prog/tech-reports/97-03.ps.
6. P. S. Bradley, O. L. Mangasarian, and W. N. Street. Clustering via concave minimization. In M. C. Mozer, M. I. Jordan, and T. Petsche, editors, Advances in Neural Information Processing Systems -9-, pages 368-374, Cambridge, MA, 1997. MIT Press. ftp://ftp.cs.wisc.edu/math-prog/tech-reports/96-03.ps.
7. P. S. Bradley, O. L. Mangasarian, and W. N. Street. Feature selection via mathematical programming. INFORMS Journal on Computing, 10(2):209-217, 1998b. ftp://ftp.cs.wisc.edu/math-prog/tech-reports/95-21.ps.
8. V. Cherkassky and F. Mulier. Learning from Data - Concepts, Theory and Methods. John Wiley & Sons, New York, 1998.
9. Using the CPLEX(TM) Linear Optimizer and CPLEX(TM) Mixed Integer Optimizer (Version 2.0). CPLEX Optimization Inc., Incline Village, Nevada, 1992.
10. N. Cristianini and J. Shawe-Taylor. An Introduction to Support Vector Machines. Cambridge University Press, Cambridge, 2000.
11. G. B. Dantzig. Linear Programming and Extensions. Princeton University Press, Princeton, New Jersey, 1963.
12. M. C. Ferris and T. S. Munson. Interior point methods for massive support vector machines. Technical Report 00-05, Computer Sciences Department, University of Wisconsin, Madison, Wisconsin, May 2000. ftp://ftp.cs.wisc.edu/pub/dmi/tech-reports/00-05.ps.
13. G. Fung and O. L. Mangasarian. Data selection for support vector machine classification. In R. Ramakrishnan and S. Stolfo, editors, Proceedings KDD-2000: Knowledge Discovery and Data Mining, August 20-23, 2000, Boston, MA, pages 64-70, New York, 2000. Asscociation for Computing Machinery, ftp://ftp.cs.wisc.edu/pub/dmi/tech-reports/00-02.ps.
14. G. Fung and O. L. Mangasarian. Proximal support vector machine classifiers. In F. Provost and R. Srikant, editors, Proceedings KDD-2001: Knowledge Discovery and Data Mining, August 26-29, 2001, San Francisco, CA, pages 77-86, New York, 2001. Asscociation for Computing Machinery, ftp://ftp.cs.wisc.edu/pub/dmi/tech-reports/01-02.ps.
15. G. Fung and O. L. Mangasarian. Incremental support vector machine classification. In H. Mannila R. Grossman and R. Motwani, editors, Proceedings of the Second SIAM International Conference on Data Mining, Arlington, Virginia, April 11-13, 2002, pages 247-260, Philadelphia, 2002. SIAM. ftp://ftp.cs.wisc.edu/pub/dmi/tech-reports/01-08.ps.
16. T. K. Ho and E. M. Kleinberg. Building projectable classifiers of arbitrary complexity. In Proceedings of the 13th International Conference on Pattern Recognition, pages 880-885, Vienna, Austria, 1996a. http://cm.bell-labs.com/who/tkh/pubs.html. Checker dataset at: ftp://ftp.cs.wisc.edu/math-prog/cpo-dataset/machine-learn/checker.
17. T. K. Ho and E. M. Kleinberg. Checkerboard dataset, 1996b. http://www.cs.wisc.edu/math-prog/mpml.html.
18. T. S. Jaakkola and D. Haussler. Probabilistic kernel regression models. In Proceedings of the 1999 Conference on AI and Statistics, San Mateo, CA, 1999. Morgan Kaufmann.
19. Y.-J. Lee and O. L. Mangasarian. RSVM: Reduced support vector machines. Technical Report 00-07, Data Mining Institute, Computer Sciences Department, University of Wisconsin, Madison, Wisconsin, July 2000. Proceedings of the First SIAM International Conference on Data Mining, Chicago, April 5-7, 2001, CD-ROM Proceedings. ftp://ftp.cs.wisc.edu/pub/dmi/tech-reports/00-07.ps.
20. Yuh-Jye Lee and O. L. Mangasarian. SSVM: A smooth support vector machine. Computational Optimization and Applications, 20:5-22, 2001. Data Mining Institute, University of Wisconsin, Technical Report 99-03. ftp://ftp.cs.wisc.edu/pub/dmi/tech-reports/99-03.ps.
21. O. L. Mangasarian. Nonlinear Programming. SIAM, Philadelphia, PA, 1994
22. O. L. Mangasarian. Machine learning via polyhedral concave minimization. In H. Fischer, B. Riedmueller, and S. Schaefler, editors, Applied Mathematics and Parallel Computing Festschrift for Klaus Ritter, pages 175-188. Physica-Verlag A Springer-Verlag Company, Heidelberg, 1996. ftp://ftp.cs.wisc.edu/math-prog/tech-reports/95-20.ps.
23. O. L. Mangasarian. Arbitrary-norm separating plane. Operations Research Letters, 24: 15-23, 1999a. ftp://ftp.cs.wisc.edu/math-prog/tech-reports/97-07r.ps.
24. O. L. Mangasarian. Minimum-support solutions of polyhedral concave programs. Optimization, 45:149-162, 1999b. ftp://ftp.cs.wisc.edu/math-prog/tech-reports/97-05.ps.
25. O. L. Mangasarian. Generalized support vector machines. In A. Smola, P. Bartlett, B. Schölkopf, and D. Schuurmans, editors, Advances in Large Margin Classifiers, pages 135-146, Cambridge, MA, 2000. MIT Press, ftp://ftp.cs.wisc.edu/math-prog/tech-reports/98-14.ps.
26. O. L. Mangasarian and R. R. Meyer. Nonlinear perturbation of linear programs. SIAM Journal on Control and Optimization, 17(6):745-752, November 1979.
27. O. L. Mangasarian and D. R. Musicant. Robust linear and support vector regression. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(9):950-955, 2000. ftp://ftp.cs.wisc.edu/pub/dmi/tech-reports/99-09.ps.
28. O. L. Mangasarian and D. R. Musicant. Active support vector machine classification. In Todd K. Leen, Thomas G. Dietterich, and Volker Tresp, editors, Advances in Neural Information Processing Systems 18, pages 577-583, Cambridge, MA, 2001a. MIT Press. ftp://ftp.cs.wisc.edu/pub/dmi/tech-reports/00-04.ps.
29. O. L. Mangasarian and D. R. Musicant. Lagrangian support vector machines. Journal of Machine Learning Research, 1:161-177, 2001b. ftp://ftp.cs.wisc.edu/pub/dmi/tech-reports/00-06.ps.
30. O. L. Mangasarian and D. R. Musicant. Large scale kernel regression via linear programming. Machine Learning, 46:255-269, 2002. ftp://ftp.cs.wisc.edu/pub/dmi/tech-reports/99-02.ps.
31. MATLAB. User's Guide. The MathWorks, Inc., Natick, MA 01760, 1994-2001. http://www.mathworks.com.
32. T. M. Mitchell. Machine Learning. McGraw-Hill, Boston, 1997.
33. P. M. Murphy and D. W. Aha. UCI machine learning repository, 1992. www.ics.uci.edu/̃mlearn/MLRepository.html.
34. M. Opper and O. Winther. Gaussian processes and SVM: Mean field and leave-one-out. In A. Smola, P. Bartlett, B. Schölkopf, and D. Schuurmans, editors, Advances in Large Margin Classifiers, pages 311-326, Cambridge, MA, 2000. MIT Press.
35. J. Rissanen. Stochastic complexity and modeling. Annals of Statistics, 14:1080-1100, 1986.
36. R. T. Rockafellar. Convex Analysis. Princeton University Press, Princeton, New Jersey, 1970.
37. B. Schölkopf, C. Burges, and A. Smola (editors). Advances in Kernel Methods: Support Vector Machines. MIT Press, Cambridge, MA, 1999. ISBN 0-262-19416-3.
38. A. Smola, P. L. Bartlett, B. Schölkopf, and J. Schuurmann (editors). Advances in Large Margin Classifiers. MIT Press, Cambridge, MA, 2000.
39. Alex J. Smola and Bernhard Schölkopf. Sparse greedy matrix approximation for machine learning. In Proc. 17th International Conf. on Machine Learning, pages 911-918. Morgan Kaufmann, San Francisco, CA, 2000. URL citeseer.nj.nec.com/smola00sparse.html.
40. M. Tipping. The relevance vector machine. In S. A. Solla, T. K. Leen, and K.-R. Müller, editors, Advances in Neural Information Processing Systems, volume 12, pages 652-658, Cambridge, MA, 2000. MIT Press.
41. V. N. Vapnik. The Nature of Statistical Learning Theory. Springer, New York, second edition, 2000.
42. V. N. Vapnik and O. Chapelle. Bounds on expectation for SVM. In A. Smola, P. Bartlett, B. Schölkopf, and D. Schuurmans, editors, Advances in Large Margin Classifiers, pages 261-280, Cambridge, MA, 2000. MIT Press.
43. J. Weston and R. Herbrich. Adaptive margin support vector machines. In A. Smola, P. Bartlett, B. Schölkopf, and D. Schuurmans, editors, Advances in Large Margin Classifiers, pages 281-295, Cambridge, MA, 2000. MIT Press.
44. Y. Ye. Interior Point Algorithms Theory and Analysis. John Wiley & Sons, New York, 1997.