Data mining via support vector machines

IFIP Advances in Information and Communication Technology

Volumn 130, Issue , 2003, Pages 91-112

  Mangasarian, O L ^a  

^a University of Wisconsin   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DATA MINING; LAGRANGE MULTIPLIERS; MATHEMATICAL PROGRAMMING; NEWTON-RAPHSON METHOD; NONLINEAR EQUATIONS;

DATA CLASSIFICATION; ITERATIVE SCHEMES; KERNEL CLASSIFIERS; LAGRANGIAN; SUPPORT VECTOR MACHINE (SVMS);

SUPPORT VECTOR MACHINES;

EID: 84904311732     PISSN: 18684238     EISSN: None     Source Type: Book Series    
DOI: None     Document Type: Conference Paper

References (39)

1. L. Armijo. Minimization of functions having Lipschitz-continuous first partial derivatives. Pacific Journal of Mathematics, 16:1-3, 1966.
2. K. P. Bennett and O. L. Mangasarian. Robust linear programming discrimination of two linearly inseparable sets. Optimization Methods and Software, 1:23-34, 1992.
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/mathprogjtech- 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. C. J. C. Burges. A tutorial on support vector machines for pattern recognition. Data Mining and Knowledge Discovery, 2(2):121-167, 1998.
6. B. Chen and P. T. Harker. Smooth approximations to nonlinear complementarity problems. SIAM Journal of Optimization, 7:403-420, 1997.
7. Chunhui Chen and O. L. Mangasarian. Smoothing methods for convex inequalities and linear complementarity problems. Mathematical Programming, 71(1):51-69, 1995.
8. Chunhui Chen and O. L. Mangasarian. A class of smoothing functions for nonlinear and mixed complementarity problems. Computational Optimization and Applications, 5(2):97-138, 1996.
9. X. Chen, L. Qi, and D. Sun. Global and superlinear convergence of the smoothing Newton method and its application to general box constrained variational inequalities. Mathematics of Computation, 67:519-540, 1998.
10. X. Chen and Y. Ye. On homotopy-smoothing methods for variational inequalities. SIAM Journal on Control and Optimization, 37:589-616, 1999.
11. V. Cherkassky and F. Mulier. Learning from Data - Concepts, Theory and Methods. John Wiley & Sons, New York, 1998.
12. P. W. Christensen and J.-S. Pang. Frictional contact algorithms based on semismooth Newton methods. In Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, M. Fukushima and L. Qi, (editors), pages 81-116, Dordrecht, Netherlands, 1999. Kluwer Academic Publishers.
13. R. Courant and D. Hilbert. Methods of Mathematical Physics. Interscience Publishers, New York, 1953.
14. CPLEX Optimization Inc., Incline Village, Nevada. Using the CPLEX(TM) Linear Optimizer and CPLEX(TM) Mixed Integer Optimizer (Version 2.0), 1992.
15. M. Frank and P. Wolfe. An algorithm for quadratic programming. Naval Research Logistics Quarterly, 3:95-110, 1956.
16. M. Fukushima and L. Qi. Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1999.
17. G. H. Golub and C. F. Van Loan. Matrix Computations. The John Hopkins University Press, Baltimore, Maryland, 3rd edition, 1996.
18. 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, 1996. http:/ /cm.belllabs. com/who/tkh/pubs.html. Checker dataset at: ftp:/ /ftp.cs.wisc.edu/mathprog/ cpo-dataset /machine-learn/ checker.
19. L. Kaufman. Solving the quadratic programming problem arising in support vector classification. In B. Schi:ilkopf, C. J. C. Burges, and A. J. Smola, editors, Advances in Kernel Methods - Support Vector Learning, pages 147-167. MIT Press, 1999.
20. 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.
21. 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.
22. O. L. Mangasarian. Nonlinear Programming. McGraw-Hill, New York, 1969. Reprint: SIAM Classic in Applied Mathematics 10, 1994, Philadelphia.
23. O. L. Mangasarian. Mathematical programming in neural networks. ORSA Journal on Computing, 5(4):349-360, 1993.
24. O. L. Mangasarian. Nonlinear Programming. SIAM, Philadelphia, PA, 1994.
25. O. L. Mangasarian. Generalized support vector machines. In A. Smola, P. Bartlett, B. Schi:ilkopf, 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 D. R. Musicant. Successive overrelaxation for support vector machines. IEEE Transactions on Neural Networks, 10:1032-1037, 1999. ftp:/ /ftp.cs.wisc.edu/math-prog/tech-reports/98-18.ps.
27. O. L. Mangasarian and D. R. Musicant. Data discrimination via nonlinear generalized support vector machines. In M. C. Ferris, 0. L. Mangasarian, and J.-S. Pang, editors, Complementarity: Applications, Algorithms and Extensions, pages 233-251, Dordrecht, January 2001. Kluwer Academic Publishers. ftp:/ /ftp.cs.wisc.edu/math-prog/tech-reports/99-03.ps.
28. O. L. Mangasarian and D. R. Musicant. Lagrangian support vector machines. Journal of Machine Learning Research, 1:161-177, 2001. ftp:/ /ftp.cs.wisc.edu/pub/dmi/tech-reports/00-06.ps.
29. 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.
30. O. L. Mangasarian and M. V. Solodov. Nonlinear complementarity as unconstrained and constrained minimization. Mathematical Programming, Series B, 62:277-297, 1993.
31. O. L. Mangasarian, W. N. Street, and W. H. Wolberg. Breast cancer diagnosis and prognosis via linear programming. Operations Research, 43(4):570-577, July-August 1995.
32. MATLAB. User's Guide. The MathWorks, Inc., Natick, MA 01760, 1994-2001. http:/ /www.mathworks.com.
33. T. M. Mitchell. Machine Learning. McGraw-Hill, Boston, 1997.
34. P. M. Murphy and D. W. Aha. UCI machine learning repository, 1992. www.ics. uci.edu/ mlearn/MLRepository.html.
35. B. Schöilkopf. Support Vector Learning. R. Oldenbourg Verlag, Munich, 1997.
36. M. Stone. Cross-validatory choice and assessment of statistical predictions. Journal of the Royal Statistical Society, 36:111-147, 1974.
37. P. Tseng. Analysis of a non-interior continuation method based on ChenMangasarian smoothing functions for complementarity problems. In Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, M. Fukushima and L. Qi, (editors), pages 381-404, Dordrecht, Netherlands, 1999. Kluwer Academic Publishers.
38. V. N. Vapnik. The Nature of Statistical Learning Theory. Springer, New York, 1995.
39. P. Wolfe. A duality theorem for nonlinear programming. Quarterly of Applied Mathematics, 19:239-244, 1961.