A geometric approach to support vector regression

Neurocomputing

Volumn 55, Issue 1-2, 2003, Pages 79-108

  Bi, Jinbo ^a   Bennett, Kristin P ^a  

^a RENSSELAER POLYTECHNIC INSTITUTE   (United States)

Author keywords

Kernel methods; Nearest point algorithms; Regression; Support vector machines

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; MATHEMATICAL MODELS; PARAMETER ESTIMATION; REGRESSION ANALYSIS; VECTORS;

KERNEL MODEL;

COMPUTATIONAL GEOMETRY;

ALGORITHM; ARTICLE; CLASSIFICATION; CONTROLLED STUDY; DATA BASE; GEOMETRY; LEARNING; PARAMETER; PRIORITY JOURNAL; REGRESSION ANALYSIS;

EID: 0242288816     PISSN: 09252312     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0925-2312(03)00380-1     Document Type: Article

References (24)

1. P. L. Bartlett, The sample complexity of pattern classification with neural networks: the size of the weights is more important than the size of the network, IEEE Trans. Inf. Theory 44 (2) (1998) 525-536.
2. P. Bartlett, J. Shawe-Taylor, Generalization performance of support vector machines and other pattern classifiers, in: B.Schölkopf, C.J.C. Burges, A.J. Smola (Eds.), Advances in Kernel Methods - Support Vector Learning, MIT Press, Cambridge, USA, 1998.
3. M.S. Bazaraa, H.D. Sherali, C.M. Shetty, Nonlinear Programming - Theory and Algorithms, 2nd Edition, Wiley, New York, 1993.
4. K.P. Bennett, E.J. Bredensteiner, Duality and geometry in SVM classifiers, in: Proceedings of the 17th International Conference on Machine Learning, Morgan Kaufmann, San Francisco, CA, 2000, pp. 57-64.
5. J. Bi, K.P. Bennett, Duality, geometry, and support vector regression, in: T.G. Dietterich, S. Becker, Z, Ghahramani (Eds.), Advances in Neural Information Processing Systems, Vol. 14, MIT Press, Cambridge, MA, 2002, pp. 593-600.
6. D. Crisp, C.J.C. Burges, A geometric interpretation of v-SVM classifiers, in: S.A. Solla, M.S. Kearns, D.A. Cohn (Eds.), Advances in Neural Information Processing Systems, Vol. 11, MIT Press, Cambridge, MA, 1999, pp. 244-251.
7. N. Cristianini, J. Shawe-Taylor, An Introduction to Support Vector Machines, Cambridge University Press, Cambridge, UK, 2000.
8. A. Demiriz, K.P. Bennett, C.M. Breneman, M.J. Embrechts, Support vector machine regression in chemometrics, Computing Science and Statistics, Proceedings of the 33rd Symposium on the Interface, American Statistical Association for the Interface Foundation of North America, Washington, D.C., 2001.
9. H. Drucker, C.J.C. Burges, L. Kaufman, A. Smola, V. Vapnik, Support vector regression machines, in: M.C. Mozer, M.I. Jordan, T.Petsche, (Eds.), Advances in Neural Information Processing Systems, Vol. 9, MIT Press, Cambridge, MA, 1997, pp. 155-161.
10. E.G. Gilbert, Minimizing the quadratic form on a convex set, SIAM J. Control 4 (1966) 61-79.
11. E.G. Gilbert, D.W. Johnson, S.S. Keerthi, A fast procedure for computing the distance between complex objects in three dimensional space, IEEE J. Robotics Automat. 4 (1988) 193-203.
12. S.S. Keerthi, S.K. Shevade, C.Bhattacharyya, K.R.K. Murthy, A fast iterative nearest point algorithm for support vector machines, Technical Report TR-ISL-99-03, Intelligent Systems Lab, Indian Institute of Science, Bangalore 560 012, India, 1999. http://guppy.mpe.nus.edu.sg/~mpessk/npa.shtml.
13. S.S. Keerthi, S.K. Shevade, C.Bhattacharyya, K.R.K. Murthy, A fast iterative nearest point algorithm for support vector machine classifier design, IEEE Trans. Neural Networks 11 (1) (2000) 124-136.
14. A. Kowalczyk, Maximal margin perceptron, in: A.J. Smola, P. Bartlett, B. Schöelkopf, C.Schuurmans (Eds.), Advances in Large Margin Classifiers, MIT Press, Cambridge, MA, 1999, pp. 75-113.
15. O.L. Mangasarian, Nonlinear Programming, SIAM, Philadelphia, 1994.
16. B.F. Mitchell, V.F. Dem'yanov, V.N. Malozemov, Finding the point of a polyhedron closest to the origin, SIAM J. Control 12 (1974) 19-26.
17. J. Platt, Sequential minimal optimization: a fast algorithm for training support vector machines, in: B. Schölkopf, C.J.C. Burges, A.J. Smola (Eds.), Advances in Kernel Methods - Support Vector Learning, MIT Press, Cambridge, MA, 1999, pp. 185-208, http://www.research.microsoft.com/~jplatt/smo.html.
18. B. Schölkopf, B. Smola, R. Williamson, Shrinking the tube: a new support vector regression algorithm, in: S.A. Solla, M.S. Kearns, D.A. Cohn, (Eds.), Advances in Neural Information Processing Systems, Vol. 11, MIT Press, Cambridge, MA, 1999, pp. 330-336.
19. B. Schölkopf, A. Smola, R.C. Williamson, P.L. Bartlett, New support vector algorithms, Neural Comput. 12 (2000) 1207-1245.
20. J. Shawe-Taylor, N. Cristianini, Robust bounds on generalization from the margin distribution, NeuroCOLT2 NC2-TR-1998-029, Royal Holloway, University of London, London, UK, 1998.
21. V.N. Vapnik, The Nature of Statistical Learning Theory, Springer, New York, 1995.
22. V.N. Vapnik, Statistical Learning Theory, Wiley, New York, 1998.
23. G. Wahba, Spline Models for Observational Data, SIAM, Philadelphia, 1990.
24. R.C. Williamson, A.J. Smola, B. Schölkopf, Generalization performance of regularization networks and support vector machines via entropy numbers of compact operators, Technical Report NC-TR-98-019, Royal Holloway College, University of London, London, UK, 1998 http://www.neurocolt.com.