Abstract
Some important geometric properties of Support Vector Machines (SVM) have been studied in the last few years, allowing researchers to develop several algorithmic aproaches to the SVM formulation for binary pattern recognition. One important property is the relationship between support vectors and the Convex Hulls of the subsets containing the classes, in the separable case. We propose an algorithm for .nding the extreme points of the Convex Hull of the data points in feature space. The key of the method is the construction of the Convex Hull in feature space using an incremental procedure that works using kernel functions and with large datasets. We show some experimental results.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
V. Vapnik. The Nature of Statistical Learning Theory. Springer, New York, 1995.
C. Cortes and V. Vapnik. Support vector networks. Machine Learning, 20:273–297, 1995.
D. Caragea, A. Silvescu, and V. Honavar. Agents that learn from distributed dynamic data sources. In Proceedings at The Fourth International Conference on Autonomous Agents, pages 53–60, Barcelona, Catalonia, Spain, 2000.
N. A. Syed, H. Liu, and K. Kay Sung. Incremental learning with support vector machines. In J. Debenham, S. Decker, R. Dieng, A. Macintosh, N. Matta, and U. Reimer, editors, Proceedings of the Sixteenth International Joint Conference on arti.cial Intelligence IJCAI-99, Stockholm, Sweden, 1999.
C. Burges. Simplified support vector decision rules. In Lorenza Saitta, editor, Proceedings or the Thirteenth International Conference on Machine Learning, pages 71–77, Bari, Italia, 1996.
C. Burges. A tutorial on support vector machines for pattern recognition. Data Mining and Knowledge Discovery, 2(2):121–167, 1998.
E. Osuna and F. Girosi. Reducing the run-time complexity of support vector machines. Advances in Kernel Methods, Support Vector Learning, 1998.
K. Bennett and E. Bredensteiner. Duality and geometry in SVM classifiers. In Proc. 17th International Conf. on Machine Learning, pages 57–64. Morgan Kaufmann, San Francisco, CA, 2000.
K. Bennett and E. Bredensteiner. Geometry in learning. In C. Gorini, E. Hart, W. Meyer, and T. Phillips, editors, Geometry at Work, Washington, D.C., 1997. Mathematical Association of America.
S. S. Keerthi, S. K. Shevade, C. Bhattacharyya, and K. R. K. Murthy. A fast iterative nearest point algorithm for support vector machine classifier design. IEEE-NN, 11(1):124, 2000.
E. Osuna. Support Vector Machines: Trainig and Applications, PhD Thesis. MIT, Cambridge, 1998.
C.B. Barber, D.P. Dobkin, and H. Huhdanpaa. Quickhull algorithm for convex hulls. ACM Transactions on Mathematical Software, 22(4), 1996.
C. Bradford Barber, David P. Dobkin, and Hannu Huhdanpaa. The quickhull algorithm for convex hulls. ACM Transactions on Mathematical Software, 22(4):469–483, 1996.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Osuna, E., De Castro, O. (2002). Convex Hull in Feature Space for Support Vector Machines. In: Garijo, F.J., Riquelme, J.C., Toro, M. (eds) Advances in Artificial Intelligence — IBERAMIA 2002. IBERAMIA 2002. Lecture Notes in Computer Science(), vol 2527. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36131-6_42
Download citation
DOI: https://doi.org/10.1007/3-540-36131-6_42
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-00131-7
Online ISBN: 978-3-540-36131-2
eBook Packages: Springer Book Archive