A Random Sampling Technique for Training Support Vector Machines

Random sampling techniques have been developed for combinatorial optimization problems. In this note, we report an application of one of these techniques for training support vector machines (more precisely, primal-form maximal-margin classifiers) that solve two-group classification problems by using hyperplane classifiers. Through this research, we are aiming (I) to design efficient and theoretically guaranteed support vector machine training algorithms, and (II) to develop systematic and efficient methods for finding "outliers", i.e., examples having an inherent error.

[1]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[2]  Federico Girosi,et al.  An improved training algorithm for support vector machines , 1997, Neural Networks for Signal Processing VII. Proceedings of the 1997 IEEE Signal Processing Society Workshop.

[3]  Emo Welzl,et al.  Random sampling in geometric optimization: new insights and applications , 2000, SCG '00.

[4]  Dimitri P. Bertsekas,et al.  Nonlinear Programming , 1997 .

[5]  Kenneth L. Clarkson,et al.  Las Vegas algorithms for linear and integer programming when the dimension is small , 1995, JACM.

[6]  Nello Cristianini,et al.  An introduction to Support Vector Machines , 2000 .

[7]  Ron Shamir,et al.  A randomized scheme for speeding up algorithms for linear and convex programming problems with high constraints-to-variables ratio , 1993, Math. Program..

[8]  Nello Cristianini,et al.  An Introduction to Support Vector Machines and Other Kernel-based Learning Methods , 2000 .

[9]  John C. Platt,et al.  Fast training of support vector machines using sequential minimal optimization, advances in kernel methods , 1999 .

[10]  Chih-Jen Lin,et al.  On the convergence of the decomposition method for support vector machines , 2001, IEEE Trans. Neural Networks.

[11]  Emo Welzl,et al.  A Simple Sampling Lemma: Analysis and Applications in Geometric Optimization , 2001, Discret. Comput. Geom..

[12]  R. Stephenson.  A and V , 1962, The British journal of ophthalmology.

[13]  O. Mangasarian,et al.  Optimization methods in massive data sets , 2002 .

[14]  Kristin P. Bennett,et al.  Duality and Geometry in SVM Classifiers , 2000, ICML.