Training v-Support Vector Regression: Theory and Algorithms

We discuss the relation between-support vector regression (-SVR) and v-support vector regression (v-SVR). In particular, we focus on properties that are different from those of C-support vector classification (C-SVC) andv-support vector classification (v-SVC). We then discuss some issues that do not occur in the case of classification: the possible range of and the scaling of target values. A practical decomposition method forv-SVR is implemented, and computational experiments are conducted. We show some interesting numerical observations specific to regression.

[1]  S. Sathiya Keerthi,et al.  Convergence of a Generalized SMO Algorithm for SVM Classifier Design , 2002, Machine Learning.

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

[3]  Chih-Jen Lin,et al.  A Simple Decomposition Method for Support Vector Machines , 2002, Machine Learning.

[4]  Vladimir Vapnik,et al.  Statistical learning theory , 1998 .

[5]  Pavel Laskov,et al.  An Improved Decomposition Algorithm for Regression Support Vector Machines , 1999, NIPS.

[6]  David J. Crisp,et al.  A Geometric Interpretation of ?-SVM Classifiers , 1999, NIPS 2000.

[7]  James Theiler,et al.  Accurate On-line Support Vector Regression , 2003, Neural Computation.

[8]  Thorsten Joachims,et al.  Making large scale SVM learning practical , 1998 .

[9]  Pao-Ta Yu,et al.  Adaptive Two-Pass Median Filter Based on Support Vector Machines for Image Restoration , 2004 .

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

[11]  Bernhard Schölkopf,et al.  New Support Vector Algorithms , 2000, Neural Computation.

[12]  Gary William Flake,et al.  Efficient SVM Regression Training with SMO , 2002, Machine Learning.

[13]  Pavel Laskov,et al.  Feasible Direction Decomposition Algorithms for Training Support Vector Machines , 2002, Machine Learning.

[14]  Bernhard Schölkopf,et al.  Shrinking the Tube: A New Support Vector Regression Algorithm , 1998, NIPS.

[15]  David J. Spiegelhalter,et al.  Machine Learning, Neural and Statistical Classification , 2009 .

[16]  S. Keerthi,et al.  Improvements to SMO Algorithm for SVM Regression 1 , 1999 .

[17]  Federico Girosi,et al.  Training support vector machines: an application to face detection , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.