From Regression to Classification in Support Vector Machines

Authors:
Massimiliano Pontil;Ryan Rifkin;Theodoros Evgeniou
Affiliations:
-;-;-
Venue:
From Regression to Classification in Support Vector Machines
Year:
1998

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A Short Review of Statistical Learning Theory

WIRN VIETRI 2002 Proceedings of the 13th Italian Workshop on Neural Nets-Revised Papers

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Abstract

We study the relation between support vector machines (SVMs) for regression (SVMR) and SVM for classification (SVMC). We show that for a given SVMC solution there exists a SVMR solution which is equivalent for a certain choice of the parameters. In particular our result is that for $\epsilon$ sufficiently close to one, the optimal hyperplane and threshold for the SVMC problem with regularization parameter C_c are equal to (1-\epsilon)^{- 1} times the optimal hyperplane and threshold for SVMR with regularization parameter C_r = (1-\epsilon)C_c. A direct consequence of this result is that SVMC can be seen as a special case of SVMR.