Finite dimensional projection for classification and statistical learning
Gilles Blanchard and Laurent Zwald
IEEE transactions on information theory Volume 54, Number 9, pp. 4169-4182, 2008. ISSN 0018-9448

Abstract

A new method for the binary classification problem is studied. It relies on empirical minimization of the hinge loss over an increasing sequence of finite-dimensional spaces. A suitable dimension is picked by minimizing the regularized loss, where the regularization term is proportional to the dimension. An oracle-type inequality is established, which ensures adequate convergence properties of the method. We suggest to select the considered sequence of subspaces by applying kernel principal components analysis. In this case the asymptotical convergence rate of the method can be better than what is known for the Support Vector Machine. Exemplary experiments are presented on benchmark datasets where the practical results of the method are comparable to the SVM.

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