Wu, Wangmeng Zuo,  Yuanyuan Zhu, Liang Lin,  [^1][^2]'
bibliography:
- 'IEEEabrv.bib'
- 'fsvm.bib'
title: 'F-SVM: Combination of Feature Transformation and SVM Learning via Convex Relaxation'
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[Shell : F-SVM: Combination of Feature Transformation and SVM Learning via Convex Relaxation]{}

Support vector machine, radius margin bound, convex relaxation, max-margin.

Introduction
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vector machine (SVM) and its extensions have been one of the most successful machine learning methods [@vapnik1998statistical; @cristianini2000introduction], and have been adopted in various fields, e.g., computer vision [@osuna1997training; @heisele2001face; @guo2001support; @wu2015linear], signal processing [@samanta2003artificial; @chen2001support], natural language processing [@collobert2011natural; @tsochantaridis2004support] and bioinformatics [@do2009feature; @weston2000feature; @guyon2002gene; @rakotomamonjy2003variable]. Despite its popularity, SVM aims to seek the optimal hyperplane with the maximum margin principle, but the generalization error of SVM actually is a function of the ratio of radius and margin [@vapnik2000bounds]. Given feature space, the radius is fixed and can be ignored, thus SVM can minimize the generalization error by maximizing the margin. However, for joint learning of feature transformation and classifier, the radius information will be valuable and cannot be ignored.

By minimizing the radius-margin ratio, the generalization error of SVM can be optimized for joint learning of feature transformation and classifier. Since the radius-margin error bound is non-convex, relaxation 