稳健的支持向量分类机的优化理论分析

An Analysis on Robust Support Vector Classification

由于在实际中,我们已知的数据往往带有试验误差或者统计误差,因此对扰动数据的处理是一个重要的课题。文[2]对输入带球形扰动的两类分类问题提出了稳健的支持向量分类机的模型,本文主要对引入核后的稳健模型的优化理论做了系统深入的研究,内容包括原始问题的解的唯一性问题、对偶问题及其与原始问题的关系,从而完善了稳健的支持向量分类机的优化理论基础,为相应的算法提供了严密理论依据。

In practice, the data have usually perturbations since they are subject to measurement or statistical errors, so dealing with the data with perturbations is currently an active research. The robust Support Vector Classification （SVC） was proposed for the training data with sphere perturbations of the 2-class classification in [2]. This paper studies the optimization theoretical foundations of the robust formulations, including： the existence and uniqueness of the primal problem and the relation between the solutions of primal problem and dual problem for robust SVC with Gaussian kernel. Therefore the optimization theoretical foundation has been set up and privdes the theoretical basis for establishing the algorithm.