This paper presents a Multiple Kernel Learning (abbreviated as MKL) framework for the Support Vector Machine (SVM) with the $(0, 1)$ loss function. Some KKT-like first-order optimality conditions are provided and then exploited to develop a fast ADMM algorithm to solve the nonsmooth nonconvex optimization problem. Numerical experiments on real data sets show that the performance of our MKL-$L_{0/1}$-SVM is comparable with the one of the leading approaches called SimpleMKL developed by Rakotomamonjy, Bach, Canu, and Grandvalet [Journal of Machine Learning Research, vol. 9, pp. 2491-2521, 2008].
翻译:本文提出了一个用于支持向量机(SVM)的$(0,1)$损失函数的多核学习(简称为MKL)框架。给出了若干类KKT条件的一阶最优性条件,并利用这些条件开发了一种快速ADMM算法,以求解该非光滑非凸优化问题。在真实数据集上的数值实验表明,本文提出的MKL-$L_{0/1}$-SVM的性能与Rakotomamonjy、Bach、Canu及Grandvalet开发的领先方法SimpleMKL(《Journal of Machine Learning Research》,第9卷,第2491-2521页,2008年)相当。