This paper presents a Multiple Kernel Learning (abbreviated as MKL) framework for the Support Vector Machine (SVM) with the $(0, 1)$ loss function. Some first-order optimality conditions are given and then exploited to develop a fast ADMM solver to deal with the nonconvex and nonsmooth optimization problem. Extensive numerical experiments on synthetic and real datasets 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:本文针对使用$(0,1)$损失函数的支持向量机(SVM),提出了一种多核学习(Multiple Kernel Learning,简称MKL)框架。文中给出了若干一阶最优性条件,并利用这些条件开发了一种快速的ADMM求解器,以处理该非凸非光滑优化问题。在合成数据集和真实数据集上的大量数值实验表明,本文提出的MKL-$L_{0/1}$-SVM的性能与Rakotomamonjy、Bach、Canu和Grandvalet在《Journal of Machine Learning Research, vol. 9, pp. 2491-2521, 2008》中提出的主流方法SimpleMKL的性能相当。