ISSN 1000-1239 CN 11-1777/TP

• 人工智能 •

### 基于近似高斯核显式描述的大规模SVM求解

1. (天津大学计算机科学与技术学院 天津 300072) (szliao@tju.edu.cn)
• 出版日期: 2014-10-01
• 基金资助:
国家自然科学基金项目(60933005)；国家“八六三”高技术研究发展计划基金项目(2011AA010702,2012AA01A401,2012AA01A402)

### Approximate Gaussian Kernel for Large-Scale SVM

Liu Yong, Jiang Shali, Liao Shizhong

1. (School of Computer Science and Technology, Tianjin University, Tianjin 300072)
• Online: 2014-10-01

Abstract: Training support vector machine (SVM) with nonlinear kernel functions on large-scale data is usually very time consuming. In contrast, there exist faster solvers to train the linear SVM. To utilize the computational efficiency of linear SVM without sacrificing the accuracy of nonlinear ones, in this paper, we present a method for solving large-scale nonlinear SVM based on an explicit description of an approximate Gaussian kernel. We first give the definition of the approximate Gaussian kernel, and establish the connection between approximate Gaussian kernel and Gaussian kernel, and also derive the error bound between these two kernel functions. Then, we present an explicit description of the reproducing kernel Hilbert space (RKHS) induced by the approximate Gaussian kernel. Thus, we can exactly depict the structure of the solutions of SVM, which can enhance the interpretability of the model and make us more deeply understand this method. Finally, we explicitly construct the feature mapping induced by the approximate Gaussian kernel, and use the mapped data as input of linear SVM. In this way, we can utilize existing efficient linear SVM to solve non-linear SVM on large-scale data. Experimental results show that the proposed method is efficient, and can achieve comparable classification accuracy to a normal nonlinear SVM.