支持向量机的关键问题和展望  

Key issues of support vector machines and future prospects

作　　者：邵元海 刘黎明[2] 黄凌伟 邓乃扬[4] Yuanhai Shao;Liming Liu;Lingwei Huang;Naiyang Deng

机构地区：[1]海南大学管理学院,海口570228 [2]首都经济贸易大学统计学院,北京100083 [3]海南大学经济学院,海口570228 [4]中国农业大学理学院,北京10083

出　　处：《中国科学：数学》2020年第9期1233-1248,共16页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11871183,61866010和11926349);海南省自然科学基金(批准号:118QN181);北京市自然科学基金(批准号:9172003)资助项目。

摘　　要：作为机器学习的主要方法之一,支持向量机不仅有坚实的统计学习理论基础,而且在众多领域中表现出优秀的泛化性能,因此受到了广泛关注.然而近几年来,相比于深度学习的蓬勃发展,支持向量机的研究进展缓慢.本文从支持向量机的本质出发,探讨支持向量机的理论方法与深度学习等机器学习热点研究的交叉与融合,提出一些新的思路.具体地,包括3个方面:支持向量机的大间隔原则及其带来的低密度性、核映射的高维划分技巧及其统计学习理论,以及支持向量机的浅层学习模式向深度学习和广度学习的拓展.同时,从这3个方面分别提出支持向量机研究中可以进一步挖掘的优良性质,并展望未来可能诱导出的理论和方法.As one of the main methods of machine learning, the support vector machine(SVM) not only has a solid theoretical foundation of statistical learning, but also shows excellent generalization performance in manyfields, so it has received extensive attention. However, in recent years, compared with the vigorous development of deep learning, the research on SVM has fallen into a trough. This paper starts from the essence of SVM,discusses the intersection and fusion of the research methods of machine learning methods, such as deep learning and the SVM, and then puts forward some new ideas. Specifically, it includes three aspects: the principle of large margin with the low density property of SVM, the high-dimensional division technique of kernel mapping and its statistical learning theory, the shallow learning of SVM and its extension to deep learning and broad learning. At the same time, the excellent properties that can be further explored from these three aspects, and the theories and methods that may be induced in the future are expected.

关 键 词：支持向量机 统计学习 核学习 机器学习 最优化 深度学习 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]