Analysis of loss functions in support vector machines  

作　　者：Huajun WANG Naihua XIU 

机构地区：[1]Department of Mathematics,School of Science,Beijing Jiaotong University,Beijing 100044,China

出　　处：《Frontiers of Mathematics in China》2023年第6期381-414,共34页中国高等学校学术文摘·数学（英文）

摘　　要：Support vector machines(SVMs)are a kind of important machine learning methods generated by the cross interaction of statistical theory and optimization,and have been extensively applied into text categorization,disease diagnosis,face detection and so on.The loss function is the core research content of SVM,and its variational properties play an important role in the analysis of optimality conditions,the design of optimization algorithms,the representation of support vectors and the research of dual problems.This paper summarizes and analyzes the 0-1 loss function and its eighteen popular surrogate loss functions in SVM,and gives three variational properties of these loss functions:subdifferential,proximal operator and Fenchel conjugate,where the nine proximal operators and fifteen Fenchel conjugates are given by this paper.

关 键 词：Support vector machines loss function SUBDIFFERENTIAL proximal operator Fenchel conjugate 

分 类 号：O17[理学—数学]