Solution path algorithm for twin multi-class support vector machine

作     者：Chen, Liuyuan Zhou, Kanglei Jing, Junchang Fan, Haiju Li, Juntao 

作者机构：Henan Normal Univ Journal Editorial Dept Xinxiang 453007 Henan Peoples R China Beihang Univ Sch Comp Sci & Engn Beijing 100191 Peoples R China Henan Univ Sci & Technol Informat Engn Coll Henan Int Joint Lab Cyberspace Secur Applicat Luoyang 471023 Peoples R China Henan Normal Univ Coll Comp & Informat Engn Xinxiang 453007 Henan Peoples R China Henan Normal Univ Coll Math & Informat Sci Xinxiang 453007 Henan Peoples R China 

出 版 物：《EXPERT SYSTEMS WITH APPLICATIONS》 (专家系统及其应用)

年 卷 期：2022年第210卷

核心收录：

学科分类：1201[管理学-管理科学与工程(可授管理学、工学学位)] 0808[工学-电气工程] 08[工学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：Natural Science Foundation of China [61203293, 61702164, 31700858] Scientific and Technological Project of Henan Province, China [162102310461, 172102310535] Foundation of Henan Educational Committee, China [18A520015] 

主　　题：Regularization parameter Solution path algorithm Multi-class classification Twin support vector machine 

摘      要：The twin support vector machine and its extensions have made great achievements in dealing with binary classification problems. However, it suffers from difficulties in effective solution of multi-classification and fast model selection. This work devotes to the fast regularization parameter tuning algorithm for the twin multi-class support vector machine. Specifically, a novel sample data set partition strategy is first adopted, which is the basis for the model construction. Then, combining the linear equations and block matrix theory, the Lagrangian multipliers are proved to be piecewise linear w.r.t. the regularization parameters, so that the regularization parameters are continuously updated by only solving the break points. Next, Lagrangian multipliers are proved to be 1 as the regularization parameter approaches infinity, thus, a simple yet effective initialization algorithm is devised. Finally, eight kinds of events are defined to seek for the starting event for the next iteration. Extensive experimental results on nine UCI data sets show that the proposed method can achieve comparable classification performance without solving any quadratic programming problem.