1.上海立信会计金融学院 信息管理学院, 上海 201209
2.复旦大学 计算机科学技术学院 上海市智能信息处理重点实验室, 上海 200433
3.华东师范大学 数据科学与工程学院, 上海 200062
许卫霞,女,讲师,现从事机器学习研究。E-mail:xuweixia@lixin.edu.cn
E-mail:sgzhou@fudan.edu.cn
网络出版日期:2024-03-26,
收稿日期:2023-07-24,
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许卫霞,周水庚,黄定江.群不变孪生支持向量机及其一致性研究[J].武汉大学学报(理学版),XXXX,XX(XX):1-12. DOI:10.14188/j.1671-8836.2023.0166.
XU Weixia,ZHOU Shuigeng,HUANG Dingjiang.Group Invariance⁃based Twin Support Vector Machines (GI⁃TWSVM): The Problem and Its Consistency [J].J Wuhan Univ (Nat Sci Ed),XXXX,XX(XX):1-12. DOI:10.14188/j.1671-8836.2023.0166(Ch).
许卫霞,周水庚,黄定江.群不变孪生支持向量机及其一致性研究[J].武汉大学学报(理学版),XXXX,XX(XX):1-12. DOI:10.14188/j.1671-8836.2023.0166. DOI:
XU Weixia,ZHOU Shuigeng,HUANG Dingjiang.Group Invariance⁃based Twin Support Vector Machines (GI⁃TWSVM): The Problem and Its Consistency [J].J Wuhan Univ (Nat Sci Ed),XXXX,XX(XX):1-12. DOI:10.14188/j.1671-8836.2023.0166(Ch). DOI:
群不变性是一种重要的先验知识,往往能提升算法性能。孪生支持向量机是一种二分类支持向量机算法,同样可以利用群不变性来提高性能。因此,本文提出将群不变性引入到孪生支持向量机框架中,定义了群不变孪生支持向量机问题,以提升其算法性能。首先,为群不变孪生支持向量机构造了具体的最优化问题,并以有界孪生支持向量机为例,提出了两种具备群不变性的有界孪生支持向量机算法,以此说明该最优化问题有解,故有实际意义。然后,系统研究了群不变孪生支持向量机的一致性,为其相关算法奠定了扎实的理论基础。最后,仍以有界孪生支持向量机为例进行实验。实验表明,群不变性能够提升孪生支持向量机算法性能。
Group invariance is one important type of prior knowledge
and is often used to improve the learning performance. As a kind of binary classification support vector machine algorithm
twin support vector machines (TWSVM) can be improved on performance by exploring group invariance. Thus in this paper
we propose to incorporate group invariance into the framework of TWSVM
and thereby define the problem of group invariance-based twin support vector machines (GI⁃TWSVM)
so as to improve the performance. First
an optimal problem is formulated for GI⁃TWSVM. Taking twin bounded support vector machine (TBSVM) as an example
we develop two TBSVM algorithms with group invariance
which show that the optimal problem is solvable
and therefore is practically significant. Then
we systematically investigate the consistency of GI⁃TWSVM
to build up a solid theoretical basis for the related algorithms. Finally
still using TBSVM as an example
experimental results have shown that group invariance can improve the performance of twin support vector machine algorithms.
不变性群不变性孪生支持向量机一致性通用一致性
invariancegroup invariancetwin support vector machineconsistencyuniversal consistency
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