群不变孪生支持向量机及其一致性研究

Group Invariance-Based Twin Support Vector Machines(GI-TWSVM):The Problem and Its Consistency

许卫霞 ¹周水庚 ²黄定江³

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作者信息

1. 上海立信会计金融学院信息管理学院,上海 201209;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
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
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摘要

群不变性是一种重要的先验知识,往往用于提升算法性能.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,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,以提升孪生支持向量机算法性能.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.

Abstract

Group invariance is a crucial type of prior knowledge often employed to enhance learning performance.As a binary classification support vector machine algorithm,twin support vector machines(TWSVM)can improve 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)to improve the performance.First,an optimization problem is formulated for GI-TWSVM.Using the Twin Bounded Support Vector Machine(TBSVM)as an example,we develop two TBSVM algorithms that incorporate group invariance,demonstrating that the optimization problem is solvable and practically significant.Then,we systematically investigate the consistency of GI-TWSVM to build a solid theoretical basis for the related algorithms.Finally,experimental results using TBSVM as an example indicate that group invariance can significantly enhance the performance of twin support vector machine algorithms.

关键词

不变性/群不变性/孪生支持向量机/一致性/通用一致性

Key words

invariance/group invariance/twin support vector machine/consistency/universal consistency

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出版年

2024

武汉大学学报(理学版)

武汉大学

武汉大学学报(理学版)

CSTPCDCSCD北大核心

影响因子：0.814

ISSN：1671-8836

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