Multi-Class Support Vector Data Description Based on Evidence Theory

ZHANG Shixing; HAN Deqiang; FAN Xiaojing

doi:10.7652/xjtuxb202302016

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Multi-Class Support Vector Data Description Based on Evidence Theory

更新时间：2025-07-09

- Multi-Class Support Vector Data Description Based on Evidence Theory
- Vol. 57, Issue 2, Pages: 151-160(2023)
- 作者机构：
  
  西安交通大学电信学部,西安,710049
- 作者简介：
- 基金信息：
- DOI：10.7652/xjtuxb202302016
  CLC： TP391
- Online First：10 February 2023，
  
  Published：2023
- 稿件说明：
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ZHANG Shixing, HAN Deqiang, FAN Xiaojing. Multi-Class Support Vector Data Description Based on Evidence Theory[J]. 2023, 57(2): 151-160.
DOI：

ZHANG Shixing, HAN Deqiang, FAN Xiaojing. Multi-Class Support Vector Data Description Based on Evidence Theory[J]. 2023, 57(2): 151-160. DOI： 10.7652/xjtuxb202302016.

摘要

针对原始多分类支持向量数据描述(SVDD)算法及其拓展算法忽略超球体之间的差异

且未能充分利用超球体的输出信息等问题

提出一种利用证据理论的多分类支持向量数据描述(证据SVDD多分类)算法。首先

为每一类样本训练一个超球体

并计算每个超球体的正确率与紧密程度; 接着使用上一步得到的正确率与紧密程度计算每个超球体的可靠程度; 然后

根据超球体的输出信息与可靠程度计算样本的信度函数

信度函数的生成方式采用三焦元法和基于评价矩阵的方法; 最后

根据Dempster组合规则融合上一步得到的信度函数

使用Pignistic法将融合后的信度函数转换为概率做出最终的判决。在两个人工数据集和多个UCI数据集上进行实验

结果表明

证据SVDD多分类算法相较传统算法可以获得更好的分类性能; 在多个数据集上的仿真结果表明

证据SVDD多分类算法比传统的SVDD多分类算法有3%的精度提升。

Abstract

Original multi-class support vector data description(SVDD)algorithm and its extension algorithm ignore the differences among hyperspheres and fail to make full use of the output information of hyperspheres. To address these problems

a multi-class support vector data description algorithm based on evidence theory(evidential multi-class SVDD algorithm)is proposed. Firstly

a hypersphere is trained for each class of samples

and the accuracy and closeness of each hypersphere are calculated. Secondly

the accuracy and closeness obtained in the previous step are used to calculate the reliability of hypersphere. After that

the output information and reliability of hypersphere are used to calculate the belief functions of samples

which are generated by two methods: the triple focal element method and the method based on payoff matrix. In the end

Dempster combination rule is used to fuse the belief functions

and Pignistic method is used to convert the fused belief functions into probability for final decision. Extensive experimental results on two artificial datasets and multiple UCI datasets show that the evidential multi-class SVDD algorithm achieves better classification performance than the traditional algorithm. Simulation results on multiple datasets show that the evidential multi-class SVDD algorithm has a 3% improvement in accuracy compared with the traditional multi-class SVDD algorithm.

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references

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