一种新的直觉模糊最小二乘支持向量机

张丹; 周水生; 张文梦

doi:10.19665/j.issn1001-2400.2022.05.015

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一种新的直觉模糊最小二乘支持向量机

计算机科学与技术 & 人工智能 | 更新时间：2023-04-10

- 一种新的直觉模糊最小二乘支持向量机
- 暂无标题
- 西安电子科技大学学报 2022年49卷第5期页码：125-136
- 作者机构：
  
  西安电子科技大学数学与统计学院,陕西西安 710126
- 作者简介：
  
  [ "张丹(1996—),女,西安电子科技大学硕士研究生,E-mail:1192908842@qq.com；" ]
  [ "周水生(1972—),男,教授,博士,E-mail:sszhou@mail.xidian.edu.cn；" ]
  [ "张文梦(1996—),女,西安电子科技大学硕士研究生,E-mail:3137710140@qq.com" ]
- 基金信息：
  
  国家自然科学基金(61772020)
- DOI：10.19665/j.issn1001-2400.2022.05.015
  中图分类号：
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张丹, 周水生, 张文梦. 一种新的直觉模糊最小二乘支持向量机[J]. 西安电子科技大学学报, 2022,49(5):125-136.
张丹, 周水生, 张文梦. 一种新的直觉模糊最小二乘支持向量机[J]. 西安电子科技大学学报, 2022,49(5):125-136. DOI： 10.19665/j.issn1001-2400.2022.05.015.

DOI：

摘要

最小二乘支持向量机只需求解一个线性方程组即可得到闭式解,训练速度快,因而广泛应用于分类问题。但最小二乘支持向量机模型容易受到离群点和噪声的影响,往往使得其分类精度下降,样本点的模糊加权是解决该问题的一种有效方法。直觉模糊集既包含样本点的隶属度信息又包含样本点的非隶属度信息,可以更加详细地刻画样本点的分布特征。为此,基于直觉模糊集,通过剔除离群点得到更加准确的类中心,再计算样本点到类中心的距离,得到样本点对其所在类的隶属度程度。同时,采用核,k,近邻的方法,查找样本点的,k,个近邻里另一类样本点的数量,进而得到样本点的非隶属度信息。最后,根据样本点的隶属度与非隶属度得到一种新的模糊值。进一步将提出的模糊值用于改进最小二乘支持向量机模型,通过赋予离群点和噪声低的模糊值,减少了它们对最小二乘支持向量机模型的影响,提高了最小二乘支持向量机模型的精度。实验结果表明,与已有算法对比,提出的算法可以有效降低离群点和噪声对最小二乘支持向量机模型的影响,提高模型的鲁棒性。

Abstract

The least square support vector machine only needs to solve a linear system of equations to get a closed solution,so it is widely used in classification problems because of its fast training speed.However,the least squares support vector machine model is easily affected by outliers and noise,which often reduces the classification accuracy.Fuzzy weighting of sample points is an effective method to solve this problem.Intuitionistic fuzzy sets contain both membership information and non-membership information of sample points,which can describe the distribution characteristics of sample points in more detail.Therefore,based on the intuitionistic fuzzy set,this paper obtains a more accurate class center by eliminating outliers,and then calculates the distance between the sample point and the class center to obtain the membership degree of the sample point to its class.At the same time,the kernel ,k-,nearest neighbor method is used to find the number of ,k, neighboring sample points of another class,and then the non-membership information of sample points is obtained.Finally,a new fuzzy value is obtained according to the membership degree and non-membership degree of sample points.Furthermore,the proposed fuzzy values are used to improve the LSSVM model.By assigning outliers and fuzzy values with low noise,their influence on the LSSVM model is reduced and the accuracy of the LSSVM model is improved.Experimental results show that,compared with the existing algorithms,the proposed algorithm can reduce the influence of outliers and noise on the LSSVM model and improve the robustness of the model.

关键词

最小二乘支持向量机模糊集离群点和噪声k近邻

Keywords

least square support vector machinefuzzy setsoutliers and noisek-nearest neighbor

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