基于马氏距离的密度加权最小二乘孪生支持向量机  

The Density-Weighted Least Squares Twin Support Vector MachineBased on Mahalanobis Distance

作　　者：吕莉[1,2] 贺智鹏 张法滢 张莹莹 康平 李院民 LYU Li;HE Zhipeng;ZHANG Faying;ZHANG Yingying;KANG Ping;LI Yuanmin(School of Information Engineering,Nanchang Institute of Technology,Nanchang Jiangxi 330099,China;Nanchang Key Laboratory of IoT Perception and Collaborative Computing for Smart City,Nanchang Jiangxi 330099,China)

机构地区：[1]南昌工程学院信息工程学院,江西南昌330099 [2]南昌市智慧城市物联感知与协同计算重点实验室,江西南昌330099

出　　处：《江西师范大学学报(自然科学版)》2025年第1期37-48,共12页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金(62066030)资助项目。

摘　　要：最小二乘孪生支持向量机基于欧氏距离判断样本相似性并搭建模型的方法未考虑样本不同维度的方差差异对决策超平面位置的影响,导致模型处理此类样本精度不高且对噪声样本敏感.鉴于此,该文提出一种基于马氏距离的密度加权最小二乘孪生支持向量机.该算法利用马氏距离替换欧氏距离构造密度加权策略,充分考虑点与分布的关系,给予噪声数据较低的权重,降低算法对噪声的敏感性;同时结合马氏距离核函数计算样本内协方差矩阵,消除样本特征值之间方差的差异,更准确地体现样本间的相关性,从而优化决策超平面.实验采用人工数据集和UCI数据集,实验结果表明:该算法比同类型分类算法具有更高的分类精确度和泛化能力,能够有效区分在样本中的噪声数据并赋予合适的权重值,提升分类器的鲁棒性.The least dquares twin support vector machine(LSTSVM)judges the similarity of samples and builds a model based on Euclidean distance,without considering the effect of the variance difference of different dimensions of the sample on the position of the decision hyperplane,resulting in low accuracy of the model in processing such samples and sensitive to noisy samples.Therefore,the density-weighted least squares twin support vector machine(MDDW-LSTSVM)based on Mahalanobis distance is proposed.MDDW-LSTSVM uses Mahalanobis distance instead of Euclidean distance to structure the density weighting strategy,fully considers the relationship between points and distribution,gives lower weight to noise data,and reduces the sensitivity of the algorithm to noise.The covariance matrix eliminates the variance difference between sample eigenvalues and more accurately reflects the correlation between samples,thereby optimizing the decision hyperplane.The artificial datasets and UCI datasets are used to conduct experiments.The experimental results show that MDDW-LSTSVM has higher classification accuracy and generalization ability than the same type of classification algorithms and can effectively distinguish noise points in samples and improve the robustness of the classifier.

关 键 词：支持向量机 马氏距离 核函数 密度加权 最小二乘损失函数 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]