哈尔滨商业大学学报（自然科学版）2025，Vol.41Issue(1)：96-103,8.
基于广义Capped l2,q范数的多项式正则化线性判别
Polynomial regularized linear discriminant based on generalized capped l2,q-norm
摘要
Abstract
Linear discriminant analysis(LDA)often had problems with the with-class scattering matrix being irreversible and beingsensitive to outliers and noise.To solve these problems,a polynomial regularized linear discriminant analysis based on generalized capped l2,q-norm was proposed in this paper.By introducing l2,q-norm into objective function and setting a threshold,it could reduce the influence of noise,identify the abnormal points of data,and reduce the influence of large norm on the projection direction.By mapping the between-class scattering matrix to the polynomial function to increase the trace of the matrix,the sample distance between different classes was further increased,thereby enhancing the discriminant ability.Regularization terms were added to the with-class scattering matrix to prevent its irreversibility.The results of simulation and real data application showed that the proposed method was superior to other similar methods in reducing the influence of outliers and noise and improving the ability of category discrimination,and had higher prediction accuracy.关键词
线性判别分析/Capped l2,q范数/多项式函数/散射矩阵/噪声处理/正则化Key words
linear discriminant analysis/capped l2,q-norm/polynomial function/scattering matrix/noise processing/regularization分类
信息技术与安全科学引用本文复制引用
杨源,周跃进..基于广义Capped l2,q范数的多项式正则化线性判别[J].哈尔滨商业大学学报（自然科学版）,2025,41(1):96-103,8.基金项目
深部煤矿采动响应与灾害防控国家中点实验室基金资助项目(SKLMRDPC22KF03) （SKLMRDPC22KF03）
