基于 l_(2,p) 范数的鲁棒核主成分分析  

Robust kernel principal component analysis based on l_(2,p) -norm

作　　者：李文君 LI Wenjun(School of Mathematics and Big Data,Anhui University of Science and Technology,Huainan 232001,China)

机构地区：[1]安徽理工大学数学与大数据学院,安徽淮南232001

出　　处：《哈尔滨商业大学学报(自然科学版)》2025年第1期75-82,共8页Journal of Harbin University of Commerce:Natural Sciences Edition

基　　金：深部煤矿采动响应与灾害防控国家重点实验室基金资助项目(No.SKLMRDPC22KF03).

摘　　要：核主成分分析(KPCA)是数据降维当中有效且常用的方法之一,应用广泛.许多基于l_(1)范数的KPCA算法被提出,虽然解决了经典KPCA易受异常值影响的问题,但都忽略了不能最大限度地减少重构误差以及具有旋转不变性的问题.针对此问题,提出一种基于l_(2,p)范数的核主成分分析算法(l_(2,p)-KPCA),采用l_(2,p)范数作为重构误差的距离度量,提高了对异常值的鲁棒性.证明了算法的收敛性以及旋转不变性,保留了PCA的旋转不变性.通过数值实验模拟和实验数据的结果表明,提出的l_(2,p)-KPCA比其他降维算法更具有优越性.Kernel principal component analysis(KPCA)is one of the effective and commonly used methods in data dimensionality reduction,with a wide range of applications.Many norm based KPCA have been proposed,although it solved the problem of classic KPCA being susceptible to outliers,they all overlooked the problem of not minimizing reconstruction errors and having rotation invariance.A kernel principal component analysis algorithm based on l_(2,p)norm(l_(2,p)-KPCA)was proposed to address this issue,which used l_(2,p)norm as the distance measure of reconstruction error,and improved robustness to outliers.This paper proved the convergence and rotation invariance of the algorithm,while preserving the rotation invariance of PCA.The application results of numerical simulation and real experimental data showed that the proposed l_(2,p)-KPCA has superior advantages over other dimensionality reduction algorithms.

关 键 词：主成分分析 l_(2 p)范数 核主成分分析 鲁棒性 数据降维 特征提取 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]