摘要
主成分分析法常被用于维数压缩和特征提取,其在处理单一高维数据集时有很大优势.在很多实际场景中需要联合处理多个数据集,此时传统的主成分分析方法面临很大挑战.本文提出了迹比率主成分分析法,该方法可以提取目标数据相对其他数据特有的低维表示,进而通过迭代算法高效求解.数值算例证实了该方法的优越性.
Principal component analysis is widely applied in dimensionality reduction and feature extraction,especially in tackling single high-dimensional dataset.However,traditional principal component analysis faces challenge when it comes to analyzing multiple datasets jointly.This paper introduces a novel approach named trace ratio principal component analysis,which can discover low-dimensional structure unique to the target data relative to others.Furthermore,trace ratio principal component analysis and its variants can be solved by efficient iterative algorithm.Numerical experiments show the efficiency of the method.
作者
赵小彤
李智
宋恩彬
ZHAO Xiao-Tong;LI Zhi;SONG En-Bin(School of Mathematics,Sichuan University,Chengdu 610064,China;School of Aeronautics&Astronautics,Sichuan University,Chengdu 610064,China;Science and Technology on Electronic Information Control Laboratory,Chengdu 610063,China)
出处
《四川大学学报（自然科学版）》
CAS
CSCD
北大核心
2021年第1期7-13,共7页
Journal of Sichuan University(Natural Science Edition)
基金
四川省科技计划项目(2019YJ0115)
四川大学基金(2020SCUNG205)
国家自然科学基金(U2066203,61473197)。
关键词
主成分分析
判别分析
维数压缩
多背景数据集
Principal component analysis
Discriminative analysis
Dimensionality reduction
Multiple background datasets
