中国科学院机构知识库网格
Chinese Academy of Sciences Institutional Repositories Grid
首页 机构 成果 学者
  
  1. CAS IR Grid
  2. 自动化研究所
  3. 中国科学院自动化研究所
  4. 多模态人工智能系统全国重点实验室
  5. 遥感图像处理团队
On the Equivalence of Linear Discriminant Analysis and Least Squares Regression

文献类型：期刊论文

作者Nie, Feiping1,2; Chen, Hong1,2; Xiang, Shiming3,4; Zhang, Changshui5,6; Yan, Shuicheng7; Li, Xuelong1,2
刊名IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
出版日期2024-04-01
卷号35期号:4页码:5710-5720
关键词Eigenvalues and eigenfunctions Principal component analysis Null space Training data Symmetric matrices Sun Optimization Least squares regression (LSR) linear discriminant analysis (LDA) linear regression minimum distance classifier (MDC) null space LDA
ISSN号2162-237X
DOI10.1109/TNNLS.2022.3208944
通讯作者Nie, Feiping(feipingnie@gmail.com)
英文摘要Studying the relationship between linear discriminant analysis (LDA) and least squares regression (LSR) is of great theoretical and practical significance. It is well-known that the two-class LDA is equivalent to an LSR problem, and directly casting multiclass LDA as an LSR problem, however, becomes more challenging. Recent study reveals that the equivalence between multiclass LDA and LSR can be established based on a special class indicator matrix, but under a mild condition which may not hold under the scenarios with low-dimensional or oversampled data. In this article, we show that the equivalence between multiclass LDA and LSR can be established based on arbitrary linearly independent class indicator vectors and without any condition. In addition, we show that LDA is also equivalent to a constrained LSR based on the data-dependent indicator vectors. It can be concluded that under exactly the same mild condition, such two regressions are both equivalent to the null space LDA method. Illuminated by the equivalence of LDA and LSR, we propose a direct LDA classifier to replace the conventional framework of LDA plus extra classifier. Extensive experiments well validate the above theoretic analysis.
资助项目National Key Research and Development Program of China
WOS研究方向Computer Science ; Engineering
语种英语
WOS记录号WOS:001197919500038
出版者IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
资助机构National Key Research and Development Program of China
源URL[http://ir.ia.ac.cn/handle/173211/58475]  
专题自动化研究所_模式识别国家重点实验室_遥感图像处理团队
通讯作者Nie, Feiping
作者单位1.Northwestern Polytech Univ, Sch Comp Sci, Sch Artificial Intelligence Opt & Elect iOPEN, Xian 710072, Shaanxi, Peoples R China
2.Northwestern Polytech Univ, Key Lab Intelligent Interact & Applicat, Minist Ind & Informat Technol, Xian 710072, Shaanxi, Peoples R China
3.Chinese Acad Sci, Inst Automat, Dept Natl Lab Pattern Recognit, Beijing 100190, Peoples R China
4.Univ Chinese Acad Sci, Sch Artificial Intelligence, Beijing 100049, Peoples R China
5.Tsinghua Univ THUAI, Inst Artificial Intelligence, Beijing 100084, Peoples R China
6.Tsinghua Univ, Beijing Natl Res Ctr Informat Sci & Technol BNRist, Dept Automat, Beijing 100084, Peoples R China
7.Natl Univ Singapore, Sea AI Lab SAIL, Singapore 117583, Singapore
推荐引用方式
GB/T 7714		 Nie, Feiping,Chen, Hong,Xiang, Shiming,et al. On the Equivalence of Linear Discriminant Analysis and Least Squares Regression[J]. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS,2024,35(4):5710-5720.
APA Nie, Feiping,Chen, Hong,Xiang, Shiming,Zhang, Changshui,Yan, Shuicheng,&Li, Xuelong.(2024).On the Equivalence of Linear Discriminant Analysis and Least Squares Regression.IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS,35(4),5710-5720.
MLA Nie, Feiping,et al."On the Equivalence of Linear Discriminant Analysis and Least Squares Regression".IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 35.4(2024):5710-5720.

入库方式： OAI收割

来源：自动化研究所

浏览0
下载0
收藏0
其他版本

除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。