Unlabeled Principal Component Analysis

doi:none

KMS > 信息科学与技术学院 > PI研究组 > Manolis Tsakiris组

	Unlabeled Principal Component Analysis
	Yao, Yunzhen; Peng, Liangzu; Tsakiris, Manolis C.
	2021
会议录名称	ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS
ISSN	1049-5258
卷号	36
页码	30452-30464
发表状态	正式接收
DOI	none
摘要	We introduce robust principal component analysis from a data matrix in which the entries of its columns have been corrupted by permutations, termed Unlabeled Principal Component Analysis (UPCA). Using algebraic geometry, we establish that UPCA is a well-defined algebraic problem in the sense that the only matrices of minimal rank that agree with the given data are row-permutations of the ground-truth matrix, arising as the unique solutions of a polynomial system of equations. Further, we propose an efficient two-stage algorithmic pipeline for UPCA suitable for the practically relevant case where only a fraction of the data have been permuted. Stage-I employs outlier-robust PCA methods to estimate the ground-truth column-space. Equipped with the column-space, Stage-II applies recent methods for unlabeled sensing to restore the permuted data. Experiments on synthetic data, face images, educational and medical records reveal the potential of UPCA for applications such as data privatization and record linkage. © 2021 Neural information processing systems foundation. All rights reserved.
关键词	Matrix algebra Medical imaging Polynomials Privatization Algebraic geometry Algorithmics Column space Data matrix Ground truth matrix Polynomial systems Principal-component analysis Robust principal component analysis Systems of equations
会议名称	35th Conference on Neural Information Processing Systems, NeurIPS 2021
会议地点	Virtual, Online
会议日期	December 6, 2021 - December 14, 2021
URL	查看原文
收录类别	EI
语种	英语
出版者	Neural information processing systems foundation
EI入藏号	20222512238286
EI主题词	Principal component analysis
EI分类号	461.1 Biomedical Engineering ; 746 Imaging Techniques ; 911.2 Industrial Economics ; 921.1 Algebra ; 922.2 Mathematical Statistics
原始文献类型	Conference article (CA)
文献类型	会议论文
条目标识符	https://kms.shanghaitech.edu.cn/handle/2MSLDSTB/251917
专题	信息科学与技术学院_PI研究组_Manolis Tsakiris组信息科学与技术学院_硕士生
作者单位	School of Information Science and Technology, ShanghaiTech University, China
第一作者单位	信息科学与技术学院
第一作者的第一单位	信息科学与技术学院
推荐引用方式 GB/T 7714	Yao, Yunzhen,Peng, Liangzu,Tsakiris, Manolis C.. Unlabeled Principal Component Analysis[C]:Neural information processing systems foundation,2021:30452-30464.