Geometric Distance Between Positive Definite Matrices of Different Dimensions

doi:10.1109/TIT.2019.2913874

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	Geometric Distance Between Positive Definite Matrices of Different Dimensions
	Lim, Lek-Heng 1; Sepulchre, Rodolphe 2; Ye, Ke3
刊名	IEEE TRANSACTIONS ON INFORMATION THEORY
	2019-09-01
卷号	65 期号:9 页码:5401-5405
关键词	Riemannian manifold geodesic distance positive definite matrices covariance matrices ellipsoids
ISSN号	0018-9448
DOI	10.1109/TIT.2019.2913874
英文摘要	We show how the geodesic distance on S-++(n), the cone of n x n real symmetric or complex Hermitian positive definite matrices regarded as a Riemannian manifold, may be used to naturally define a distance between two such matrices of different dimensions. Given that S-++(n) also parameterizes n-dimensional ellipsoids, inner products on R-n, and n x n covariances of nondegenerate probability distributions, this gives us a natural way to define a geometric distance between a pair of such objects of different dimensions.
资助项目	Defense Advanced Research Projects Agency (DARPA)[D15AP00109] ; National Science Foundation[IIS 1546413] ; DARPA Director's Fellowship ; Eckhardt Faculty Fund through The University of Chicago ; European Research Council[670645] ; National Natural Science Foundation of China (NSFC)[11688101] ; National Natural Science Foundation of China (NSFC)[11801548] ; National Key R&D Program of China[2018YFA0306702] ; Hundred Talents Program of the Chinese Academy of Sciences ; Thousand Talents Plan of the State Council of China
WOS研究方向	Computer Science ; Engineering
语种	英语
出版者	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
WOS记录号	WOS:000481981000009
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/35502]
专题	系统科学研究所
通讯作者	Lim, Lek-Heng
作者单位	1.Univ Chicago, Dept Stat, Computat & Appl Math Initiat, Chicago, IL 60637 USA 2.Univ Cambridge, Dept Engn, Cambridge CB2 1PZ, England 3.Chinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Lim, Lek-Heng,Sepulchre, Rodolphe,Ye, Ke. Geometric Distance Between Positive Definite Matrices of Different Dimensions[J]. IEEE TRANSACTIONS ON INFORMATION THEORY,2019,65(9):5401-5405.
APA	Lim, Lek-Heng,Sepulchre, Rodolphe,&Ye, Ke.(2019).Geometric Distance Between Positive Definite Matrices of Different Dimensions.IEEE TRANSACTIONS ON INFORMATION THEORY,65(9),5401-5405.
MLA	Lim, Lek-Heng,et al."Geometric Distance Between Positive Definite Matrices of Different Dimensions".IEEE TRANSACTIONS ON INFORMATION THEORY 65.9(2019):5401-5405.