Geometric Distance Between Positive Definite Matrices of Different Dimensions
文献类型：期刊论文
| 作者 | Lim, Lek-Heng1; Sepulchre, Rodolphe2; Ye, Ke3
|
| 刊名 | IEEE TRANSACTIONS ON INFORMATION THEORY
 |
| 出版日期 | 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 |
| WOS记录号 | WOS:000481981000009 |
| 出版者 | IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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