Curvature of the Manifold of Fixed-Rank Positive-Semidefinite Matrices Endowed with the Bures-Wasserstein Metric

被引：9

作者：

Massart, Estelle ^{[1
]}

Hendrickx, Julien M. ^{[1
,2
]}

Absil, P-A ^{[1
]}

机构：

[1] UCLouvain, ICTEAM, Louvain La Neuve, Belgium

[2] Boston Univ, Boston, MA 02215 USA

来源：

GEOMETRIC SCIENCE OF INFORMATION | 2019年 / 11712卷

关键词：

OPTIMIZATION; GEOMETRY;

D O I：

10.1007/978-3-030-26980-7_77

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

We consider the manifold of rank-p positive-semidefinite matrices of size n, seen as a quotient of the set of full-rank n-by-p matrices by the orthogonal group in dimension p. The resulting distance coincides with theWasserstein distance between centered degenerate Gaussian distributions. We obtain expressions for the Riemannian curvature tensor and the sectional curvature of the manifold. We also provide tangent vectors spanning planes associated with the extreme values of the sectional curvature.

引用

页码：739 / 748

页数：10

共 13 条

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