Geometric mean and geodesic regression on Grassmannians

被引：28

作者：

Batzies, E. ^{[1
]}

Hueper, K. ^{[2
]}

Machado, L. ^{[3
,4
]}

Leite, F. Silva ^{[4
,5
]}

机构：

[1] Hsch Furtwangen Univ, Fac Elect & Comp Engn, D-78120 Furtwangen, Germany

[2] Univ Wurzburg, Dept Math, D-97074 Wurzburg, Germany

[3] Univ Tras Os Montes & Alto Douro UTAD, Dept Math, P-5001801 Vila Real, Portugal

[4] Univ Coimbra Polo II, Inst Syst & Robot, P-3030290 Coimbra, Portugal

[5] Univ Coimbra, Dept Math, P-3001454 Coimbra, Portugal

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2015年 / 466卷

关键词：

Grassmann manifold; Geodesic distance; Geometric mean; CENTER-OF-MASS; MANIFOLDS; SPLINES;

D O I：

10.1016/j.laa.2014.10.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The main objective of this paper is to solve the problem of finding a geodesic that best fits a given set of time-labelled points on the Grassmann manifold. To achieve this goal, we first derive a very useful simplified formula for the geodesic arc joining two points on the Grassmannian depending explicitly only on the given points. This allows to simplify the expression for the geodesic distance, which is crucial to generalize the fitting problem, and is also used to obtain a simpler characterization of the geometric mean of a finite set of points lying on the Grassmannian, where the given points enter explicitly. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：83 / 101

页数：19

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