Riemannian subspace tracking algorithms on Grassmann manifolds

被引：0

作者：

Baumann, M. ^{[1
]}

Helmke, U. ^{[1
]}

机构：

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

来源：

PROCEEDINGS OF THE 46TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-14 | 2007年

关键词：

adaptive subspace tracking; eigenvalue methods; Newton algorithm; Riemannian metrics; Grassmann manifolds;

D O I：

暂无

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Based on the differential geometry of the Grassmann manifold, we propose a new class of Newton-type algorithms for adaptively computing the principal and minor subspaces of a time-varying family of symmetric matrices. Using local parameterization of the Grassmann manifold, simple expressions for the subspace tracking schemes are derived. Key benefits of the algorithms are (a) the reduced computational complexity due to efficient parametrizations of the Grassmannian and (b) their guaranteed accuracy during all iterates. Numerical simulations illustrate the feasibility of the approach.

引用

页码：553 / 558

页数：6

共 50 条

[21] Coordinate Descent Without Coordinates: Tangent Subspace Descent on Riemannian Manifolds
Gutman, David H.
Ho-Nguyen, Nam
MATHEMATICS OF OPERATIONS RESEARCH, 2023, 48 (01) : 127 - 159
[22] Kernel-Based Subspace Learning on Riemannian Manifolds for Visual Recognition
Xi Liu
Zhengming Ma
Neural Processing Letters, 2020, 51 : 147 - 165
[23] Riemannian optimization method on generalized flag manifolds for complex and subspace ICA
Nishimori, Yasunori
Akaho, Shotaro
Plumbley, Mark D.
BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING, 2006, 872 : 89 - 96
[24] RIEMANNIAN OPTIMIZATION ON TENSOR PRODUCTS OF GRASSMANN MANIFOLDS: APPLICATIONS TO GENERALIZED RAYLEIGH-QUOTIENTS
Curtef, O.
Dirr, G.
Helmke, U.
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2012, 33 (01) : 210 - 234
[25] Inexact trust-region algorithms on Riemannian manifolds
Kasai, Hiroyuki
Mishra, Bamdev
ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 31 (NIPS 2018), 2018, 31
[26] GRASSMANN MANIFOLDS AND THE GRASSMANN IMAGE OF SUBMANIFOLDS
BORISENKO, AA
NIKOLAEVSKII, YA
RUSSIAN MATHEMATICAL SURVEYS, 1991, 46 (02) : 45 - 94
[27] Riemannian adaptive stochastic gradient algorithms on matrix manifolds
Kasai, Hiroyuki
Jawanpuria, Pratik
Mishra, Bamdev
INTERNATIONAL CONFERENCE ON MACHINE LEARNING, VOL 97, 2019, 97
[28] Subgradient algorithms on Riemannian manifolds of lower bounded curvatures
Wang, X. M.
OPTIMIZATION, 2018, 67 (01) : 179 - 194
[29] ε-subgradient algorithms for locally lipschitz functions on Riemannian manifolds
P. Grohs
S. Hosseini
Advances in Computational Mathematics, 2016, 42 : 333 - 360
[30] ε-subgradient algorithms for locally lipschitz functions on Riemannian manifolds
Grohs, P.
Hosseini, S.
ADVANCES IN COMPUTATIONAL MATHEMATICS, 2016, 42 (02) : 333 - 360

← 1 2 3 4 5 →