Differential-geometric Newton method for the best rank-(R 1, R 2, R 3) approximation of tensors

被引：42
|
作者：
Ishteva, Mariya [1 ]
De Lathauwer, Lieven [1 ,2 ]
Absil, P. -A. [3 ]
Van Huffel, Sabine [1 ]
机构：
[1] Katholieke Univ Leuven, ESAT SCD, B-3001 Louvain, Belgium
[2] Katholieke Univ Leuven, Subfac Sci & Technol, B-8500 Kortrijk, Belgium
[3] Catholic Univ Louvain, Dept Engn Math, B-1348 Louvain, Belgium
来源：
NUMERICAL ALGORITHMS | 2009年 / 51卷 / 02期
关键词：
Multilinear algebra; Higher-order tensor; Higher-order singular value decomposition; Rank-(R-1; R-2; R-3); reduction; Quotient manifold; Differential-geometric optimization; Newton's method; Tucker compression; HIGHER-ORDER TENSOR; INDEPENDENT COMPONENT ANALYSIS; CANONICAL DECOMPOSITION; RIEMANNIAN-MANIFOLDS; MULTILINEAR-ALGEBRA;
D O I：
10.1007/s11075-008-9251-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
An increasing number of applications are based on the manipulation of higher-order tensors. In this paper, we derive a differential-geometric Newton method for computing the best rank-(R (1), R (2), R (3)) approximation of a third-order tensor. The generalization to tensors of order higher than three is straightforward. We illustrate the fast quadratic convergence of the algorithm in a neighborhood of the solution and compare it with the known higher-order orthogonal iteration (De Lathauwer et al., SIAM J Matrix Anal Appl 21(4):1324-1342, 2000). This kind of algorithms are useful for many problems.
引用
收藏
页码：179 / 194
页数：16
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