Title: Left vs right representations for solving weighted low-rank approximation problems
Authors: Markovsky, Ivan ×
Van Huffel, Sabine #
Issue Date: Apr-2007
Publisher: North Holland
Series Title: Linear Algebra and Its Applications vol:422 issue:2-3 pages:540-552
Abstract: The weighted low-rank approximation problem in general has no analytical solution in terms of the singular value decomposition and is solved numerically using optimization methods. Four representations of the rank constraint that turn the abstract problem formulation into parameter optimization problems are presented. The parameter optimization problem is partially solved analytically, which results in an equivalent quadratically constrained problem. A commonly used re-parameterization avoids the quadratic constraint and makes the equivalent problem a nonlinear least squares problem, however, it might be necessary to change this re-parameterization during the iteration process. It is shown how the cost function can be computed efficiently in two special cases: row-wise and column-wise weighting. (c) 2006 Elsevier Inc. All rights reserved.
ISSN: 0024-3795
Publication status: published
KU Leuven publication type: IT
Appears in Collections:ESAT - STADIUS, Stadius Centre for Dynamical Systems, Signal Processing and Data Analytics
× corresponding author
# (joint) last author

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