A Riemannian rank-adaptive method for low-rank optimization
Authors
Guifang Zhou, Wen Huang, Kyle A. Gallivan, Paul Van Dooren, P.-A. Absil
Abstract
This paper presents an algorithm that solves optimization problems on a matrix manifold $\mathcal{M} \subseteq \mathbb{R}^{m \times n}$ with an additional rank inequality constraint. The algorithm resorts to well-known Riemannian optimization schemes on fixed-rank manifolds, combined with new mechanisms to increase or decrease the rank. The convergence of the algorithm is analyzed and a weighted low-rank approximation problem is used to illustrate the efficiency and effectiveness of the algorithm.
Status
Neurocomputing, 192, 72-80, June 2016.
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BibTex entry
- Technical Report
@TECHREPORT{HAG2015,
author = "Guifang Zhou and Wen Huang and Kyle A. Gallivan and Paul Van Dooren and P.-A. Absil",
title = "A Riemannian rank-adaptive method for low-rank optimization",
institution = "U.C.Louvain",
number = "UCL-INMA-2015.05",
year = 2015,
}