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A Riemannian rank-adaptive method for low-rank optimization

Guifang Zhou (zhouguifang2009***at***gmail.com)
Wen Huang (huwst08***at***gmail.com)
Kyle A. Gallivan (kgallivan***at***fsu.edu)
Paul Van Dooren (Paul.Vandooren***at***uclouvain.be)
P.-A. Absil (absil***at***inma.ucl.ac.be)

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.

Keywords: low-rank optimization; rank-constrained optimization; Riemannian manifold; fixed-rank manifold; low-rank approximation

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 2: Applications -- Science and Engineering (Data-Mining )

Citation: Technical report UCL-INMA-2015.05

Download: [PDF]

Entry Submitted: 01/27/2016
Entry Accepted: 01/27/2016
Entry Last Modified: 02/05/2016

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