A Non-Convex Relaxation for Fixed-Rank Approximation
Paper in proceeding, 2017

This paper considers the problem of finding a low rank matrix from observations of linear combinations of its elements. It is well known that if the problem fulfills a restricted isometry property (RIP), convex relaxations using the nuclear norm typically work well and come with theoretical performance guarantees. On the other hand these formulations suffer from a shrinking bias that can severely degrade the solution in the presence of noise. In this theoretical paper we study an alternative non-convex relaxation that in contrast to the nuclear norm does not penalize the leading singular values and thereby avoids this bias. We show that despite its non-convexity the proposed formulation will in many cases have a single stationary point if a RIP holds. Our numerical tests show that our approach typically converges to a better solution than nuclear norm based alternatives even in cases when the RIP does not hold.

Author

Carl Olsson

Chalmers, Signals and Systems, Signal Processing and Biomedical Engineering

Marcus Carlsson

Lund University

Erik Bylow

Lund University

IEEE International Conference on Computer Vision Workshops

2473-9936 (ISSN)

Vol. 2018-January 1809-1817
978-1-5386-1034-3 (ISBN)

16th IEEE International Conference on Computer Vision (ICCV)
Venice, Italy,

Subject Categories

Applied Mechanics

Computational Mathematics

Probability Theory and Statistics

DOI

10.1109/ICCVW.2017.214

More information

Latest update

7/12/2024