Bilinear parameterization for differentiable rank-regularization

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceeding

Abstract

Low rank approximation is a commonly occurring problem in many computer vision and machine learning applications. There are two common ways of optimizing the resulting models. Either the set of matrices with a given rank can be explicitly parametrized using a bilinear factorization, or low rank can be implicitly enforced using regularization terms penalizing non-zero singular values. While the former approach results in differentiable problems that can be efficiently optimized using local quadratic approximation, the latter is typically not differentiable (sometimes even discontinuous) and requires first order subgradient or splitting methods. It is well known that gradient based methods exhibit slow convergence for ill-conditioned problems.In this paper we show how many non-differentiable regularization methods can be reformulated into smooth objectives using bilinear parameterization. This allows us to use standard second order methods, such as Levenberg- Marquardt (LM) and Variable Projection (VarPro), to achieve accurate solutions for ill-conditioned cases. We show on several real and synthetic experiments that our second order formulation converges to substantially more accurate solutions than competing state-of-the-art methods.1

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Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Computational Mathematics
Original languageEnglish
Title of host publicationProceedings - 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, CVPRW 2020
PublisherIEEE Computer Society
Pages1416-1425
Number of pages10
ISBN (Electronic)9781728193601
Publication statusPublished - 2020 Jun 1
Publication categoryResearch
Peer-reviewedYes
Event2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, CVPRW 2020 - Virtual, Online, United States
Duration: 2020 Jun 142020 Jun 19

Publication series

NameIEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops
Volume2020-June
ISSN (Print)2160-7508
ISSN (Electronic)2160-7516

Conference

Conference2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, CVPRW 2020
CountryUnited States
CityVirtual, Online
Period2020/06/142020/06/19