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A unified optimization framework for low-rank inducing penalties

Örnhag, Marcus Valtonen LU and Olsson, Carl LU (2020) 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2020 In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition p.8471-8480
Abstract

In this paper we study the convex envelopes of a new class of functions. Using this approach, we are able to unify two important classes of regularizers from unbiased non-convex formulations and weighted nuclear norm penalties. This opens up for possibilities of combining the best of both worlds, and to leverage each method’s contribution to cases where simply enforcing one of the regularizers are insufficient. We show that the proposed regularizers can be incorporated in standard splitting schemes such as Alternating Direction Methods of Multipliers (ADMM), and other subgradient methods. Furthermore, we provide an efficient way of computing the proximal operator. Lastly, we show on real non-rigid structure-from-motion (NRSfM) datasets,... (More)

In this paper we study the convex envelopes of a new class of functions. Using this approach, we are able to unify two important classes of regularizers from unbiased non-convex formulations and weighted nuclear norm penalties. This opens up for possibilities of combining the best of both worlds, and to leverage each method’s contribution to cases where simply enforcing one of the regularizers are insufficient. We show that the proposed regularizers can be incorporated in standard splitting schemes such as Alternating Direction Methods of Multipliers (ADMM), and other subgradient methods. Furthermore, we provide an efficient way of computing the proximal operator. Lastly, we show on real non-rigid structure-from-motion (NRSfM) datasets, the issues that arise from using weighted nuclear norm penalties, and how this can be remedied using our proposed method.

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Please use this url to cite or link to this publication:
author
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organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)
series title
Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
pages
10 pages
conference name
2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2020
conference location
Virtual, Online, United States
conference dates
2020-06-14 - 2020-06-19
external identifiers
  • scopus:85094558803
ISSN
1063-6919
ISBN
978-1-7281-7168-5
DOI
10.1109/CVPR42600.2020.00850
language
English
LU publication?
yes
id
aead0315-05ab-4687-908e-6a581b636ad9
date added to LUP
2020-11-23 09:43:07
date last changed
2022-05-12 07:57:00
@inproceedings{aead0315-05ab-4687-908e-6a581b636ad9,
  abstract     = {{<p>In this paper we study the convex envelopes of a new class of functions. Using this approach, we are able to unify two important classes of regularizers from unbiased non-convex formulations and weighted nuclear norm penalties. This opens up for possibilities of combining the best of both worlds, and to leverage each method’s contribution to cases where simply enforcing one of the regularizers are insufficient. We show that the proposed regularizers can be incorporated in standard splitting schemes such as Alternating Direction Methods of Multipliers (ADMM), and other subgradient methods. Furthermore, we provide an efficient way of computing the proximal operator. Lastly, we show on real non-rigid structure-from-motion (NRSfM) datasets, the issues that arise from using weighted nuclear norm penalties, and how this can be remedied using our proposed method.</p>}},
  author       = {{Örnhag, Marcus Valtonen and Olsson, Carl}},
  booktitle    = {{2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)}},
  isbn         = {{978-1-7281-7168-5}},
  issn         = {{1063-6919}},
  language     = {{eng}},
  pages        = {{8471--8480}},
  series       = {{Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition}},
  title        = {{A unified optimization framework for low-rank inducing penalties}},
  url          = {{http://dx.doi.org/10.1109/CVPR42600.2020.00850}},
  doi          = {{10.1109/CVPR42600.2020.00850}},
  year         = {{2020}},
}