Learning to optimize on SPD manifolds

Zhi Gao, Yuwei Wu, Yunde Jia, Mehrtash Harandi

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

16 Citations (Scopus)

Abstract

Many tasks in computer vision and machine learning are modeled as optimization problems with constraints in the form of Symmetric Positive Definite (SPD) matrices. Solving such optimization problems is challenging due to the non-linearity of the SPD manifold, making optimization with SPD constraints heavily relying on expert knowledge and human involvement. In this paper, we propose a meta-learning method to automatically learn an iterative optimizer on SPD manifolds. Specifically, we introduce a novel recurrent model that takes into account the structure of input gradients and identifies the updating scheme of optimization. We parameterize the optimizer by the recurrent model and utilize Riemannian operations to ensure that our method is faithful to the geometry of SPD manifolds. Compared with existing SPD optimizers, our optimizer effectively exploits the underlying data distribution and learns a better optimization trajectory in a data-driven manner. Extensive experiments on various computer vision tasks including metric nearness, clustering, and similarity learning demonstrate that our optimizer outperforms existing state-of-the-art methods consistently.

Original languageEnglish
Title of host publicationProceedings - 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2020
EditorsCe Liu, Greg Mori, Kate Saenko, Silvio Savarese
Place of PublicationPiscataway NJ USA
Pages7697-7706
Number of pages10
ISBN (Electronic)9781728171685
DOIs
Publication statusPublished - 2020
EventIEEE Conference on Computer Vision and Pattern Recognition 2020 - Virtual, China
Duration: 14 Jun 202019 Jun 2020
http://cvpr2020.thecvf.com (Website )
https://openaccess.thecvf.com/CVPR2020 (Proceedings)
https://ieeexplore.ieee.org/xpl/conhome/9142308/proceeding (Proceedings)

Conference

ConferenceIEEE Conference on Computer Vision and Pattern Recognition 2020
Abbreviated titleCVPR 2020
Country/TerritoryChina
CityVirtual
Period14/06/2019/06/20
Internet address

Cite this