Riemannian coding and dictionary learning: kernels to the rescue

Mehrtash Harandi, Mathieu Salzmann

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

55 Citations (Scopus)

Abstract

While sparse coding on non-flat Riemannian manifolds has recently become increasingly popular, existing solutions either are dedicated to specific manifolds, or rely on optimization problems that are difficult to solve, especially when it comes to dictionary learning. In this paper, we propose to make use of kernels to perform coding and dictionary learning on Riemannian manifolds. To this end, we introduce a general Riemannian coding framework with its kernel-based counterpart. This lets us (i) generalize beyond the special case of sparse coding; (ii) introduce efficient solutions to two coding schemes; (iii) learn the kernel parameters; (iv) perform unsupervised and supervised dictionary learning in a much simpler manner than previous Riemannian coding methods. We demonstrate the effectiveness of our approach on three different types of non-flat manifolds, and illustrate its generality by applying it to Euclidean spaces, which also are Riemannian manifolds.

Original languageEnglish
Title of host publication2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
EditorsKristen Grauman, Erik Learned-Miller, Antonio Torralba, Andrew Zisserman
Place of PublicationPiscataway NJ USA
PublisherIEEE, Institute of Electrical and Electronics Engineers
Pages3926-3935
Number of pages10
ISBN (Electronic)9781467369640
DOIs
Publication statusPublished - 2015
Externally publishedYes
EventIEEE Conference on Computer Vision and Pattern Recognition 2015 - Hynes Convention Center, Boston, United States of America
Duration: 7 Jun 201512 Jun 2015
http://www.pamitc.org/cvpr15/ (Website)
https://ieeexplore.ieee.org/xpl/conhome/7293313/proceeding (Proceedings)

Publication series

NameProceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
PublisherIEEE, Institute of Electrical and Electronics Engineers
ISSN (Print)1063-6919

Conference

ConferenceIEEE Conference on Computer Vision and Pattern Recognition 2015
Abbreviated titleCVPR 2015
Country/TerritoryUnited States of America
CityBoston
Period7/06/1512/06/15
Internet address

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