Riemannian coding and dictionary learning: Kernels to the rescue

Mehrtash Harandi, Mathieu Salzmann

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

    69 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 publicationIEEE Conference on Computer Vision and Pattern Recognition, CVPR 2015
    PublisherIEEE Computer Society
    Pages3926-3935
    Number of pages10
    ISBN (Electronic)9781467369640
    DOIs
    Publication statusPublished - 14 Oct 2015
    EventIEEE Conference on Computer Vision and Pattern Recognition, CVPR 2015 - Boston, United States
    Duration: 7 Jun 201512 Jun 2015

    Publication series

    NameProceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
    Volume07-12-June-2015
    ISSN (Print)1063-6919

    Conference

    ConferenceIEEE Conference on Computer Vision and Pattern Recognition, CVPR 2015
    Country/TerritoryUnited States
    CityBoston
    Period7/06/1512/06/15

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