Optimizing over radial kernels on compact manifolds

Sadeep Jayasumana, Richard Hartley, Mathieu Salzmann, Hongdong Li, Mehrtash Harandi

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18 Citations (Scopus)


We tackle the problem of optimizing over all possible positive definite radial kernels on Riemannian manifolds for classification. Kernel methods on Riemannian manifolds have recently become increasingly popular in computer vision. However, the number of known positive definite kernels on manifolds remain very limited. Furthermore, most kernels typically depend on at least one parameter that needs to be tuned for the problem at hand. A poor choice of kernel, or of parameter value, may yield significant performance drop-off. Here, we show that positive definite radial kernels on the unit n-sphere, the Grassmann manifold and Kendall's shape manifold can be expressed in a simple form whose parameters can be automatically optimized within a support vector machine framework. We demonstrate the benefits of our kernel learning algorithm on object, face, action and shape recognition.

Original languageEnglish
Title of host publicationProceedings - 2014 IEEE Conference on Computer Vision and Pattern Recognition
EditorsRonen Basri, Cornelia Fermuller, Aleix Martinez, René Vidal
Place of PublicationPiscataway NJ USA
PublisherIEEE, Institute of Electrical and Electronics Engineers
Number of pages8
ISBN (Electronic)9781479951178
Publication statusPublished - 2014
Externally publishedYes
EventIEEE Conference on Computer Vision and Pattern Recognition 2014 - Columbus, United States of America
Duration: 23 Jun 201428 Jun 2014
http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=6909096 (IEEE Conference Proceedings)

Publication series

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


ConferenceIEEE Conference on Computer Vision and Pattern Recognition 2014
Abbreviated titleCVPR 2014
CountryUnited States of America
Internet address


  • Grassmann
  • kernel methods
  • kernels on manifolds
  • MKL
  • Riemannian manifolds
  • shape analysis

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