Expanding the Family of Grassmannian Kernels: An Embedding Perspective

  • Mehrtash T. Harandi
  • Mathieu Salzmann
  • Sadeep Jayasumana
  • Richard Hartley
  • Hongdong Li
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8695)


Modeling videos and image-sets as linear subspaces has proven beneficial for many visual recognition tasks. However, it also incurs challenges arising from the fact that linear subspaces do not obey Euclidean geometry, but lie on a special type of Riemannian manifolds known as Grassmannian. To leverage the techniques developed for Euclidean spaces (e.g., support vector machines) with subspaces, several recent studies have proposed to embed the Grassmannian into a Hilbert space by making use of a positive definite kernel. Unfortunately, only two Grassmannian kernels are known, none of which -as we will show- is universal, which limits their ability to approximate a target function arbitrarily well. Here, we introduce several positive definite Grassmannian kernels, including universal ones, and demonstrate their superiority over previously-known kernels in various tasks, such as classification, clustering, sparse coding and hashing.


Grassmann manifolds kernel methods Plücker embedding 

Supplementary material

978-3-319-10584-0_27_MOESM1_ESM.pdf (488 kb)
Electronic Supplementary Material (PDF 488 KB)


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Mehrtash T. Harandi
    • 1
    • 2
  • Mathieu Salzmann
    • 1
    • 2
  • Sadeep Jayasumana
    • 1
    • 2
  • Richard Hartley
    • 1
    • 2
  • Hongdong Li
    • 1
    • 2
  1. 1.Australian National UniversityCanberraAustralia
  2. 2.NICTACanberraAustralia

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