Dictionary learning and sparse coding on Grassmann Manifolds: An extrinsic solution

Mehrtash Harandi, Conrad Sanderson, Chunhua Shen, Brian Lovell

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

90 Citations (Scopus)


Recent advances in computer vision and machine learning suggest that a wide range of problems can be addressed more appropriately by considering non-Euclidean geometry. In this paper we explore sparse dictionary learning over the space of linear subspaces, which form Riemannian structures known as Grassmann manifolds. To this end, we propose to embed Grassmann manifolds into the space of symmetric matrices by an isometric mapping, which enables us to devise a closed-form solution for updating a Grassmann dictionary, atom by atom. Furthermore, to handle non-linearity in data, we propose a kernelised version of the dictionary learning algorithm. Experiments on several classification tasks (face recognition, action recognition, dynamic texture classification) show that the proposed approach achieves considerable improvements in discrimination accuracy, in comparison to state-of-the-art methods such as kernelised Affine Hull Method and graph-embedding Grassmann discriminant analysis.

Original languageEnglish
Title of host publicationProceedings - 2013 IEEE International Conference on Computer Vision, ICCV 2013
PublisherIEEE, Institute of Electrical and Electronics Engineers
Number of pages8
ISBN (Print)9781479928392
Publication statusPublished - 1 Jan 2013
Externally publishedYes
Event2013 14th IEEE International Conference on Computer Vision, ICCV 2013 - Sydney, NSW, Australia
Duration: 1 Dec 20138 Dec 2013

Publication series

NameProceedings of the IEEE International Conference on Computer Vision


Conference2013 14th IEEE International Conference on Computer Vision, ICCV 2013
CitySydney, NSW


  • action recognition
  • dictionary learning
  • dynamic texture classification
  • Grassmann manifolds
  • image-set
  • sparse coding

Cite this