Extrinsic methods for coding and dictionary learning on grassmann manifolds

Harandi, Mehrtash, Hartley, Richard, Shen, Chunhua, Lovell, Brian and Sanderson, Conrad (2015) Extrinsic methods for coding and dictionary learning on grassmann manifolds. International Journal of Computer Vision, 114 2-3: 113-136. doi:10.1007/s11263-015-0833-x


Author Harandi, Mehrtash
Hartley, Richard
Shen, Chunhua
Lovell, Brian
Sanderson, Conrad
Title Extrinsic methods for coding and dictionary learning on grassmann manifolds
Journal name International Journal of Computer Vision   Check publisher's open access policy
ISSN 1573-1405
0920-5691
Publication date 2015-06-07
Sub-type Article (original research)
DOI 10.1007/s11263-015-0833-x
Volume 114
Issue 2-3
Start page 113
End page 136
Total pages 24
Place of publication New York, United States
Publisher Springer New York
Collection year 2016
Language eng
Abstract Sparsity-based representations have recently led to notable results in various visual recognition tasks. In a separate line of research, Riemannian manifolds have been shown useful for dealing with features and models that do not lie in Euclidean spaces. With the aim of building a bridge between the two realms, we address the problem of sparse coding and dictionary learning in Grassmann manifolds, i.e., the space of linear subspaces. To this end, we propose to embed Grassmann manifolds into the space of symmetric matrices by an isometric mapping. This in turn enables us to extend two sparse coding schemes to Grassmann manifolds. Furthermore, we propose an algorithm for learning a Grassmann dictionary, atom by atom. Lastly, to handle non-linearity in data, we extend the proposed Grassmann sparse coding and dictionary learning algorithms through embedding into higher dimensional Hilbert spaces. Experiments on several classification tasks (gender recognition, gesture classification, scene analysis, face recognition, action recognition and dynamic texture classification) show that the proposed approaches achieve considerable improvements in discrimination accuracy, in comparison to state-of-the-art methods such as kernelized Affine Hull Method and graph-embedding Grassmann discriminant analysis.
Keyword Dictionary learning
Grassmann manifolds
Riemannian geometry
Sparse coding
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ
Additional Notes Published online 7 June 2015.

Document type: Journal Article
Sub-type: Article (original research)
Collections: Official 2016 Collection
School of Information Technology and Electrical Engineering Publications
 
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