Extrinsic Methods for Coding and Dictionary Learning on Grassmann Manifolds

Loading...
Thumbnail Image
File version

Accepted Manuscript (AM)

Author(s)
Harandi, Mehrtash
Hartley, Richard
Shen, Chunhua
Lovell, Brian
Sanderson, Conrad
Griffith University Author(s)
Primary Supervisor
Other Supervisors
Editor(s)
Date
2015
Size
File type(s)
Location
License
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.

Journal Title

International Journal of Computer Vision

Conference Title
Book Title
Edition
Volume

114

Issue

2-Mar

Thesis Type
Degree Program
School
Publisher link
Patent number
Funder(s)
Grant identifier(s)
Rights Statement
Rights Statement

© 2015 Springer. This is an electronic version of an article published in International Journal of Computer Vision, 2015, 114 (2-3), pp. 113-136. European Journal of Nutrition is available online at: http://link.springer.com/ with the open URL of your article.

Item Access Status
Note
Access the data
Related item(s)
Subject

Artificial Intelligence and Image Processing

Persistent link to this record
Citation

Harandi, M; Hartley, R; Shen, C; Lovell, B; Sanderson, C, Extrinsic Methods for Coding and Dictionary Learning on Grassmann Manifolds, International Journal of Computer Vision, 2015, 114 (2-3), pp. 113-136

Collections