Random projections on manifolds of symmetric positive definite matrices for image classification

Alavi, Azadeh, Wiliem, Arnold, Zhao, Kun, Lovell, Brian C. and Sanderson, Conrad (2014). Random projections on manifolds of symmetric positive definite matrices for image classification. In: 2014 IEEE Winter Conference on Applications of Computer Vision (WACV). IEEE Winter Conference on Applications of Computer Vision (WACV 2014), Steamboat Springs, CO, United States, (301-308). 24-26 March 2014. doi:10.1109/WACV.2014.6836085

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Author Alavi, Azadeh
Wiliem, Arnold
Zhao, Kun
Lovell, Brian C.
Sanderson, Conrad
Title of paper Random projections on manifolds of symmetric positive definite matrices for image classification
Conference name IEEE Winter Conference on Applications of Computer Vision (WACV 2014)
Conference location Steamboat Springs, CO, United States
Conference dates 24-26 March 2014
Convener IEEE
Proceedings title 2014 IEEE Winter Conference on Applications of Computer Vision (WACV)   Check publisher's open access policy
Journal name 2014 Ieee Winter Conference On Applications of Computer Vision (Wacv)   Check publisher's open access policy
Place of Publication Piscataway, NJ, United States
Publisher Institute of Electrical and Electronics Engineers
Publication Year 2014
Sub-type Fully published paper
DOI 10.1109/WACV.2014.6836085
Open Access Status
ISBN 9781479949847
ISSN 1550-5790
Start page 301
End page 308
Total pages 8
Collection year 2015
Language eng
Formatted Abstract/Summary
Recent advances suggest that encoding images through Symmetric Positive Definite (SPD) matrices and then interpreting such matrices as points on Riemannian manifolds can lead to increased classification performance. Taking into account manifold geometry is typically done via (1) embedding the manifolds in tangent spaces, or (2) embedding into Reproducing Kernel Hilbert Spaces (RKHS). While embedding into tangent spaces allows the use of existing Euclidean-based learning algorithms, manifold shape is only approximated which can cause loss of discriminatory information. The RKHS approach retains more of the manifold structure, but may require non-trivial effort to kernelise Euclidean-based learning algorithms. In contrast to the above approaches, in this paper we offer a novel solution that allows SPD matrices to be used with unmodified Euclidean-based learning algorithms, with the true manifold shape well-preserved. Specifically, we propose to project SPD matrices using a set of random projection hyperplanes over RKHS into a random projection space, which leads to representing each matrix as a vector of projection coefficients. Experiments on face recognition, person re-identification and texture classification show that the proposed approach outperforms several recent methods, such as Tensor Sparse Coding, Histogram Plus Epitome, Riemannian Locality Preserving Projection and Relational Divergence Classification.
Q-Index Code E1
Q-Index Status Confirmed Code
Institutional Status UQ

 
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Created: Thu, 09 Jan 2014, 14:59:23 EST by Azadeh Alavi on behalf of School of Information Technol and Elec Engineering