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

Alavi, Azadeh, Wiliem, Arnold, Zhao, Kun, Lovell, Brian, & Sanderson, Conrad (2014) Random projections on manifolds of symmetric positive definite matrices for image classification. In IEEE Winter Conference on the Applications of Computer Vision, March 24-26, 2014, Steamboat Springs, CO.

Abstract

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.

Impact and interest:

3 citations in Scopus
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2 citations in Web of Science®

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ID Code: 71629
Item Type: Conference Paper
Refereed: Yes
Additional URLs:
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200)
Australian and New Zealand Standard Research Classification > INFORMATION AND COMPUTING SCIENCES (080000)
Australian and New Zealand Standard Research Classification > INFORMATION AND COMPUTING SCIENCES (080000) > ARTIFICIAL INTELLIGENCE AND IMAGE PROCESSING (080100) > Computer Vision (080104)
Australian and New Zealand Standard Research Classification > INFORMATION AND COMPUTING SCIENCES (080000) > ARTIFICIAL INTELLIGENCE AND IMAGE PROCESSING (080100) > Image Processing (080106)
Australian and New Zealand Standard Research Classification > INFORMATION AND COMPUTING SCIENCES (080000) > ARTIFICIAL INTELLIGENCE AND IMAGE PROCESSING (080100) > Pattern Recognition and Data Mining (080109)
Australian and New Zealand Standard Research Classification > ENGINEERING (090000) > ELECTRICAL AND ELECTRONIC ENGINEERING (090600) > Signal Processing (090609)
Divisions: Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2014 [please consult the author]
Deposited On: 15 May 2014 00:55
Last Modified: 01 Aug 2014 11:06

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