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2018 IEEE International Conference on Multimedia and Expo (ICME) (2018)
San Diego, CA, USA
July 23, 2018 to July 27, 2018
ISSN: 1945-7871
ISBN: 978-1-5386-1738-0
pp: 1-6
Hao Cheng , School of Computer Science and Technology, Tianjin University, Tianjin, 300350, China
Pengfei Zhu , School of Computer Science and Technology, Tianjin University, Tianjin, 300350, China
Qilong Wang , School of Computer Science and Technology, Tianjin University, Tianjin, 300350, China
Changqing Zhang , School of Computer Science and Technology, Tianjin University, Tianjin, 300350, China
Qinghua Hu , School of Computer Science and Technology, Tianjin University, Tianjin, 300350, China
ABSTRACT
The manifold of symmetric positive definite (SPD) matrices has drawn significant attention because of its widespread applications. SPD matrices provide compact nonlinear representations of data and form a special type of Riemannian manifold. The direct application of support vector machines on SPD manifold maybe fails due to lack of samples per class. In this paper, we propose a support vector metric learning (SVML) model on SPD manifold. We define a positive definite kernel for point pairs on SPD manifold and transform metric learning on SPD manifold to a point pair classification problem. The metric learning problem can be efficiently solved by standard support vector machines. Compared with classifying points on SPD manifold by support vector machines directly, SVML effectively learns a distance metric for SPD matrices by training a binary support vector machine model. Experiments on video based face recognition, image set classification, and material classification show that SVML outperforms the state-of-the-art metric learning algorithms on SPD manifold.
INDEX TERMS
Manifolds, Kernel, Support vector machines, Matrix converters, Symmetric matrices, Extraterrestrial measurements
CITATION

H. Cheng, P. Zhu, Q. Wang, C. Zhang and Q. Hu, "Support Vector Metric Learning on Symmetric Positive Definite Manifold," 2018 IEEE International Conference on Multimedia and Expo (ICME), San Diego, CA, USA, 2018, pp. 1-6.
doi:10.1109/ICME.2018.8486518
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