Journal
NEURAL NETWORKS
Volume 151, Issue -, Pages 94-110Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.neunet.2022.03.012
Keywords
SPD manifold neural network; Image set classification; Metric learning; Riemannian barycenter; Riemannian optimization
Funding
- National Natural Science Foundation of China [62020106012, U1836218, 61672265, 621060 89 62006097]
- 111 Project of Ministry of Education of China [B12018]
- Natural Science Foundation of Jiangsu Province, China [BK20200593]
- Postgraduate Research & Practice Innovation Program of Jiangsu Province, China [KYCX21-2006]
- UK EPSRC [EP/N00 7743/1]
- MURI/EPSRC/DSTL, UK [MURI/EPSRC/DSTL]
- National Key Research and Development Program of China [UK EP/R018456/1]
- National Key Research and Development Program of China [2017YFC1601800]
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This paper investigates pattern analysis on the symmetric positive definite manifold and designs two Riemannian operation modules for neural networks. Experimental results demonstrate the effectiveness of the proposed approach.
Performing pattern analysis over the symmetric positive definite (SPD) manifold requires specific mathematical computations, characterizing the non-Euclidian property of the involved data points and learning tasks, such as the image set classification problem. Accompanied with the advanced neural networking techniques, several architectures for processing the SPD matrices have recently been studied to obtain fine-grained structured representations. However, existing approaches are challenged by the diversely changing appearance of the data points, begging the question of how to learn invariant representations for improved performance with supportive theories. Therefore, this paper designs two Riemannian operation modules for SPD manifold neural network. Specifically, a Riemannian batch regularization (RBR) layer is firstly proposed for the purpose of training a discriminative manifold-to-manifold transforming network with a novelly-designed metric learning regularization term. The second module realizes the Riemannian pooling operation with geometric computations on the Riemannian manifolds, notably the Riemannian barycenter, metric learning, and Riemannian optimization. Extensive experiments on five benchmarking datasets show the efficacy of the proposed approach.(C)& nbsp; 2022 Published by Elsevier Ltd.
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