U-SPDNet: An SPD manifold learning-based neural network for visual classification.

With the development of neural networking techniques, several architectures for symmetric positive definite (SPD) matrix learning have recently been put forward in the computer vision and pattern recognition (CV&PR) community for mining fine-grained geometric features. However, the degradation of structural information during multi-stage feature transformation limits their capacity. To cope with this issue, this paper develops a U-shaped neural network on the SPD manifolds (U-SPDNet) for visual classification. The designed U-SPDNet contains two subsystems, one of which is a shrinking path (encoder) making up of a prevailing SPD manifold neural network (SPDNet (Huang and Van Gool, 2017)) for capturing compact representations from the input data. Another is a constructed symmetric expanding path (decoder) to upsample the encoded features, trained by a reconstruction error term. With this design, the degradation problem will be gradually alleviated during training. To enhance the representational capacity of U-SPDNet, we also append skip connections from encoder to decoder, realized by manifold-valued geometric operations, namely Riemannian barycenter and Riemannian optimization. On the MDSD, Virus, FPHA, and UAV-Human datasets, the accuracy achieved by our method is respectively 6.92%, 8.67%, 1.57%, and 1.08% higher than SPDNet, certifying its effectiveness.