Learning a discriminative SPD manifold neural network for image set classification.

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.