Heterogeneous Riemannian Few-Shot Learning Network.

How to learn and accurately distinguish new concepts from few samples, as humans do, is a long-standing concern in artificial intelligence (AI). Studies in brain science and neuroscience have shown that human brain perception is based on nonlinear manifolds, and high-dimensional manifolds can facilitate concept learning in neural circuits. Based on this inspiration, in this paper, we propose a heterogeneous Riemannian few-shot learning network (HRFL-Net), which is the first few-shot learning method to perform end-to-end deep learning on heterogeneous Riemannian manifolds. Specifically, to enhance the geometric invariance of the image representation, the image features are projected into three heterogeneous Riemannian manifold spaces. Then, the implicit Riemannian kernel function maps the manifolds to the separable high-dimensional reproducing Hilbert space. It is assumed that the embedded kernel features of the complementary manifolds are mapped to the same common subspace. Thus, a novel neural network-based Riemannian metric learning method is designed to solve the subspace feature vectors by imposing orthogonal normalized projection, which overcomes the data extension limitation of the Riemannian metric. Finally, with the optimization objective of increasing the interclass distance and decreasing the intraclass distance in Hilbert space, the HRFL-Net is trained with end-to-end stochastic optimization, and the optimal aggregation subspace is learned during the gradient descent process. Thus, the proposed HRFL-Net can be easily generalized to challenging nonconvex data. The evaluation of four public datasets shows that the proposed HRFL-Net has significant superiority and also achieves competitive results compared with the state-of-the-art methods.