Deep Manifold-to-Manifold Transforming Network for Skeleton-Based Action Recognition

In this paper, we will investigate skeleton-based action recognition by employing high-order statistics feature and first-order statistics feature, where the high-order statistics feature is characterized by symmetric positive definite (SPD) matrices. Noting that SPD matrices are theoretically embedded on Riemannian manifolds, we propose an end-to-end deep manifold-to-manifold transforming network (DMT-Net), which can make SPD matrices flow from one Riemannian manifold to another one for facilitating the action recognition task. To learn discriminative SPD features from both spatial and temporal dependencies, we propose a neural network model with three novel layers on manifolds: i.e., (1) the local SPD convolutional layer, (2) the non-linear SPD activation layer, and (3) the Riemannian-preserved recursive layer. The SPD property is preserved through all layers without the singular value decomposition (SVD) operation, which has to be conducted in the existing methods with expensive computation cost. Furthermore, a diagonalizing SPD layer is designed to efficiently calculate the final metric for the classification task. Finally, DMT-Net is further fused with a first order layer to capture temporal evolution information. To evaluate our proposed method, we conduct extensive experiments on the task of action recognition, where the input signals are represented as SPD matrices. The experimental results demonstrate that the proposed method is competitive over state-of-the-art methods.