Riemannian Local Mechanism for SPD Neural Networks
This work addresses a domain-specific problem for researchers and practitioners in computer vision and related fields using SPD matrices, representing an incremental improvement by adapting local mechanisms from Euclidean methods to Riemannian manifolds.
The paper tackles the problem of preserving local geometric information in deep neural networks for Symmetric Positive Definite (SPD) matrices by proposing a Riemannian local mechanism, and experiments on multiple visual tasks validate its effectiveness.
The Symmetric Positive Definite (SPD) matrices have received wide attention for data representation in many scientific areas. Although there are many different attempts to develop effective deep architectures for data processing on the Riemannian manifold of SPD matrices, very few solutions explicitly mine the local geometrical information in deep SPD feature representations. Given the great success of local mechanisms in Euclidean methods, we argue that it is of utmost importance to ensure the preservation of local geometric information in the SPD networks. We first analyse the convolution operator commonly used for capturing local information in Euclidean deep networks from the perspective of a higher level of abstraction afforded by category theory. Based on this analysis, we define the local information in the SPD manifold and design a multi-scale submanifold block for mining local geometry. Experiments involving multiple visual tasks validate the effectiveness of our approach. The supplement and source code can be found in https://github.com/GitZH-Chen/MSNet.git.