2022/01/25 by Ziheng Chen, Chen, Ziheng, Tianyang Xu +9 · 2 citations
Computer Science · Engineering · Mathematics · #3D Shape Modeling and Analysis #Abstraction #Algebra over a field #Artificial intelligence #Artificial neural network #Block (permutation group theory) #Computer science #Convolution (computer science) #Deep learning #Engineering #Euclidean geometry #Face and Expression Recognition #Feature (linguistics) #Geometry #Image Retrieval and Classification Techniques #Manifold (fluid mechanics) #Mathematics #Pure mathematics #Representation (politics) #Riemannian manifold #Submanifold #Theoretical computer science
paper · pdf · doi:10.48550/arxiv.2201.10145
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2022/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/09
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.