U-SPDNet: An SPD manifold learning-based neural network for visual classification.

Area of Science:

• Computer Vision
• Pattern Recognition
• Machine Learning

Background:

• Neural network architectures for symmetric positive definite (SPD) matrix learning are emerging in computer vision and pattern recognition.
• Existing methods struggle with the degradation of structural information during multi-stage feature transformation, limiting their capacity.

Purpose of the Study:

• To develop a novel neural network architecture, U-SPDNet, designed to learn SPD matrices on manifolds.
• To address the limitation of structural information degradation in existing SPD matrix learning techniques.
• To improve visual classification accuracy by preserving fine-grained geometric features.

Main Methods:

• A U-shaped neural network (U-SPDNet) was developed, featuring an encoder (SPDNet) and a symmetric decoder.
• The decoder is trained using a reconstruction error term to alleviate information degradation.
• Skip connections are implemented using manifold-valued geometric operations like Riemannian barycenter and optimization.

Main Results:

• U-SPDNet demonstrated improved accuracy on multiple datasets (MDSD, Virus, FPHA, UAV-Human) compared to SPDNet.
• Accuracy gains ranged from 1.08% to 8.67% across the tested datasets.
• The proposed architecture effectively preserves structural information during feature transformation.

Conclusions:

• U-SPDNet effectively mitigates the degradation of structural information in SPD matrix learning.
• The novel architecture offers enhanced representational capacity for visual classification tasks.
• The method shows significant improvements over existing SPDNet approaches.