Riemannian Networks over Full-Rank Correlation Matrices
For researchers in geometric deep learning, this work provides a new framework for processing correlation matrices, which are underexplored compared to SPD matrices.
This paper introduces Riemannian networks over the manifold of full-rank correlation matrices, extending basic neural network layers to five correlation geometries. Experiments show the approach outperforms existing SPD and Grassmannian networks on several tasks.
Representations on the Symmetric Positive Definite (SPD) manifold have garnered significant attention across different applications. In contrast, the manifold of full-rank correlation matrices, a normalized alternative to SPD matrices, remains largely underexplored. This paper introduces Riemannian networks over the correlation manifold, leveraging five recently developed correlation geometries. We systematically extend basic layers, including Multinomial Logistic Regression (MLR), Fully Connected (FC), and convolutional layers, to these geometries. Besides, we present methods for accurate backpropagation for two correlation geometries. Experiments comparing our approach against existing SPD and Grassmannian networks demonstrate its effectiveness.