Riemannian Networks on Correlation Manifolds Introduced
A team of researchers has unveiled Riemannian networks that operate on the manifold of full-rank correlation matrices, serving as a normalized substitute for the Symmetric Positive Definite (SPD) manifold. This research enhances fundamental neural network components—Multinomial Logistic Regression (MLR), Fully Connected (FC), and convolutional layers—by applying them to five newly established correlation geometries. Additionally, the study offers methods for precise backpropagation in two of these geometries. Experimental results indicate that this new approach surpasses the performance of current SPD and Grassmannian networks. The findings are available on arXiv within the domains of computer science and machine learning.
Key facts
- Riemannian networks over full-rank correlation matrices are introduced.
- Five recently developed correlation geometries are leveraged.
- Basic layers (MLR, FC, convolutional) are extended to these geometries.
- Accurate backpropagation methods are provided for two correlation geometries.
- Experiments compare against existing SPD and Grassmannian networks.
- The approach demonstrates effectiveness over existing methods.
- The paper is listed under Computer Science > Machine Learning.
- Published on arXiv with ID 2605.19073.
Entities
Institutions
- arXiv