Riemannian Multinomial Logistics Regression for SPD Neural Networks
This work addresses the need for intrinsic classifiers in SPD networks for applications like radar and EEG, but it is incremental as it builds on existing hyperbolic neural networks and SPD methods.
The authors tackled the problem of classification in SPD networks by proposing Riemannian Multinomial Logistics Regression (RMLR) to better capture the geometry of SPD manifolds, achieving effectiveness in radar recognition, human action recognition, and EEG classification.
Deep neural networks for learning Symmetric Positive Definite (SPD) matrices are gaining increasing attention in machine learning. Despite the significant progress, most existing SPD networks use traditional Euclidean classifiers on an approximated space rather than intrinsic classifiers that accurately capture the geometry of SPD manifolds. Inspired by Hyperbolic Neural Networks (HNNs), we propose Riemannian Multinomial Logistics Regression (RMLR) for the classification layers in SPD networks. We introduce a unified framework for building Riemannian classifiers under the metrics pulled back from the Euclidean space, and showcase our framework under the parameterized Log-Euclidean Metric (LEM) and Log-Cholesky Metric (LCM). Besides, our framework offers a novel intrinsic explanation for the most popular LogEig classifier in existing SPD networks. The effectiveness of our method is demonstrated in three applications: radar recognition, human action recognition, and electroencephalography (EEG) classification. The code is available at https://github.com/GitZH-Chen/SPDMLR.git.