Riemannian Multinomial Logistics Regression for SPD Neural Networks
arxiv(2023)
Abstract
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.
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