Riemannian Multiclass Logistics Regression for SPD Neural Networks
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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 approximated spaces rather than intrinsic classifiers that accurately capture the geometry of SPD manifolds. Inspired by the success of hyperbolic neural networks (HNNs), we propose Riemannian multiclass logistics regression (RMLR) for SPD networks. We introduce a general unified framework for a family of Riemannian metrics on SPD manifolds and showcase the specific n-invariant Log-Euclidean Metrics for SPD networks. Moreover, we encompass the most popular classifier in existing SPD networks as a special case of our framework. Extensive experiments on popular SPD learning benchmarks demonstrate the superiority of our classifiers.
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