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. In-spired 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.

Riemannian Multinomial Logistics Regression for SPD Neural Networks / Chen, Ziheng; Song, Yue; Liu, Gaowen; Kompella, Ramana Rao; Wu, Xiao-Jun; Sebe, Nicu. - (2024), pp. 17086-17096. (Intervento presentato al convegno 2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) tenutosi a Seattle, WA, USA nel 16-22 June 2024) [10.1109/cvpr52733.2024.01617].

Riemannian Multinomial Logistics Regression for SPD Neural Networks

Chen, Ziheng;Song, Yue;Liu, Gaowen;Sebe, Nicu
2024-01-01

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. In-spired 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.
2024
2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition
Piscataway, NJ USA
IEEE
979-8-3503-5300-6
979-8-3503-5301-3
Chen, Ziheng; Song, Yue; Liu, Gaowen; Kompella, Ramana Rao; Wu, Xiao-Jun; Sebe, Nicu
Riemannian Multinomial Logistics Regression for SPD Neural Networks / Chen, Ziheng; Song, Yue; Liu, Gaowen; Kompella, Ramana Rao; Wu, Xiao-Jun; Sebe, Nicu. - (2024), pp. 17086-17096. (Intervento presentato al convegno 2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) tenutosi a Seattle, WA, USA nel 16-22 June 2024) [10.1109/cvpr52733.2024.01617].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/432610
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