mlsanityData to 7 Oct 2026

Riemannian Multinomial Logistics Regression for SPD Neural Networks

arXiv 2305.11288 ↗First posted 18 May 2023cs.LGcited by 11

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Abstract (arXiv)

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.

Key facts. Cited by 11 papers in the map (data through 7 Oct 2026). Builds on 24 of its 60 references that are in the map. First posted on arXiv 18 May 2023.

Builds on

24 of 60 references.

References · 24

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2018Hyperbolic Neural Networkscited by 393
  3. 2018Riemannian Adaptive Optimization Methodscited by 187
  4. 2016A Riemannian Network for SPD Matrix Learningcited by 162
  5. 2018MOABB: Trustworthy algorithm benchmarking for BCIscited by 80
  6. 2019Riemannian batch normalization for SPD neural networkscited by 72
  7. 2022SPD domain-specific batch normalization to crack interpretable unsupervised domain adaptation in EEGcited by 53
  8. 2019A neural network based on SPD manifold learning for skeleton-based hand gesture recognitioncited by 46
  9. 2019Deep CNNs Meet Global Covariance Pooling: Better Representation and Generalizationcited by 42
  10. 2021On Riemannian Optimization over Positive Definite Matrices with the Bures-Wasserstein Geometrycited by 32
  11. 2016Dimensionality Reduction on SPD Manifolds: The Emergence of Geometry-Aware Methodscited by 29
  12. 2021GeomNet: A Neural Network Based on Riemannian Geometries of SPD Matrix Space and Cholesky Space for 3D Skeleton-Based Interaction Recognitioncited by 27
12 more
  1. 2021Why Approximate Matrix Square Root Outperforms Accurate SVD in Global Covariance Pooling?cited by 24
  2. 2021Vector-valued Distance and Gyrocalculus on the Space of Symmetric Positive Definite Matricescited by 22
  3. 2022Riemannian Local Mechanism for SPD Neural Networkscited by 22
  4. 2018Parallel Transport on the Cone Manifold of SPD Matrices for Domain Adaptationcited by 20
  5. 2021Distribution Knowledge Embedding for Graph Poolingcited by 19
  6. 2018A Statistical Recurrent Model on the Manifold of Symmetric Positive Definite Matricescited by 18
  7. 2023Building Neural Networks on Matrix Manifolds: A Gyrovector Space Approachcited by 18
  8. 2022Fast Differentiable Matrix Square Root and Inverse Square Rootcited by 16
  9. 2019Dilated Convolutional Neural Networks for Sequential Manifold-valued Datacited by 11
  10. 2022On the Eigenvalues of Global Covariance Pooling for Fine-grained Visual Recognitioncited by 10
  11. 2017DeepKSPD: Learning Kernel-matrix-based SPD Representation for Fine-grained Image Recognitioncited by 7
  12. 2017Learning a Robust Representation via a Deep Network on Symmetric Positive Definite Manifoldscited by 7

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 3; 2025: 2; 2026: 5.

11 papers.

  1. 2024Understanding Matrix Function Normalizations in Covariance Pooling through the Lens of Riemannian Geometrycited by 9
  2. 2024A Lie Group Approach to Riemannian Batch Normalizationcited by 8
  3. 2024RMLR: Extending Multinomial Logistic Regression into General Geometriescited by 8
  4. 2025Wrapped Gaussian on the manifold of Symmetric Positive Definite Matricescited by 5
  5. 2026Neural Networks on Symmetric Spaces of Noncompact Typecited by 5
  6. 2023Leveraging Optimal Transport via Projections on Subspaces for Machine Learning Applicationscited by 1
  7. 2025Siegel Neural Networkscited by 1
  8. 2026Beyond Rigid Geometries: The Spline-Pullback Metric for Universal Diffeomorphic SPD Representation Learningcited by 1
  9. 2026Riemannian Networks over Full-Rank Correlation Matricescited by 0
  10. 2026A Sliced-Wasserstein Framework on Correlation Matrices for EEG Decodingcited by 0
  11. 2026Text-Driven Fusion for Infrared and Visible Images: Achieving Image Scene Adaptation on Hyperbolic Spacecited by 0