mlsanityData to 14 Oct 2026

SPD Matrix Learning for Neuroimaging Analysis: Perspectives, Methods, and Challenges

arXiv 2504.18882 ↗First posted 26 Apr 2025cs.LG cs.AI eess.IVcited by 6

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Abstract (arXiv)

Neuroimaging provides essential tools for characterizing brain activity, structure, and connectivity through modalities that capture complementary aspects of brain organization. Across these diverse modalities, a unifying perspective arises when measurements are modeled as symmetric positive-definite (SPD)-valued representations through appropriate estimation or regularization procedures. Endowed with Riemannian geometry, the SPD manifold provides a non-Euclidean framework for principled statistical inference and machine learning on these representations. This review organizes these analytical and learning approaches within a framework for SPD matrix learning that connects classical geometric statistics with modern machine learning across neuroimaging and neurophysiological applications. We systematically survey the progression from modality-specific representations to geometric shallow and deep learning paradigms, highlighting how SPD matrix learning preserves underlying structural constraints while extending to modern AI applications in neuroimaging and brain-computer interfaces.

Key facts. Cited by 6 papers in the map (data through 14 Oct 2026). Builds on 45 of its 204 references that are in the map. First posted on arXiv 26 Apr 2025.

Builds on

45 of 204 references.

References · 45

  1. 2017A Unified Approach to Interpreting Model Predictionscited by 6,555
  2. 2017Axiomatic Attribution for Deep Networkscited by 3,384
  3. 2018Riemannian Adaptive Optimization Methodscited by 194
  4. 2016A Riemannian Network for SPD Matrix Learningcited by 162
  5. 2020Geoopt: Riemannian Optimization in PyTorchcited by 114
  6. 2013Manopt, a Matlab toolbox for optimization on manifoldscited by 113
  7. 2016Pymanopt: A Python Toolbox for Optimization on Manifolds using Automatic Differentiationcited by 94
  8. 2019Trivializations for Gradient-Based Optimization on Manifoldscited by 79
  9. 2019Riemannian batch normalization for SPD neural networkscited by 72
  10. 2018geomstats: a Python Package for Riemannian Geometry in Machine Learningcited by 71
  11. 2014Machine Learning for Neuroimaging with Scikit-Learncited by 70
  12. 2017Towards Faster Training of Global Covariance Pooling Networks by Iterative Matrix Square Root Normalizationcited by 65
33 more
  1. 2022SPD domain-specific batch normalization to crack interpretable unsupervised domain adaptation in EEGcited by 53
  2. 2022MAtt: A Manifold Attention Network for EEG Decodingcited by 44
  3. 2018Reconstructing Faces from fMRI Patterns using Deep Generative Neural Networkscited by 43
  4. 2020Federated Transfer Learning for EEG Signal Classificationcited by 37
  5. 2016Dimensionality Reduction on SPD Manifolds: The Emergence of Geometry-Aware Methodscited by 29
  6. 2014From Manifold to Manifold: Geometry-Aware Dimensionality Reduction for SPD Matricescited by 22
  7. 2021Vector-valued Distance and Gyrocalculus on the Space of Symmetric Positive Definite Matricescited by 22
  8. 2022Tensor-CSPNet: A Novel Geometric Deep Learning Framework for Motor Imagery Classificationcited by 21
  9. 2014Kernel Methods on the Riemannian Manifold of Symmetric Positive Definite Matricescited by 20
  10. 2018Parallel Transport on the Cone Manifold of SPD Matrices for Domain Adaptationcited by 20
  11. 2023Sliced-Wasserstein on Symmetric Positive Definite Matrices for M/EEG Signalscited by 19
  12. 2023Building Neural Networks on Matrix Manifolds: A Gyrovector Space Approachcited by 18
  13. 2019Manifold-regression to predict from MEG/EEG brain signals without source modelingcited by 17
  14. 2022Fast Differentiable Matrix Square Root and Inverse Square Rootcited by 16
  15. 2022Graph Neural Networks on SPD Manifolds for Motor Imagery Classification: A Perspective from the Time-Frequency Analysiscited by 15
  16. 2024Matrix Manifold Neural Networks++cited by 13
  17. 2014Regularized Tyler's Scatter Estimator: Existence, Uniqueness, and Algorithmscited by 12
  18. 2022Deep Riemannian Networks for End-to-End EEG Decodingcited by 11
  19. 2024Geodesic Optimization for Predictive Shift Adaptation on EEG datacited by 10
  20. 2019Analyzing Dynamical Brain Functional Connectivity As Trajectories on Space of Covariance Matricescited by 9
  21. 2021On the interpretation of linear Riemannian tangent space model parameters in M/EEGcited by 8
  22. 2022Deep Optimal Transport for Domain Adaptation on SPD Manifoldscited by 6
  23. 2013A New Generation of Brain-Computer Interface Based on Riemannian Geometrycited by 5
  24. 2023Differential geometry with extreme eigenvalues in the positive semidefinite conecited by 5
  25. 2023The Fisher-Rao geometry of CES distributionscited by 5
  26. 2023Deep Geometric Learning with Monotonicity Constraints for Alzheimer's Disease Progressioncited by 4
  27. 2024Exploring the Enigma of Neural Dynamics Through A Scattering-Transform Mixer Landscape for Riemannian Manifoldcited by 4
  28. 2019Tangent space spatial filters for interpretable and efficient Riemannian classificationcited by 3
  29. 2024Physics-informed and Unsupervised Riemannian Domain Adaptation for Machine Learning on Heterogeneous EEG Datasetscited by 3
  30. 2024Weakly supervised covariance matrices alignment through Stiefel matrices estimation for MEG applicationscited by 2
  31. 2025Scalable Geometric Learning with Correlation-Based Functional Brain Networkscited by 2
  32. 2016Dimensionality reduction based on Distance Preservation to Local Mean (DPLM) for SPD matrices and its application in BCIcited by 1
  33. 2023Score-Based Data Generation for EEG Spatial Covariance Matrices: Towards Boosting BCI Performancecited by 1

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 6.

6 papers.

  1. 2026Sheaf Neural Networks on SPD Manifolds: Second-Order Geometric Representation Learningcited by 3
  2. 2026SPD Learn: A Geometric Deep Learning Python Library for Neural Decoding Through Trivializationcited by 2
  3. 2026Generalized Kalman filter based temporal difference reinforcement learningcited by 0
  4. 2026Rectifying Geometric Misalignment: Online Source-Free Adaptation for Class-Imbalanced EEGcited by 0
  5. 2026High-Resolution Dynamic Functional Connectivity Generation with Graph-Variate Flow Matchingcited by 0
  6. 2026SPDAlign: Interpretable Riemannian Alignment for EEG Forward Modeling Shiftscited by 0