mlsanityData to 7 Oct 2026

Sliced-Wasserstein on Symmetric Positive Definite Matrices for M/EEG Signals

arXiv 2303.05798 ↗First posted 10 Mar 2023cs.LG eess.SP stat.MLcited by 19

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Abstract (arXiv)

When dealing with electro or magnetoencephalography records, many supervised prediction tasks are solved by working with covariance matrices to summarize the signals. Learning with these matrices requires using Riemanian geometry to account for their structure. In this paper, we propose a new method to deal with distributions of covariance matrices and demonstrate its computational efficiency on M/EEG multivariate time series. More specifically, we define a Sliced-Wasserstein distance between measures of symmetric positive definite matrices that comes with strong theoretical guarantees. Then, we take advantage of its properties and kernel methods to apply this distance to brain-age prediction from MEG data and compare it to state-of-the-art algorithms based on Riemannian geometry. Finally, we show that it is an efficient surrogate to the Wasserstein distance in domain adaptation for Brain Computer Interface applications.

Key facts. Cited by 19 papers in the map (data through 7 Oct 2026). Builds on 22 of its 85 references that are in the map. First posted on arXiv 10 Mar 2023.

Builds on

22 of 85 references.

References · 22

  1. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,277
  2. 2015Optimal Transport for Domain Adaptationcited by 457
  3. 2016A Riemannian Network for SPD Matrix Learningcited by 162
  4. 2020Geoopt: Riemannian Optimization in PyTorchcited by 109
  5. 2019Subspace Robust Wasserstein Distancescited by 89
  6. 2019Learning with minibatch Wasserstein : asymptotic and gradient propertiescited by 83
  7. 2020Statistical and Topological Properties of Sliced Probability Divergencescited by 83
  8. 2017Sliced Wasserstein Kernel for Persistence Diagramscited by 77
  9. 2019Riemannian batch normalization for SPD neural networkscited by 72
  10. 2015Sliced Wasserstein Kernels for Probability Distributionscited by 64
  11. 2021HoroPCA: Hyperbolic Dimensionality Reduction via Horospherical Projectionscited by 47
  12. 2019Asymptotic Guarantees for Learning Generative Models with the Sliced-Wasserstein Distancecited by 43
10 more
  1. 2022Spherical Sliced-Wassersteincited by 31
  2. 2016Dimensionality Reduction on SPD Manifolds: The Emergence of Geometry-Aware Methodscited by 29
  3. 2019Minimax Confidence Intervals for the Sliced Wasserstein Distancecited by 24
  4. 2022Distribution Regression with Sliced Wasserstein Kernelscited by 18
  5. 2019Manifold-regression to predict from MEG/EEG brain signals without source modelingcited by 17
  6. 2022Hyperbolic Sliced-Wasserstein via Geodesic and Horospherical Projectionscited by 16
  7. 2019Unsupervised Hierarchy Matching with Optimal Transport over Hyperbolic Spacescited by 14
  8. 2020Intrinsic Sliced Wasserstein Distances for Comparing Collections of Probability Distributions on Manifolds and Graphscited by 7
  9. 2021Statistical and Topological Properties of Gaussian Smoothed Sliced Probability Divergencescited by 7
  10. 2018Fast and Accurate Multiclass Inference for MI-BCIs Using Large Multiscale Temporal and Spectral Featurescited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 8; 2025: 5; 2026: 5.

19 papers.

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  1. 2024Sliced Wasserstein with Random-Path Projecting Directionscited by 15
  2. 2024Geodesic Optimization for Predictive Shift Adaptation on EEG datacited by 9
  3. 2024Hierarchical Hybrid Sliced Wasserstein: A Scalable Metric for Heterogeneous Joint Distributionscited by 6
  4. 2025SPD Matrix Learning for Neuroimaging Analysis: Perspectives, Methods, and Challengescited by 5
  5. 2025Fast Estimation of Wasserstein Distances via Regression on Sliced Wasserstein Distancescited by 5
  6. 2025Slicing Wasserstein Over Wasserstein Via Functional Optimal Transportcited by 5
  7. 2026Neural Networks on Symmetric Spaces of Noncompact Typecited by 5
  8. 2024Summarizing Bayesian Nonparametric Mixture Posterior -- Sliced Optimal Transport Metrics for Gaussian Mixturescited by 4
  9. 2024Schur's Positive-Definite Network: Deep Learning in the SPD cone with structurecited by 3
  10. 2024Learning to Embed Distributions via Maximum Kernel Entropycited by 3
  11. 2024Weakly supervised covariance matrices alignment through Stiefel matrices estimation for MEG applicationscited by 2
  12. 2024EEG-MACS: Manifold Attention and Confidence Stratification for EEG-based Cross-Center Brain Disease Diagnosis under Unreliable Annotationscited by 2
7 more
  1. 2025EEG-ReMinD: Enhancing Neurodegenerative EEG Decoding through Self-Supervised State Reconstruction-Primed Riemannian Dynamicscited by 2
  2. 2023Brain Age Revisited: Investigating the State vs. Trait Hypotheses of EEG-derived Brain-Age Dynamics with Deep Learningcited by 1
  3. 2025Busemann Functions in the Wasserstein Space: Existence, Closed-Forms, and Applications to Slicingcited by 1
  4. 2026Revisiting the Sliced Wasserstein Kernel for persistence diagrams: a Figalli-Gigli approachcited by 0
  5. 2026Wasserstein-type Gaussian Process Regressions for Input Measurement Uncertaintycited by 0
  6. 2026A Sliced-Wasserstein Framework on Correlation Matrices for EEG Decodingcited by 0
  7. 2026Geometric Feature Learning for Functional Data Valued on the Symmetric Positive Definite Manifoldcited by 0