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Parallel Transport on the Cone Manifold of SPD Matrices for Domain Adaptation

arXiv 1807.10479 ↗First posted 27 Jul 2018eess.SPcited by 20

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Abstract (arXiv)

In this paper, we consider the problem of domain adaptation. We propose to view the data through the lens of covariance matrices and present a method for domain adaptation using parallel transport on the cone manifold of symmetric positive-definite matrices. We provide rigorous analysis using Riemanninan geometry, illuminating the theoretical guarantees and benefits of the presented method. In addition, we demonstrate these benefits using experimental results on simulations and real-measured data.

Key facts. Cited by 20 papers in the map (data through 7 Oct 2026). First posted on arXiv 27 Jul 2018.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 5; 2023: 2; 2024: 5; 2025: 3; 2026: 4.

20 papers.

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  1. 2022SPD domain-specific batch normalization to crack interpretable unsupervised domain adaptation in EEGcited by 53
  2. 2021GeomNet: A Neural Network Based on Riemannian Geometries of SPD Matrix Space and Cholesky Space for 3D Skeleton-Based Interaction Recognitioncited by 27
  3. 2023Adaptive Log-Euclidean Metrics for SPD Matrix Learningcited by 13
  4. 2024SPDIM: Source-Free Unsupervised Conditional and Label Shift Adaptation in EEGcited by 12
  5. 2023Riemannian Multinomial Logistics Regression for SPD Neural Networkscited by 11
  6. 2024A Lie Group Approach to Riemannian Batch Normalizationcited by 8
  7. 2024RMLR: Extending Multinomial Logistic Regression into General Geometriescited by 8
  8. 2022Riemannian block SPD coupling manifold and its application to optimal transportcited by 7
  9. 2025Revisiting Euclidean Alignment for Transfer Learning in EEG-Based Brain-Computer Interfacescited by 7
  10. 2022Deep Optimal Transport for Domain Adaptation on SPD Manifoldscited by 6
  11. 2022Spatiotemporal Analysis Using Riemannian Composition of Diffusion Operatorscited by 6
  12. 2024Tree-Wasserstein Distance for High Dimensional Data with a Latent Feature Hierarchycited by 5
8 more
  1. 2025SPD Matrix Learning for Neuroimaging Analysis: Perspectives, Methods, and Challengescited by 5
  2. 2024Physics-informed and Unsupervised Riemannian Domain Adaptation for Machine Learning on Heterogeneous EEG Datasetscited by 3
  3. 2022Unsupervised Learning Discriminative MIG Detectors in Nonhomogeneous Cluttercited by 1
  4. 2026Riemannian Geometry-Preserving Variational Autoencoder for MI-BCI Data Augmentationcited by 1
  5. 2025Learning Topology-Driven Multi-Subspace Fusion for Grassmannian Deep Networkcited by 0
  6. 2026Geometric structures and deviations on James' symmetric positive-definite matrix bicone domaincited by 0
  7. 2026Transfer learning via interpolating structurescited by 0
  8. 2026LieBN: Batch Normalization over Lie Groupscited by 0