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

arXiv: https://arxiv.org/abs/1807.10479 · HTML: https://mlsanity.com/paper/1807.10479/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jul 2018.

## Built on by (most cited first, 20 of 20)

- [SPD domain-specific batch normalization to crack interpretable unsupervised domain adaptation in EEG](https://mlsanity.com/paper/2206.01323/) (2022)
- [GeomNet: A Neural Network Based on Riemannian Geometries of SPD Matrix Space and Cholesky Space for 3D Skeleton-Based Interaction Recognition](https://mlsanity.com/paper/2111.13089/) (2021)
- [Adaptive Log-Euclidean Metrics for SPD Matrix Learning](https://mlsanity.com/paper/2303.15477/) (2023)
- [SPDIM: Source-Free Unsupervised Conditional and Label Shift Adaptation in EEG](https://mlsanity.com/paper/2411.07249/) (2024)
- [Riemannian Multinomial Logistics Regression for SPD Neural Networks](https://mlsanity.com/paper/2305.11288/) (2023)
- [A Lie Group Approach to Riemannian Batch Normalization](https://mlsanity.com/paper/2403.11261/) (2024)
- [RMLR: Extending Multinomial Logistic Regression into General Geometries](https://mlsanity.com/paper/2409.19433/) (2024)
- [Riemannian block SPD coupling manifold and its application to optimal transport](https://mlsanity.com/paper/2201.12933/) (2022)
- [Revisiting Euclidean Alignment for Transfer Learning in EEG-Based Brain-Computer Interfaces](https://mlsanity.com/paper/2502.09203/) (2025)
- [Deep Optimal Transport for Domain Adaptation on SPD Manifolds](https://mlsanity.com/paper/2201.05745/) (2022)
- [Spatiotemporal Analysis Using Riemannian Composition of Diffusion Operators](https://mlsanity.com/paper/2201.08530/) (2022)
- [SPD Matrix Learning for Neuroimaging Analysis: Perspectives, Methods, and Challenges](https://mlsanity.com/paper/2504.18882/) (2025)
- [Tree-Wasserstein Distance for High Dimensional Data with a Latent Feature Hierarchy](https://mlsanity.com/paper/2410.21107/) (2024)
- [Physics-informed and Unsupervised Riemannian Domain Adaptation for Machine Learning on Heterogeneous EEG Datasets](https://mlsanity.com/paper/2403.15415/) (2024)
- [Unsupervised Learning Discriminative MIG Detectors in Nonhomogeneous Clutter](https://mlsanity.com/paper/2204.11278/) (2022)
- [Riemannian Geometry-Preserving Variational Autoencoder for MI-BCI Data Augmentation](https://mlsanity.com/paper/2603.10563/) (2026)
- [Learning Topology-Driven Multi-Subspace Fusion for Grassmannian Deep Network](https://mlsanity.com/paper/2511.08628/) (2025)
- [Geometric structures and deviations on James' symmetric positive-definite matrix bicone domain](https://mlsanity.com/paper/2603.02483/) (2026)
- [Transfer learning via interpolating structures](https://mlsanity.com/paper/2603.22621/) (2026)
- [LieBN: Batch Normalization over Lie Groups](https://mlsanity.com/paper/2607.08783/) (2026)

## 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.