# Deep Optimal Transport for Domain Adaptation on SPD Manifolds

arXiv: https://arxiv.org/abs/2201.05745 · HTML: https://mlsanity.com/paper/2201.05745/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 86 references that are in the map.
- First posted on arXiv 15 Jan 2022.

## Builds on (most cited first, 16 of 16)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Deep CORAL: Correlation Alignment for Deep Domain Adaptation](https://mlsanity.com/paper/1607.01719/) (2016)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Deep Visual Domain Adaptation: A Survey](https://mlsanity.com/paper/1802.03601/) (2018)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [A Survey of Unsupervised Deep Domain Adaptation](https://mlsanity.com/paper/1812.02849/) (2018)
- [Joint Distribution Optimal Transportation for Domain Adaptation](https://mlsanity.com/paper/1705.08848/) (2017)
- [DeepJDOT: Deep Joint Distribution Optimal Transport for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1803.10081/) (2018)
- [A Riemannian Network for SPD Matrix Learning](https://mlsanity.com/paper/1608.04233/) (2016)
- [Correlation Alignment for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1612.01939/) (2016)
- [Riemannian batch normalization for SPD neural networks](https://mlsanity.com/paper/1909.02414/) (2019)
- [Deep Learning on Lie Groups for Skeleton-based Action Recognition](https://mlsanity.com/paper/1612.05877/) (2016)
- [Federated Transfer Learning for EEG Signal Classification](https://mlsanity.com/paper/2004.12321/) (2020)
- [Multi-source Domain Adaptation via Weighted Joint Distributions Optimal Transport](https://mlsanity.com/paper/2006.12938/) (2020)
- [Parallel Transport on the Cone Manifold of SPD Matrices for Domain Adaptation](https://mlsanity.com/paper/1807.10479/) (2018)
- [On the interpretation of linear Riemannian tangent space model parameters in M/EEG](https://mlsanity.com/paper/2107.14398/) (2021)

## Built on by (most cited first, 6 of 6)

- [Graph Neural Networks on SPD Manifolds for Motor Imagery Classification: A Perspective from the Time-Frequency Analysis](https://mlsanity.com/paper/2211.02641/) (2022)
- [SPD Matrix Learning for Neuroimaging Analysis: Perspectives, Methods, and Challenges](https://mlsanity.com/paper/2504.18882/) (2025)
- [Schur's Positive-Definite Network: Deep Learning in the SPD cone with structure](https://mlsanity.com/paper/2406.09023/) (2024)
- [Leveraging Optimal Transport via Projections on Subspaces for Machine Learning Applications](https://mlsanity.com/paper/2311.13883/) (2023)
- [Transfer learning via interpolating structures](https://mlsanity.com/paper/2603.22621/) (2026)
- [A Sliced-Wasserstein Framework on Correlation Matrices for EEG Decoding](https://mlsanity.com/paper/2606.06104/) (2026)

## Abstract (arXiv)

Recent progress in geometric deep learning has drawn increasing attention from the machine learning community toward domain adaptation on symmetric positive definite (SPD) manifolds, especially for neuroimaging data that often suffer from distribution shifts across sessions. These data, typically represented as covariance matrices of brain signals, inherently lie on SPD manifolds due to their symmetry and positive definiteness. However, conventional domain adaptation methods often overlook this geometric structure when applied directly to covariance matrices, which can result in suboptimal performance. To address this issue, we introduce a new geometric deep learning framework that combines optimal transport theory with the geometry of SPD manifolds. Our approach aligns data distributions while respecting the manifold structure, effectively reducing both marginal and conditional discrepancies. We validate our method on three cross-session brain computer interface datasets, KU, BNCI2014001, and BNCI2015001, where it consistently outperforms baseline approaches while maintaining the intrinsic geometry of the data. We also provide quantitative results and visualizations to better illustrate the behavior of the learned embeddings.