# Subspace Alignment For Domain Adaptation

arXiv: https://arxiv.org/abs/1409.5241 · HTML: https://mlsanity.com/paper/1409.5241/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Sep 2014.

## Built on by (most cited first, 10 of 10)

- [Domain Adaptation with Cauchy-Schwarz Divergence](https://mlsanity.com/paper/2405.19978/) (2024)
- [FediOS: Decoupling Orthogonal Subspaces for Personalization in Feature-skew Federated Learning](https://mlsanity.com/paper/2311.18559/) (2023)
- [Subspace Alignment for Vision-Language Model Test-time Adaptation](https://mlsanity.com/paper/2601.08139/) (2026)
- [Composite Active Learning: Towards Multi-Domain Active Learning with Theoretical Guarantees](https://mlsanity.com/paper/2402.02110/) (2024)
- [Deep Transfer Learning for Kidney Cancer Diagnosis](https://mlsanity.com/paper/2408.04318/) (2024)
- [A physics-based domain adaptation framework for modelling and forecasting building energy systems](https://mlsanity.com/paper/2208.09456/) (2022)
- [Consistency Regularization for Domain Adaptation](https://mlsanity.com/paper/2208.11084/) (2022)
- [Operational Learning-based Boundary Estimation in Electromagnetic Medical Imaging](https://mlsanity.com/paper/2108.03233/) (2021)
- [Identification of diffracted vortex beams at different propagation distances using deep learning](https://mlsanity.com/paper/2203.16539/) (2022)
- [EMG subspace alignment and visualization for cross-subject hand gesture classification](https://mlsanity.com/paper/2401.05386/) (2023)

## Abstract (arXiv)

In this paper, we introduce a new domain adaptation (DA) algorithm where the source and target domains are represented by subspaces spanned by eigenvectors. Our method seeks a domain invariant feature space by learning a mapping function which aligns the source subspace with the target one. We show that the solution of the corresponding optimization problem can be obtained in a simple closed form, leading to an extremely fast algorithm. We present two approaches to determine the only hyper-parameter in our method corresponding to the size of the subspaces. In the first approach we tune the size of subspaces using a theoretical bound on the stability of the obtained result. In the second approach, we use maximum likelihood estimation to determine the subspace size, which is particularly useful for high dimensional data. Apart from PCA, we propose a subspace creation method that outperform partial least squares (PLS) and linear discriminant analysis (LDA) in domain adaptation. We test our method on various datasets and show that, despite its intrinsic simplicity, it outperforms state of the art DA methods.