# Domain Adaptation on Graphs by Learning Aligned Graph Bases

arXiv: https://arxiv.org/abs/1803.05288 · HTML: https://mlsanity.com/paper/1803.05288/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Mar 2018.

## Built on by (most cited first, 24 of 24)

- [Graph Domain Adaptation: A Generative View](https://mlsanity.com/paper/2106.07482/) (2021)
- [Unsupervised Domain Adaptation with Variational Approximation for Cardiac Segmentation](https://mlsanity.com/paper/2106.08752/) (2021)
- [Learning Transferable Parameters for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2108.06129/) (2021)
- [Graph-Relational Domain Adaptation](https://mlsanity.com/paper/2202.03628/) (2022)
- [Graph Learning under Distribution Shifts: A Comprehensive Survey on Domain Adaptation, Out-of-distribution, and Continual Learning](https://mlsanity.com/paper/2402.16374/) (2024)
- [Collaborative Semantic Aggregation and Calibration for Federated Domain Generalization](https://mlsanity.com/paper/2110.06736/) (2021)
- [Towards Data-centric Graph Machine Learning: Review and Outlook](https://mlsanity.com/paper/2309.10979/) (2023)
- [Graph Domain Adaptation: Challenges, Progress and Prospects](https://mlsanity.com/paper/2402.00904/) (2024)
- [Semi-supervised Domain Adaptive Structure Learning](https://mlsanity.com/paper/2112.06161/) (2021)
- [Adaptive Betweenness Clustering for Semi-Supervised Domain Adaptation](https://mlsanity.com/paper/2401.11448/) (2024)
- [Taxonomy-Structured Domain Adaptation](https://mlsanity.com/paper/2306.07874/) (2023)
- [Attention Regularized Laplace Graph for Domain Adaptation](https://mlsanity.com/paper/2210.08170/) (2022)
- [Unsupervised Domain Adaptation via Distilled Discriminative Clustering](https://mlsanity.com/paper/2302.11984/) (2023)
- [GraphBridge: Towards Arbitrary Transfer Learning in GNNs](https://mlsanity.com/paper/2502.19252/) (2025)
- [Learning Structure-Semantic Evolution Trajectories for Graph Domain Adaptation](https://mlsanity.com/paper/2602.10506/) (2026)
- [Heterogeneous Domain Adaptation for IoT Intrusion Detection: A Geometric Graph Alignment Approach](https://mlsanity.com/paper/2301.09801/) (2023)
- [Spectral Maps for Learning on Subgraphs](https://mlsanity.com/paper/2205.14938/) (2022)
- [DELTA: Dual Consistency Delving with Topological Uncertainty for Active Graph Domain Adaptation](https://mlsanity.com/paper/2409.08946/) (2024)
- [Sparse Causal Discovery with Generative Intervention for Unsupervised Graph Domain Adaptation](https://mlsanity.com/paper/2507.07621/) (2025)
- [A Few-shot Learning Graph Multi-Trajectory Evolution Network for Forecasting Multimodal Baby Connectivity Development from a Baseline Timepoint](https://mlsanity.com/paper/2110.03535/) (2021)
- [Semi-supervised Learning with Deterministic Labeling and Large Margin Projection](https://mlsanity.com/paper/2208.08058/) (2022)
- [A Unified Pre-training and Adaptation Framework for Combinatorial Optimization on Graphs](https://mlsanity.com/paper/2312.11547/) (2023)
- [Inter-Domain Alignment for Predicting High-Resolution Brain Networks Using Teacher-Student Learning](https://mlsanity.com/paper/2110.03452/) (2021)
- [A Survey of Reasoning for Substitution Relationships: Definitions, Methods, and Directions](https://mlsanity.com/paper/2404.08687/) (2024)

## Abstract (arXiv)

A common assumption in semi-supervised learning with graph models is that the class label function varies smoothly on the data graph, resulting in the rather strict prior that the label function has low-frequency content. Meanwhile, in many classification problems, the label function may vary abruptly in certain graph regions, resulting in high-frequency components. Although the semi-supervised estimation of class labels is an ill-posed problem in general, in several applications it is possible to find a source graph on which the label function has similar frequency content to that on the target graph where the actual classification problem is defined. In this paper, we propose a method for domain adaptation on graphs motivated by these observations. Our algorithm is based on learning the spectrum of the label function in a source graph with many labeled nodes, and transferring the information of the spectrum to the target graph with fewer labeled nodes. While the frequency content of the class label function can be identified through the graph Fourier transform, it is not easy to transfer the Fourier coefficients directly between the two graphs, since no one-to-one match exists between the Fourier basis vectors of independently constructed graphs in the domain adaptation setting. We solve this problem by learning a transformation between the Fourier bases of the two graphs that flexibly ``aligns'' them. The unknown class label function on the target graph is then reconstructed such that its spectrum matches that on the source graph while also ensuring the consistency with the available labels. The proposed method is tested in the classification of image, online product review, and social network data sets. Comparative experiments suggest that the proposed algorithm performs better than recent domain adaptation methods in the literature in most settings.