# Hierarchical Optimal Transport for Unsupervised Domain Adaptation

arXiv: https://arxiv.org/abs/2112.02073 · HTML: https://mlsanity.com/paper/2112.02073/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 83 references that are in the map.
- First posted on arXiv 3 Dec 2021.

## Builds on (most cited first, 26 of 26)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Unsupervised Domain Adaptation by Backpropagation](https://mlsanity.com/paper/1409.7495/) (2014)
- [Learning Transferable Features with Deep Adaptation Networks](https://mlsanity.com/paper/1502.02791/) (2015)
- [Deep Hashing Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1706.07522/) (2017)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Deep Transfer Learning with Joint Adaptation Networks](https://mlsanity.com/paper/1605.06636/) (2016)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [DeCAF: A Deep Convolutional Activation Feature for Generic Visual Recognition](https://mlsanity.com/paper/1310.1531/) (2013)
- [A Survey of Unsupervised Deep Domain Adaptation](https://mlsanity.com/paper/1812.02849/) (2018)
- [Bridging Theory and Algorithm for Domain Adaptation](https://mlsanity.com/paper/1904.05801/) (2019)
- [Joint Distribution Optimal Transportation for Domain Adaptation](https://mlsanity.com/paper/1705.08848/) (2017)
- [Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration](https://mlsanity.com/paper/1705.09634/) (2017)
- [Fast Computation of Wasserstein Barycenters](https://mlsanity.com/paper/1310.4375/) (2013)
- [DeepJDOT: Deep Joint Distribution Optimal Transport for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1803.10081/) (2018)
- [A review of domain adaptation without target labels](https://mlsanity.com/paper/1901.05335/) (2019)
- [Scatter Component Analysis: A Unified Framework for Domain Adaptation and Domain Generalization](https://mlsanity.com/paper/1510.04373/) (2015)
- [Optimal Transport for Multi-source Domain Adaptation under Target Shift](https://mlsanity.com/paper/1803.04899/) (2018)
- [Regularized Discrete Optimal Transport](https://mlsanity.com/paper/1307.5551/) (2013)
- [Hierarchical Optimal Transport for Document Representation](https://mlsanity.com/paper/1906.10827/) (2019)
- [Multilevel Clustering via Wasserstein Means](https://mlsanity.com/paper/1706.03883/) (2017)
- [Hierarchical Optimal Transport for Multimodal Distribution Alignment](https://mlsanity.com/paper/1906.11768/) (2019)
- [Structured Optimal Transport](https://mlsanity.com/paper/1712.06199/) (2017)
- [Wasserstein barycenters can be computed in polynomial time in fixed dimension](https://mlsanity.com/paper/2006.08012/) (2020)
- [Dimensionality Reduction for Wasserstein Barycenter](https://mlsanity.com/paper/2110.08991/) (2021)

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

- [Scalable Optimal Transport Methods in Machine Learning: A Contemporary Survey](https://mlsanity.com/paper/2305.05080/) (2023)
- [Hierarchical Refinement: Optimal Transport to Infinity and Beyond](https://mlsanity.com/paper/2503.03025/) (2025)
- [Slicing Wasserstein Over Wasserstein Via Functional Optimal Transport](https://mlsanity.com/paper/2509.22138/) (2025)
- [Modeling Hierarchical Structural Distance for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2211.11424/) (2022)
- [Optimal Transport for Domain Adaptation through Gaussian Mixture Models](https://mlsanity.com/paper/2403.13847/) (2024)
- [Generative Modeling by Minimizing the Wasserstein-2 Loss](https://mlsanity.com/paper/2406.13619/) (2024)
- [OT-Net: A Reusable Neural Optimal Transport Solver](https://mlsanity.com/paper/2306.08233/) (2023)
- [Theoretical Guarantees for Domain Adaptation with Hierarchical Optimal Transport](https://mlsanity.com/paper/2210.13331/) (2022)
- [Unsupervised Domain Adaptation Using Compact Internal Representations](https://mlsanity.com/paper/2401.07207/) (2024)
- [Collaborative Multi-source Domain Adaptation Through Optimal Transport](https://mlsanity.com/paper/2404.06599/) (2024)

## Abstract (arXiv)

In this paper, we propose a novel approach for unsupervised domain adaptation, that relates notions of optimal transport, learning probability measures and unsupervised learning. The proposed approach, HOT-DA, is based on a hierarchical formulation of optimal transport, that leverages beyond the geometrical information captured by the ground metric, richer structural information in the source and target domains. The additional information in the labeled source domain is formed instinctively by grouping samples into structures according to their class labels. While exploring hidden structures in the unlabeled target domain is reduced to the problem of learning probability measures through Wasserstein barycenter, which we prove to be equivalent to spectral clustering. Experiments on a toy dataset with controllable complexity and two challenging visual adaptation datasets show the superiority of the proposed approach over the state-of-the-art.