# Correlation Alignment for Unsupervised Domain Adaptation

arXiv: https://arxiv.org/abs/1612.01939 · HTML: https://mlsanity.com/paper/1612.01939/

## Key facts

- Cited by 147 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Dec 2016.

## Built on by (most cited first, 30 of 147)

- [SHIFT: A Synthetic Driving Dataset for Continuous Multi-Task Domain Adaptation](https://mlsanity.com/paper/2206.08367/) (2022)
- [Maximizing Confidence Alone Improves Reasoning](https://mlsanity.com/paper/2505.22660/) (2025)
- [Test-Time Adaptation via Conjugate Pseudo-labels](https://mlsanity.com/paper/2207.09640/) (2022)
- [Source-Free Domain Adaptation via Distribution Estimation](https://mlsanity.com/paper/2204.11257/) (2022)
- [Visual Prompt Tuning for Test-time Domain Adaptation](https://mlsanity.com/paper/2210.04831/) (2022)
- [Prototypical Cross-domain Self-supervised Learning for Few-shot Unsupervised Domain Adaptation](https://mlsanity.com/paper/2103.16765/) (2021)
- [Deep Clustering: A Comprehensive Survey](https://mlsanity.com/paper/2210.04142/) (2022)
- [Test-Time Adaptation to Distribution Shift by Confidence Maximization and Input Transformation](https://mlsanity.com/paper/2106.14999/) (2021)
- [Diversify and Disambiguate: Learning From Underspecified Data](https://mlsanity.com/paper/2202.03418/) (2022)
- [Divide and Contrast: Source-free Domain Adaptation via Adaptive Contrastive Learning](https://mlsanity.com/paper/2211.06612/) (2022)
- [ADATIME: A Benchmarking Suite for Domain Adaptation on Time Series Data](https://mlsanity.com/paper/2203.08321/) (2022)
- [Towards Robust and Adaptive Motion Forecasting: A Causal Representation Perspective](https://mlsanity.com/paper/2111.14820/) (2021)
- [Video Test-Time Adaptation for Action Recognition](https://mlsanity.com/paper/2211.15393/) (2022)
- [Unsupervised Domain Generalization by Learning a Bridge Across Domains](https://mlsanity.com/paper/2112.02300/) (2021)
- [Domain Adaptation under Open Set Label Shift](https://mlsanity.com/paper/2207.13048/) (2022)
- [Leveraging sparse and shared feature activations for disentangled representation learning](https://mlsanity.com/paper/2304.07939/) (2023)
- [RLSbench: Domain Adaptation Under Relaxed Label Shift](https://mlsanity.com/paper/2302.03020/) (2023)
- [Predicting is not Understanding: Recognizing and Addressing Underspecification in Machine Learning](https://mlsanity.com/paper/2207.02598/) (2022)
- [T-SVDNet: Exploring High-Order Prototypical Correlations for Multi-Source Domain Adaptation](https://mlsanity.com/paper/2107.14447/) (2021)
- [Domain Adaptation for Time-Series Classification to Mitigate Covariate Shift](https://mlsanity.com/paper/2204.03342/) (2022)
- [Out-of-Domain Robustness via Targeted Augmentations](https://mlsanity.com/paper/2302.11861/) (2023)
- [Gradual Domain Adaptation in the Wild:When Intermediate Distributions are Absent](https://mlsanity.com/paper/2106.06080/) (2021)
- [PCGen: Point Cloud Generator for LiDAR Simulation](https://mlsanity.com/paper/2210.08738/) (2022)
- [Localized Adversarial Domain Generalization](https://mlsanity.com/paper/2205.04114/) (2022)
- [Source-Free Domain Adaptation with Temporal Imputation for Time Series Data](https://mlsanity.com/paper/2307.07542/) (2023)
- [DC-Check: A Data-Centric AI checklist to guide the development of reliable machine learning systems](https://mlsanity.com/paper/2211.05764/) (2022)
- [A Concise Review of Transfer Learning](https://mlsanity.com/paper/2104.02144/) (2021)
- [On The Effects Of Data Normalisation For Domain Adaptation On EEG Data](https://mlsanity.com/paper/2210.01081/) (2022)
- [Unsupervised Model Adaptation for Source-free Segmentation of Medical Images](https://mlsanity.com/paper/2211.00807/) (2022)
- [UDApter -- Efficient Domain Adaptation Using Adapters](https://mlsanity.com/paper/2302.03194/) (2023)

## Abstract (arXiv)

In this chapter, we present CORrelation ALignment (CORAL), a simple yet effective method for unsupervised domain adaptation. CORAL minimizes domain shift by aligning the second-order statistics of source and target distributions, without requiring any target labels. In contrast to subspace manifold methods, it aligns the original feature distributions of the source and target domains, rather than the bases of lower-dimensional subspaces. It is also much simpler than other distribution matching methods. CORAL performs remarkably well in extensive evaluations on standard benchmark datasets. We first describe a solution that applies a linear transformation to source features to align them with target features before classifier training. For linear classifiers, we propose to equivalently apply CORAL to the classifier weights, leading to added efficiency when the number of classifiers is small but the number and dimensionality of target examples are very high. The resulting CORAL Linear Discriminant Analysis (CORAL-LDA) outperforms LDA by a large margin on standard domain adaptation benchmarks. Finally, we extend CORAL to learn a nonlinear transformation that aligns correlations of layer activations in deep neural networks (DNNs). The resulting Deep CORAL approach works seamlessly with DNNs and achieves state-of-the-art performance on standard benchmark datasets. Our code is available at:~urlhttps://github.com/VisionLearningGroup/CORAL