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Correlation Alignment for Domain Adaptation

Welcome to the website of CORAL framework. CORrelation ALignment or CORAL in short is 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. There are mainly three parts of the CORAL framework. In the CORAL paper (reference 1 in the Citation Section below), we 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) (reference 2 in the Citation Section below) 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 (reference 3 in the Citation Section below) approach works seamlessly with DNNs and achieves state-of-the-art performance on standard benchmark datasets.

Source Code and Data

  1. CORAL: the source code is in code/, the data used in reference 1 is included in /dataset folder
  2. CORAL-LDA: the code and data can be found here. As can be seen from the title of the paper (From Virtual to Reality: Fast Adaptation of Virtual Object Detectors to Real Domains), another major contribution is ''From Virtual to Reality''. In this paper, we ''(1) we show that freely available non-photorealistic 3D models can be used to train 2D object detectors, in a first such study that evaluates across a large variety of categories; (2) we eliminate the need to generate images that match real-image statistics by utilizing domain-specific image statistics; (3) we present a supervised adaptation approach, and show improved results on a multi-domain dataset.'' Please refer to this webpage for more detailed information.
  3. Deep-CORAL: the source code is in code/, sample protofiles and parameters can be found in code/, the data used is the standard Office31 dataset

Tips for (Visual) Domain Adaptation

The following tips are based on my personal experience and discussions (in person or via email) with others (special thanks to Prof. Mingsheng Long). I found them to be useful to design/apply domain adaptation algorithms yet seldom mentioned/explained in the literature. I put them here and hope it helps :-)

  1. Data Processing for Domain Adaptation

Data processing is very importrant for domain adaptation applications even though it is seldom mentioned (or not emphasised enough) in the literature. It is extremely true for ''shallow'' approaches as many of them (i.e., CORAL) are doing asymmetric transformation (applying transformation to source/target only). For example, suppose we normalize BOTH the source AND target to have the same distribution (i.e., zero mean and unit variance). Then after the asymmetric transformation, the distribution/normalization of the transformed source might be different to the target. To achieve good performance on the target data, the distribution/normalization on which the classifier/detector is trained on need to be as close to the target as possible. We used the same trick (please refer to the SVM_Accuracy function in Ex_CORAL.m) as SA to ensure this. The most commonly used data pre-processing approach for visual domain adaptation is l1 normalization and zscore (the one used in the source code of CORAL, SA, GFK, etc.). l2 normalization also works pretty well (or even better than l1/zscore) on deep features (for the ''shallow'' methods). For deep methods, as the raw image is feeded into the network and same/similar transformations are applied to BOTH source AND target data, there is little need of extra data processing.

  1. Domain Adaptation Equilibrium

As EXPLICITLY mentioned in Deep CORAL, there is an equilibrium between aligning the distributions (between the source and target) and keeping the discriminative power of the features (i.e., high classification accuracy). ''Minimizing the classification loss itself is likely to lead to overfitting to the source domain, causing reduced performance on the target domain. On the other hand, minimizing the CORAL loss alone might lead to degenerated features. For example, the network could project all of the source and target data to a single point, making the CORAL loss trivially zero.'' This equilibrium is also IMPLICITLY used in many ''shallow'' methods in a different way. For example, constraining the transformation to be linear can be think of an IMPLICIT way of regularization.

  1. Parameter/Hyper-parameter Tuning

For the most common unsupervised domain adaptation scenario where there is NO labeled TARGET data during training, traditional cross-validation based paramter/hyper-paremeter tuning approaches are impossible. In practice, the parameters/hyper-paramters are usually set to certain number empricially. For CORAL, there is only ONE papameter -- regularization parameter (λ) which was set to 1 empricically. For Deep CORAL, the main parameter/hyper-parameter (other parameters like the learning rate, weight decay were set in the same way as classical fine-tuning procedures) is the weight of CORAL Loss. As mentioned in the Deep CORAL paper, this parameter is set in this way: ''The weight of the CORAL loss (λ) is set in such way that at the end of training the classification loss and CORAL loss are roughly the same. It seems be a reasonable choice as we want to have a feature representation that is both discriminative and also minimizes the distance between the source and target domains.''


I highly recommend you to read the book chapter for a compresensive introduction of the CORAL framework. Each individual paper listed in this section talks about one part of the framework only.

If you find this project is useful in your research, please consider citing:

Reference 1: CORAL

  author={Baochen Sun and Jiashi Feng and Kate Saenko},
  title={Return of Frustratingly Easy Domain Adaptation},

Reference 2: CORAL-LDA

    Author={Baochen Sun and Kate Saenko},
    Title={From Virtual to Reality: Fast Adaptation of Virtual Object Detectors to Real Domains},

Reference 3: Deep CORAL

  author={Baochen Sun and Kate Saenko},
  title={Deep CORAL: Correlation Alignment for Deep Domain Adaptation},
  booktitle={ECCV 2016 Workshops},


Please send your further questions to baochens AT gmail DOT com


Correlation Alignment for Domain Adaptation






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