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:~\url{https://github.com/VisionLearningGroup/CORAL}

本文提出了一种简单且有效的无监督领域自适应方法——CORrelation ALignment(CORAL)，通过对齐源域和目标域的二阶统计信息来最小化领域偏移，而不需要目标标签。相比于子空间流形方法，CORAL原始特征分布不需要低维子空间基项的对齐，且比其他分布匹配方法更为简单。CORAL还扩展到了非线性转换对齐深度神经网络中的层激活的相关性，通过在标准基准数据集上取得了最新的性能，最终获得了Deep CORAL方法。

无监督域自适应的相关性对齐