  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}
