Correlation Alignment by Riemannian Metric for Domain Adaptation
This work addresses domain adaptation for machine learning models by proposing a theoretically sound method to handle the non-Euclidean structure of covariance matrices, though it is incremental as it builds on existing covariance alignment approaches.
The paper tackled the problem of domain shift in unsupervised domain adaptation by aligning covariance matrices of source and target domains using a Riemannian metric instead of the Euclidean distance, resulting in improved performance on the Office dataset benchmark.
Domain adaptation techniques address the problem of reducing the sensitivity of machine learning methods to the so-called domain shift, namely the difference between source (training) and target (test) data distributions. In particular, unsupervised domain adaptation assumes no labels are available in the target domain. To this end, aligning second order statistics (covariances) of target and source domains have proven to be an effective approach ti fill the gap between the domains. However, covariance matrices do not form a subspace of the Euclidean space, but live in a Riemannian manifold with non-positive curvature, making the usual Euclidean metric suboptimal to measure distances. In this paper, we extend the idea of training a neural network with a constraint on the covariances of the hidden layer features, by rigorously accounting for the curved structure of the manifold of symmetric positive definite matrices. The resulting loss function exploits a theoretically sound geodesic distance on such manifold. Results show indeed the suboptimal nature of the Euclidean distance. This makes us able to perform better than previous approaches on the standard Office dataset, a benchmark for domain adaptation techniques.