Deep Domain Adaptation by Geodesic Distance Minimization

In this paper, we propose a new approach called Deep LogCORAL for unsupervised visual domain adaptation. Our work builds on the recently proposed Deep CORAL method, which aims to train a convolutional neural network and simultaneously minimize the Euclidean distance of convariance matrices between the source and target domains. By observing that the second order statistical information (i.e. the covariance matrix) lies on a Riemannian manifold, we propose to use the Riemannian distance, approximated by Log-Euclidean distance, to replace the naive Euclidean distance in Deep CORAL. We also consider first-order information, and minimize the distance of mean vectors between two domains. We build an end-to-end model, in which we minimize both the classification loss, and the domain difference based on the first-order and second-order information between two domains. Our experiments on the benchmark Office dataset demonstrates the improvements of our newly proposed Deep LogCORAL approach over the Deep CORAL method, as well as the further improvement when optimizing both orders of information.