Interpretable domain adaptation via optimization over the Stiefel manifold

In domain adaptation, the goal is to find common ground between two, potentially differently distributed, data sets. By finding common concepts present in two sets of words pertaining to different domains, one could leverage the performance of a classifier for one domain for use on the other domain. We propose a solution to the domain adaptation task, by efficiently solving an optimization problem through Stochastic Gradient Descent. We provide update rules that allow us to run Stochastic Gradient Descent directly on a matrix manifold: the steps compel the solution to stay on the Stiefel manifold. This manifold encompasses projection matrices of word vectors onto low-dimensional latent feature representations, which allows us to interpret the results: the rotation magnitude of the word vector projection for a given word corresponds to the importance of that word towards making the adaptation. Beyond this interpretability benefit, experiments show that the Stiefel manifold method performs better than state-of-the-art methods.