Multi-source domain adaptation using C⁁1-smooth subspaces interpolation

Manifold-based domain adaptation algorithms are receiving increasing attention in computer vision to model distribution shifts between source and target domain. In contrast to early works, that mainly explore intermediate subspaces along geodesics, in this work we propose to interpolate subspaces through C1-smooth curves on the Grassmann manifold. The new methodis based on the geometric Casteljau algorithm that is used to generate smooth interpolating polynomial curves on non-euclidean spaces and can be extended to generate polynomial splines that interpolate a given set of data on the Grassmann manifold. To evaluate the usefulness of the proposed interpolating curves on vision related problems, several experiments were conducted. We show the advantage of using smooth subspaces interpolation in multi-source unsupervised domain adaptation problems and in object recognition problems across datasets.