Learning Euclidean-to-Riemannian Metric for Point-to-Set Classification

In this paper, we focus on the problem of point-to-set classification, where single points are matched against sets of correlated points. Since the points commonly lie in Euclidean space while the sets are typically modeled as elements on Riemannian manifold, they can be treated as Euclidean points and Riemannian points respectively. To learn a metric between the heterogeneous points, we propose a novel Euclidean-to-Riemannian metric learning framework. Specifically, by exploiting typical Riemannian metrics, the Riemannian manifold is first embedded into a high dimensional Hilbert space to reduce the gaps between the heterogeneous spaces and meanwhile respect the Riemannian geometry of the manifold. The final distance metric is then learned by pursuing multiple transformations from the Hilbert space and the original Euclidean space (or its corresponding Hilbert space) to a common Euclidean subspace, where classical Euclidean distances of transformed heterogeneous points can be measured. Extensive experiments clearly demonstrate the superiority of our proposed approach over the state-of-the-art methods.