Transductive Learning Via Improved Geodesic Sampling

Youshan Zhang, Sihong Xie, Brian D. Davison

Abstract: Transductive learning exploits the connection between training and test data to improve classification performance, and the geometry of the manifold underlying the training and the test data is essential to make this connection explicit. Existing approaches primarily focus on Grassmannian manifolds, while much less is known regarding other manifolds, which can potentially bring increased computational and learning performance. In this paper, we close the gap and formulate a novel and more general geodesic sampling approach on Riemannian manifolds (GSM) that encompasses Sphere, Kendall, and Grassmannian manifolds. To provide practical guidance for classification, we explore extensive hyperparameter settings and baselines, including deep transfer learning models. The results show that the new method can enable more accurate and less computationally expensive geodesic sampling on the sphere manifold, which is not possible to achieve using the existing Grassmannian manifold.