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. However, existing approaches primarily focused on the Grassmannian manifold, while much is less known for other manifolds which can bring better computational and learning performance. In this paper, we define a novel, more general formulation of geodesic sampling on Riemannian manifolds (GSM), which is applicable to manifolds beyond Grassmannian. We demonstrate the use of the GSM model on three manifolds. To provide practical guidance for classification, we explore hyperparameter settings with extensive experiments and propose a Target-focused GSM (TGSM) with a single sample that is close to the target (test data) on a spherical manifold. These choices produce the highest accuracy and least computation time over state-of-the-art methods.
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