Learning and Regression on manifolds: Data on Grassmannian manifolds

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In this paper, we introduce a new method for learning and regression from a finite set of noisy points on Grassmann manifolds. In contrast to previously existing methods, we propose a new Riemannian Monte Carlo method to sample from the posterior distribution of the tangent space of a Grassmann manifold. Specifically, we investigate and exploit the geometric structure of this manifold which can be used as a solid basis to extend the proposed method to other manifolds in a similar manner. We demonstrate our method for regression using different setups and datasets.