Learning Deep Robotic Skills on Riemannian Manifolds

Dictionary Learning on Riemannian Manifolds

Existing dictionary learning algorithms rely heavily on the assumption that the data points are vectors in some Euclidean space R, and the dictionary is learned from the input data using only the vector space structure of R. However, in many applications, features and data points often belong to some Riemannian manifold with its intrinsic metric structure that is potentially important and criti...

A Geometry Preserving Kernel over Riemannian Manifolds

Abstract- Kernel trick and projection to tangent spaces are two choices for linearizing the data points lying on Riemannian manifolds. These approaches are used to provide the prerequisites for applying standard machine learning methods on Riemannian manifolds. Classical kernels implicitly project data to high dimensional feature space without considering the intrinsic geometry of data points. ...

Flowers on Riemannian manifolds

In this paper we will present two upper bounds for the length of a smallest “flower-shaped” geodesic net in terms of the volume and the diameter of a manifold. Minimal geodesic nets are critical points of the length functional on the space of graphs immersed into a Riemannian manifold. Let Mn be a closed Riemannian manifold of dimension n. We prove that there exists a minimal geodesic net that ...

Learning and approximation by Gaussians on Riemannian manifolds

SVM Learning and L Approximation by Gaussians on Riemannian Manifolds

We confirm by the multi-Gaussian support vector machine (SVM) classification that the intrinsic dimension of Riemannian manifolds improves the efficiency (learning rates) of learning algorithms. The essential analysis lies in the study of approximation in Lp (1 ≤ p < ∞) of Lp functions by their convolutions with the Gaussian kernel with variance σ → 0. This covers the SVM case when the approxim...