The lecture provides an overview of the recent work Riemannian-geometry-based machine
learning approaches with a particular focus on robotics applications. An introduction to
Riemannian geometry will first be provided, including an overview of the Riemannian manifolds
of interest for robotics and machine learning problems. Various methods and algorithms, their
applications in robotics, and the current state of research will then be discussed. The following
topics will be covered: geodesic regression, Riemannian clustering approaches, Riemannian
kernel methods and Gaussian processes, learning from demonstrations on Riemannian manifolds,
Riemannian manifold learning from data, dimensionality reduction on Riemannian manifolds,
Riemannian gradient-based optimization algorithms, Riemannian black-box optimization
algorithms, and geometric deep learning. Students deepen their knowledge of the methods and
algorithms by independently working on problems and discussing them in the exercise. In
particular, students can gain practical programming experience with tools and software libraries
commonly used in the context geometric machine learning and optimization for robotics.