A Data Structure for High-dimensional Manifold Representation Amenable to Riemannian Optimization

Ryan Robinett University of Chicago


The field of Riemannian Optimization generalizes optimization techniques from Euclidean state-spaces to Riemannian manifolds. While the theory of Riemannian optimization is well developed, it is scarcely implemented due to “update-and-project” methods on representations of Riemannian manifolds within a higher-dimensional Euclidean space being costly. Conjugately, while dimensionality reduction techniques allow for insightful, simplifying looks into high-dimensional data, only linear dimensionality reduction techniques succeed in preserving metric information to a degree necessary to perform Riemannian optimization on the reduced space. In this talk, we demonstrate a data structure which allows the user to implement Riemannian optimization algorithms on a pseudo-Riemannian simplicial complex which closely approximates a manifold learned from point cloud data.

Feb 2, 2022 12:30 PM — 1:30 PM
Theory Lunch
JCL 390

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