Riemannian Metric Matching for Scalable Geometric Modeling of Distributions (opens in new tab)

High-dimensional datasets often concentrate near low-dimensional structures, but estimating their geometry from samples typically relies on graphs and kernels that scale poorly with dataset size and dimension. We propose Riemannian metric matching: a denoising probabilistic framework for learning the Riemannian geometry of data using neural networks. Specifically, we learn the carr\'e du champ operator, which, using diffusion geometry, gives us ...