Sketching the Heat Kernel: Using Gaussian Processes to Embed Data

arXiv:2403.07929v1 Announce Type: new
Abstract: This paper introduces a novel, non-deterministic method for embedding data in low-dimensional Euclidean space based on computing realizations of a Gaussian process depending on the geometry of the data. This type of embedding first appeared in (Adler et al, 2018) as a theoretical model for a generic manifold in high dimensions.
In particular, we take the covariance function of the Gaussian process to be the heat kernel, and computing the embedding amounts to sketching a …

abstract arxiv computing cs.lg cs.na data embed embedding gaussian processes geometry heat kernel low math.na novel paper process processes space stat.ml type