Pulling back symmetric Riemannian geometry for data analysis

arXiv:2403.06612v1 Announce Type: cross
Abstract: Data sets tend to live in low-dimensional non-linear subspaces. Ideal data analysis tools for such data sets should therefore account for such non-linear geometry. The symmetric Riemannian geometry setting can be suitable for a variety of reasons. First, it comes with a rich mathematical structure to account for a wide range of non-linear geometries that has been shown to be able to capture the data geometry through empirical evidence from classical non-linear embedding. Second, many …

abstract analysis analysis tools arxiv cs.lg data data analysis data sets geometry linear low math.dg non-linear tools type