Manifold Topology Divergence: a Framework for Comparing Data Manifolds. (arXiv:2106.04024v2 [cs.LG] CROSS LISTED)

We develop a framework for comparing data manifolds, aimed, in particular,
towards the evaluation of deep generative models. We describe a novel tool,
Cross-Barcode(P,Q), that, given a pair of distributions in a high-dimensional
space, tracks multiscale topology spacial discrepancies between manifolds on
which the distributions are concentrated. Based on the Cross-Barcode, we
introduce the Manifold Topology Divergence score (MTop-Divergence) and apply it
to assess the performance of deep generative models in various domains: images,
3D-shapes, time-series, and on different datasets: …

arxiv data divergence framework lg manifold topology