Applications of No-Collision Transportation Maps in Manifold Learning

arXiv:2304.00199v4 Announce Type: replace
Abstract: In this work, we investigate applications of no-collision transportation maps introduced in [Nurbekyan et. al., 2020] in manifold learning for image data. Recently, there has been a surge in applying transportation-based distances and features for data representing motion-like or deformation-like phenomena. Indeed, comparing intensities at fixed locations often does not reveal the data structure. No-collision maps and distances developed in [Nurbekyan et. al., 2020] are sensitive to geometric features similar to optimal transportation (OT) maps …

abstract applications arxiv collision cs.cv cs.lg data features image image data indeed locations manifold maps stat.ml transportation type work