Wassmap: Wasserstein Isometric Mapping for Image Manifold Learning

In this paper, we propose Wasserstein Isometric Mapping (Wassmap), a nonlinear dimensionality reduction technique that provides solutions to some drawbacks in existing global algorithms imaging applications. Wassmap represents images via probability measures space, then uses pairwise distances between the associated produce low-dimensional, approximately isometric embedding. We show algorithm is able exactly recover parameters of image manifolds, including those generated by translations or dilations fixed generating measure. Additionally, discrete version retrieves from manifolds providing theoretical bridge transfer recovery results functional data data. Testing proposed on various shows yields good embeddings compared with other and local techniques.