Shamap: Shape-based Manifold Learning

Abstract

For manifold learning, it is assumed that high-dimensional sample/data points are embedded on a low-dimensional manifold. Usually, distances among samples are computed to capture an underlying data structure. Here we propose a metric according to angular changes along a geodesic line, thereby reflecting the underlying shape-oriented information or a topological similarity between high- and low-dimensional representations of a data cloud. Our results demonstrate the feasibility and merits of the proposed dimensionality reduction scheme.