Shamap: Shape-based Manifold Learning

For manifold learning, it is assumed that high-dimensional sample/data points are on an embedded low-dimensional manifold. Usually, distances among samples are computed to represent the underlying data structure, for a specified distance measure such as the Euclidean distance or geodesic distance. For manifold learning, here we propose a metric according to the angular change along a geodesic line, thereby reflecting the underlying shape-oriented information or the similarity between high- and low-dimensional representations of a data cloud. Our numerical results are described to demonstrate the feasibility and merits of the proposed dimensionality reduction scheme