Shamap: Shape-based Manifold Learning

TL;DR

Shamap introduces a shape-based manifold learning method that uses angular geodesic distances to better capture topological similarities in high-dimensional data, improving dimensionality reduction.

Contribution

The paper proposes a novel shape-oriented metric for manifold learning based on angular changes along geodesics, enhancing data structure preservation.

Findings

Feasibility demonstrated through experiments

Merits shown in capturing topological similarities

Improved data embedding quality

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.