Shamap: Shape-based Manifold Learning
This work addresses dimensionality reduction for data analysis, but it appears incremental as it builds on existing manifold learning concepts without claiming major breakthroughs.
The authors tackled the problem of manifold learning by proposing a shape-based metric that uses angular changes along geodesics to capture topological similarity between high- and low-dimensional data representations, demonstrating its feasibility and merits.
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.