Weighted Geodesic Distance Following Fermat's Principle

Facundo Sapienza, Pablo Groisman, Matthieu Jonckheere

Abstract: We propose a density-based estimator for weighted geodesic distances suitable for data lying on a manifold of lower dimension than ambient space and sampled from a possibly nonuniform distribution. After discussing its properties and implementation, we evaluate its performance as a tool for clustering tasks. A discussion on the consistency of the estimator is also given.

Keywords: distance learning, manifold learning, clustering.

TL;DR: We propose a new estimator for weighted geodesic distances that takes into account the underlying density of the data.