Nonhomogeneous Euclidean first-passage percolation and distance learning - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Bernoulli Année : 2022

Nonhomogeneous Euclidean first-passage percolation and distance learning

Résumé

Consider an i.i.d. sample from an unknown density function supported on an unknown manifold embedded in a high dimensional Euclidean space. We tackle the problem of learning a distance between points, able to capture both the geometry of the manifold and the underlying density. We define such a sample distance and prove the convergence, as the sample size goes to infinity, to a macroscopic one that we call Fermat distance as it minimizes a path functional, resembling Fermat principle in optics. The proof boils down to the study of geodesics in Euclidean first-passage percolation for nonhomogeneous Poisson point processes.

Dates et versions

hal-03625693 , version 1 (31-03-2022)

Identifiants

Citer

Pablo Groisman, Matthieu Jonckheere, Facundo Sapienza. Nonhomogeneous Euclidean first-passage percolation and distance learning. Bernoulli, 2022, 28 (1), pp.255-276. ⟨10.3150/21-BEJ1341⟩. ⟨hal-03625693⟩
19 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More