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- W4289373336 abstract "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 prove the convergence of this microscopic distance, 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." @default.
- W4289373336 created "2022-08-02" @default.
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- W4289373336 date "2018-10-22" @default.
- W4289373336 modified "2023-09-23" @default.
- W4289373336 title "Nonhomogeneous Euclidean first-passage percolation and distance learning" @default.
- W4289373336 doi "https://doi.org/10.48550/arxiv.1810.09398" @default.
- W4289373336 hasPublicationYear "2018" @default.
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