Diffusion map: Difference between revisions

Revision as of 16:50, 3 December 2019

Revision as of 14:20, 17 February 2020

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In the paper,<ref name="Nadler05diffusionmaps" /> Nadler et. al. showed how to design a kernel that reproduces the diffusion induced by a [[Fokker–Planck equation]]. Also, they explained that, when the data approximate a manifold, one can recover the geometry of this manifold by computing an approximation of the [[Laplace–Beltrami operator]]. This computation is completely insensitive

to the distribution of the points and therefore provides a separation of the statistics and the geometry of the

data. Since diffusion maps gives a global description of the data-set, it can measure the distances between pair of sample points in the manifold in which the data is embedded. Applications based on diffusion maps include [[facial recognition system|face recognition]],<ref name="vmrs">{{cite journal

| last1 = Barkan

| first1 = Oren