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 theyalso 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 givesgive a global description of the data-set, itthey can measure the distances between pairpairs 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
