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Due to the spectrum decay of the eigenvalues, only a few terms are necessary to achieve a given relative accuracy in this sum.
====Parameter
The reason to introduce the normalization step involving <math>\alpha</math> is to tune the influence of the data point density on the infinitesimal transition of the diffusion. In some applications, the sampling of the data is generally not related to the geometry of the manifold we are interested in describing. In this case, we can set <math>\alpha=1</math> and the diffusion operator approximates the Laplace–Beltrami operator. We then recover the Riemannian geometry of the data set regardless of the distribution of the points. To describe the long-term behavior of the point distribution of a system of stochastic differential equations, we can use <math>\alpha=0.5</math> and the resulting Markov chain approximates the [[Fokker–Planck equation|Fokker–Planck diffusion]]. With <math>\alpha=0</math>, it reduces to the classical graph Laplacian normalization.
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