Banisch, R. and Trstanova, Z. and Bittracher, A. and Klus, S. and Koltai, P. (2020) Diffusion maps tailored to arbitrary nondegenerate Ito processes. Applied and computational harmonic analysis, 48 (1). pp. 242265. ISSN 10635203, 1096603X

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Official URL: https://dx.doi.org/10.1016/j.acha.2018.05.001
Abstract
We present two generalizations of the popular diffusion maps algorithm. The first generalization replaces the drift term in diffusion maps, which is the gradient of the sampling density, with the gradient of an arbitrary density of interest which is known up to a normalization constant. The second generalization allows for a diffusion map type approximation of the forward and backward generators of general Ito diffusions with given drift and diffusion coefficients. We use the local kernels introduced by Berry and Sauer, but allow for arbitrary sampling densities. We provide numerical illustrations to demonstrate that this opens up many new applications for diffusion maps as a tool to organize point cloud data, including biased or corrupted samples, dimension reduction for dynamical systems, detection of almost invariant regions in flow fields, and importance sampling.
Item Type:  Article 

Additional Information:  SFB 1114 Preprint in arXiv:1710.03484 
Subjects:  Mathematical and Computer Sciences > Mathematics Mathematical and Computer Sciences > Mathematics > Applied Mathematics 
Divisions:  Department of Mathematics and Computer Science > Institute of Mathematics 
ID Code:  2139 
Deposited By:  Silvia Hoemke 
Deposited On:  27 Nov 2017 14:20 
Last Modified:  22 Sep 2020 09:38 
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