Repository: Freie Universit├Ąt Berlin, Math Department

Diffusion maps tailored to arbitrary non-degenerate Ito processes

Banisch, R. and Trstanova, Z. and Bittracher, A. and Klus, S. and Koltai, P. (2017) Diffusion maps tailored to arbitrary non-degenerate Ito processes. SFB 1114 Preprint in arXiv:1710.03484 . pp. 1-24. (Unpublished)

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Official URL: https://arxiv.org/abs/1710.03484

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
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > BioComputing Group
ID Code:2139
Deposited By: Silvia Hoemke
Deposited On:27 Nov 2017 14:20
Last Modified:28 Nov 2017 10:03

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