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Detecting intrinsic slow variables in stochastic dynamical systems by anisotropic diffusion maps

By A Singer, R. Erban, I. G. Kevrekidis and R Coifman

Abstract

Nonlinear independent component analysis is combined with diffusion-map data analysis techniques to detect good observables in high-dimensional dynamic data. These detections are achieved by integrating local principal component analysis of simulation bursts by using eigenvectors of a Markov matrix describing anisotropic diffusion. The widely applicable procedure, a crucial step in model reduction approaches, is illustrated on stochastic chemical reaction network simulations

Topics: Biology and other natural sciences
Publisher: PNAS
Year: 2009
DOI identifier: 10.1073/pnas.0905547106
OAI identifier: oai:generic.eprints.org:1637/core69

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