title: Detecting intrinsic slow variables in stochastic dynamical systems by anisotropic diffusion maps.
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.
authors.affiliation: Department of Mathematics and Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, USA. amits@math.princeton.edu
authors.forename: Amit
authors.initials: A
authors.lastname: Singer
authors.forename: Radek
authors.initials: R
authors.lastname: Erban
authors.forename: Ioannis G
authors.initials: IG
authors.lastname: Kevrekidis
authors.forename: Ronald R
authors.initials: RR
authors.lastname: Coifman
mesh_terms: D000465:Algorithms; D016880:Anisotropy; D003198:Computer Simulation; D008390:Markov Chains; D008956:Models, Chemical; D017711:Nonlinear Dynamics; D025341:Principal Component Analysis; D013269:Stochastic Processes; D013997:Time Factors
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