Detecting intrinsic slow variables in stochastic dynamical systems by anisotropic diffusion maps
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...
| Main Authors: | , , , |
|---|---|
| Format: | Journal article |
| Published: |
PNAS
2009
|
| _version_ | 1797102826307977216 |
|---|---|
| author | Singer, A Erban, R Kevrekidis, I Coifman, R |
| author_facet | Singer, A Erban, R Kevrekidis, I Coifman, R |
| author_sort | Singer, A |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T06:11:17Z |
| format | Journal article |
| id | oxford-uuid:ef96fcdc-09c6-4cf4-8b13-21fde18f3e22 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T06:11:17Z |
| publishDate | 2009 |
| publisher | PNAS |
| record_format | dspace |
| spelling | oxford-uuid:ef96fcdc-09c6-4cf4-8b13-21fde18f3e222022-03-27T11:41:21ZDetecting intrinsic slow variables in stochastic dynamical systems by anisotropic diffusion mapsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:ef96fcdc-09c6-4cf4-8b13-21fde18f3e22Mathematical Institute - ePrintsPNAS2009Singer, AErban, RKevrekidis, ICoifman, RNonlinear 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. |
| spellingShingle | Singer, A Erban, R Kevrekidis, I Coifman, R Detecting intrinsic slow variables in stochastic dynamical systems by anisotropic diffusion maps |
| title | Detecting intrinsic slow variables in stochastic dynamical systems by anisotropic diffusion maps |
| title_full | Detecting intrinsic slow variables in stochastic dynamical systems by anisotropic diffusion maps |
| title_fullStr | Detecting intrinsic slow variables in stochastic dynamical systems by anisotropic diffusion maps |
| title_full_unstemmed | Detecting intrinsic slow variables in stochastic dynamical systems by anisotropic diffusion maps |
| title_short | Detecting intrinsic slow variables in stochastic dynamical systems by anisotropic diffusion maps |
| title_sort | detecting intrinsic slow variables in stochastic dynamical systems by anisotropic diffusion maps |
| work_keys_str_mv | AT singera detectingintrinsicslowvariablesinstochasticdynamicalsystemsbyanisotropicdiffusionmaps AT erbanr detectingintrinsicslowvariablesinstochasticdynamicalsystemsbyanisotropicdiffusionmaps AT kevrekidisi detectingintrinsicslowvariablesinstochasticdynamicalsystemsbyanisotropicdiffusionmaps AT coifmanr detectingintrinsicslowvariablesinstochasticdynamicalsystemsbyanisotropicdiffusionmaps |