Diffusion Maps, Reduction Coordinates, and Low Dimensional Representation of Stochastic Systems
نویسندگان
چکیده
منابع مشابه
Diffusion Maps, Reduction Coordinates, and Low Dimensional Representation of Stochastic Systems
The concise representation of complex high dimensional stochastic systems via a few reduced coordinates is an important problem in computational physics, chemistry and biology. In this paper we use the first few eigenfunctions of the backward Fokker-Planck diffusion operator as a coarse grained low dimensional representation for the long term evolution of a stochastic system, and show that they...
متن کاملDiffusion Maps, Spectral Clustering and Reaction Coordinates of Dynamical Systems
A central problem in data analysis is the low dimensional representation of high dimensional data and the concise description of its underlying geometry and density. In the analysis of large scale simulations of complex dynamical systems, where the notion of time evolution comes into play, important problems are the identification of slow variables and dynamically meaningful reaction coordinate...
متن کاملOn the infinite-dimensional representation of stochastic controlled systems with delayed control in the diffusion term
In the deterministic context a series of well established results allow to reformulate delay differential equations (DDEs) as evolution equations in infinite dimensional spaces. Several models in the theoretical economic literature have been studied using this reformulation. On the other hand, in the stochastic case only few results of this kind are available and only for specific problems. The...
متن کاملNonlinear low-dimensional regression using auxiliary coordinates
When doing regression with inputs and outputs that are high-dimensional, it often makes sense to reduce the dimensionality of the inputs before mapping to the outputs. Much work in statistics and machine learning, such as reduced-rank regression, sliced inverse regression and their variants, has focused on linear dimensionality reduction, or on estimating the dimensionality reduction first and ...
متن کاملLow-dimensional Representation
Ordination is a generic name for methods for providing a low-dimensionaL view of points in multi-dimensional space, such that “similar” objects are near each other and dissimilar objects are separated. The plot(s) from an ordination in 2 or 3 dimensions may provide useful visual clues on clusters in the data and on outliers. If data can be separated into known classes that should be reflected i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Multiscale Modeling & Simulation
سال: 2008
ISSN: 1540-3459,1540-3467
DOI: 10.1137/070696325