Author: Marko Budisic marko@math.wisc.edu
This is my implementation of Coifman/Lafon algorithm for efficient embeddings of high-dimensional data sets, specifically geared towards analysis of dynamical systems.
The use of the code is showcased by three examples:
exampleDynamics.m: demonstrate how algorithm is used on trajectories of a dynamical system
exampleSaddle.m: demonstrate how algorithm performs when analyzing non-recurrent dynamics
exampleTorus.m: demonstrate that Diffusion Coordinates successfully embed a torus (non-dynamical example)
The easiest way to set up and demo the code is running setup.m file in the toolbox folder.
References:
- Coifman, Lafon, 2006: http://dx.doi.org/10.1016/j.acha.2006.04.006
- Budisic, Mezic, 2012: http://dx.doi.org/10.1016/j.physd.2012.04.006
- Budisic, 2012 (PhD Thesis): https://dl.dropbox.com/u/14017882/budisic_2012_dissertation.pdf
- Lee, 2010, http://dx.doi.org/10.1198/jasa.2010.tm09754
A brief overview of functionalities in their calling order is provided below. Each M-function contains commented code, so please refer to source for details.
The easiest way to set up and demo the code is running setup.m file in the toolbox folder.
Most of the code is written in Matlab and requires no specific installation. For speed, however, averaging observables along trajectories is implemented in C++ (in addition to Matlab). Running mex computeAverages.cpp in Matlab should build a MEX file that replicates functionality of computeAverages.m at much shorter run-time.
Diffusion Maps for Dynamics
written by Marko Budisic, while at UC Santa Barbara, 2013.
current e-mail: marko@math.wisc.edu
Copyright (c) 2013, Regents of the University of California All rights reserved.
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