Author: Marko Budisic [email protected]
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: [email protected]
Copyright (c) 2013, Regents of the University of California All rights reserved.
Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. Neither the name of the University of California, Santa Barbara nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.