lorenz_ode_cluster_test

lorenz_ode_cluster_test, a MATLAB code which takes N points on a trajectory of solutions to the Lorenz system of ordinary differential equations (ODE), and applies the K-Means algorithm to organize the data into K clusters.

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

Languages:

lorenz_ode_cluster_test is available in a MATLAB version.

Related Data and Programs:

kmeans, a MATLAB code which contains several different algorithms for the K-Means problem, which organizes a set of N points in M dimensions into K clusters;

kmeans_fast, a MATLAB code which contains several different algorithms for the K-Means problem, which organizes a set of N points in M dimensions into K clusters, by Charles Elkan.

lorenz_ode, a MATLAB code which approximates solutions to the Lorenz system, creating output files that can be displayed by Gnuplot.

lorenz_sensitivity_test, a MATLAB code which demonstrates sensitivity to initial conditions in the Lorenz system, using an approach suggested by John D Cook.

matlab_kmeans, MATLAB codes which illustrate the use of MATLAB's kmeans() function for clustering N sets of M-dimensional data into K clusters.

Reference:

1. Eurika Kaiser, Bernd Noack, Laurent Cordier, Andreas Spohn, Marc Segond, Markus Abel, Guillaume Daviller, Robert Niven,
   Cluster-based reduced-order modelling of a mixing layer,
   Submitted to Journal of Fluid Mechanics.

Source Code:

• lorenz_ode_cluster_test.m, calls all the tests.
• lorenz_ode_cluster_test.sh, runs all the tests.
• lorenz_ode_cluster_test.txt, the output file.

• lorenz_ode_cluster_test01.m, divides a 4001 point dataset into 10 clusters.

There are data files read by the sample code:

• x_m3_n4001.txt, 4001 points on a trajectory of solutions of the Lorenz equations.
• x_m3_n4001.png, an image of the points.
• x_m3_n4001_k10.png, an image of the points color-coded into 10 clusters.