Skip to content

README.md

Latest commit

 

History

History
50 lines (38 loc) · 1.8 KB

README.md

File metadata and controls

50 lines (38 loc) · 1.8 KB

MATLAB NLSA code

This directory contains a MATLAB implementation of nonlinear Laplacian spectral analysis (NLSA) and related operator methods for feature extraction and prediction of observables of dynamical systems.

Usage

  1. Clone down the project repository:
git clone https://github.com/dg227/NLSA
  1. Add directory NLSA/MATLAB/nlsa to the MATLAB search path. This can be done by launching MATLAB, cd'ing to directory NLSA/MATLAB, and executing the command:
addpath(genpath('nlsa'))

Examples

  • Rectification of variable-speed periodic oscillator using Koopman eigenfunctions:
NLSA/MATLAB/examples/circle/demoKoopman.m
  • Extraction of an approximately cyclical observable of the Lorenz 63 (L63) chaotic system using kernel integral operators with delays:
NLSA/MATLAB/examples/circle/demoNLSA.m
  • Kernel analog forecasting of the L63 state vector components:
NLSA/MATLAB/examples/l63/demoKAF.m

Implementation

NLSA implements a MATLAB class nlsaModel which encodes the attributes of the machine learning procedure to be carried out. This includes:

  • Specification of training and test data.
  • Delay-coordinate embedding.
  • Pairwise distance functions.
  • Density estimation for variable-bandwidth kernels.
  • Symmetric and non-symmetric Markov kernels.
  • Koopman operators.
  • Projection and reconstruction of target data.
  • Nystrom out-of-sample extension.

Each of the elements above are implemented as MATLAB classes. See NLSA/MATLAB/nlsa/classes for further information and basic documentation.

Results from each stage of the computation are written on disk in a directory tree with (near-) unique names based on the nlsaModel parameters.

Known issues

  • In Windows environments, errors can occur due to long file/directory names.