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

Clone down the project repository:

git clone https://github.com/dg227/NLSA

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.