LMN Tool

This object-oriented MATLAB toolbox provides two algorithms for constructing local model networks (also known as Takagi-Sugeno fuzzy systems) from data:

LOLIMOT (LOcal LInear MOdel tree)
HILOMOT (HIerarchical LOcal MOdel Tree)

Download MATLAB Source Code (Version 1.5.2.1) (For non-commercial use only; see the included license file):

After downloading, rename the file extension from .txt to .zip!

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

LOLIMOT (LOcal LInear MOdel tree)

• Axis-orthogonal partitioning into hyper-rectangles
• Normalized Gaussian validity functions
• Orthogonal splits in a 1:1 ratio are tested

HILOMOT (HIerarchical LOcal MOdel Tree)

• Axes-oblique partitioning into arbitrary shapes
• Sigmoidal validity functions constructed hierarchically
• Oblique splits with optimized ratio and direction
• Split optimization is a separable nonlinear least squares problem
  - Outer loop: Constrained nonlinear split optimizations
  - Inner loop: Local weighted least squares estimation of local model parameters

These are the key features of local model networks as applied here:

• Tree construction builds an incrementally growing network
• Separation between inputs/variables that
  - influence the nonlinear behavior (premise space z)
  - influence the local (linear) models (consequents space x)
• Local models are estimated locally using weighted least squares
• The locally worst model is split
• Good interpretability
• Ability to transfer or adapt solutions for linear problems to the nonlinear domain
• Adapting the model in specific regions is straightforward (no unlearning!)
  → The model’s behavior is adjusted only in regions with new data

These are the key features of this toolbox:

• Object-oriented implementation using classes
• Reasonable default values make it easy to use: LMNTrain(data)
• Individual settings can be configured by modifying the class properties
  The termination criterion for tree construction is a 2x increase in AICC (default)
• Dynamic models are possible with arbitrary delays for inputs and outputs
• Splitting can be performed based on the output or simulation error
• Local models are polynomials of arbitrary degree (default is 1 or 2)
• Training, validation (optional), and testing (optional) data can be used
• Splitting smoothness is set to a reasonable default value

If you wish to publish results generated with this toolbox, please acknowledge our work by citing the following article:
Hartmann B., Ebert T., Fischer T., Belz J., Kampmann G., Nelles O.: "LMNtool - Toolbox for the Automatic Training of Local Model Networks," 22nd Workshop on Computational Intelligence, Dortmund, December 2012.

Function Generator

The polynomial-based function generator is designed to simulate regression problems. It should be a helpful tool during the development of algorithms for experimental modeling and related topics. An arbitrary number of synthetic examples can be generated effortlessly. Unlike available benchmark datasets, the user can freely define key properties of the synthetic examples, such as the amount of data, the dimensionality (number of inputs), the strength of the nonlinearity, the data distribution, and the noise level.

Download the function generator (MATLAB class) here!

After downloading, rename the file extension from .txt to .zip!

If you wish to publish results generated using this function generator, please acknowledge our work by citing the following article:
Julian Belz, Oliver Nelles: “Proposal for a Function Generator and Extrapolation Analysis,” Innovations in Intelligent Systems and Applications (INISTA), 2015 International Symposium on, pp. 282–287, Madrid, September 2015.

EDLS - Extended Deterministic Local Search for Latin Hypercube Design

EDLS generates an optimal Latin Hypercube design with respect to the specified distance criterion. To do so, it swaps design points to maximize the distance between them. Run EDLS without parameters to execute a demo (Latin Hypercube with 25 samples and 2 inputs, including visualization).

Download the EDLS MATLAB function here!

After downloading, rename the file extension from .txt to .m!

If you wish to publish results generated using EDLS, please acknowledge our work by citing the following article:
Tobias Ebert, Torsten Fischer, Julian Belz, Tim Oliver Heinz, Geritt Kampmann, Oliver Nelles: “Extended Deterministic Local Search Algorithm for Maximin Latin Hypercube Designs,” IEEE Symposium Series on Computational Intelligence (SSCI), Cape Town, South Africa, December 2015