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LMN-Tool: Matlab-Toolbox for Local Model Networks

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LMN-Tool Example

This object-oriented Matlab toolbox covers two algorithms for building local model networks (also called Takagi-Sugeno fuzzy systems) from data:

LOLIMOT  (LOcal LInear MOdel tree)

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

HILOMOT  (HIerarchical LOcal MOdel Tree)

  • Axes-oblique partitioning into arbitrary shapes
  • Sigmoidal validity functions constructed hierarchically
  • Oblique splits in 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 with weighted least squares
  • Locally worst model is split
  • Good interpretability
  • Possibility to transfer/adapt solutions for linear problems to the nonlinear world
  • Adaption of the model in specific regions unproblematic (no unlearning!)
    → only in regions with fresh data the model behavior is adjusted

These are the key features of this toolbox:

  • Object-oriented implementation with classes
  • Reasonable default values allow simple usage: LMNTrain(data)
  • Individual setting can be assigned by changing the class properties
  • Termination criterion of tree-construction is a 2x increasing AICC (default)
  • Dynamic models are possible with arbitrary delays for inputs and outputs
  • Splitting can be performed according to the output/simulation error
  • Local models are polynomials of arbitrary degree (default is 1 and 2)
  • Training, validation (optional), and testing (optional) data can be used
  • Splitting smoothness is set to a reasonable default value


If you want to publish your 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 zum automatischen Trainieren lokaler Modellnetze", 22. Workshop Computational Intelligence, Dortmund, Dezember 2012.

Keywords: Local model network, Takagi-Sugeno fuzzy system, neural network, neuro-fuzzy, LOLIMOT, HILOMOT, machine learning, nonlinear system identification, nonlinear dynamic model, local regression, least squares, tree-construction, Gaussian, sigmoid, normalized, hierarchical