LMN-Tool: Matlab-Toolbox for Local Model Networks

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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