Gianluca Bontempi - Associate Professor - Département d'Informatique - ULB Brussels, Belgium
Mauro Birattari - Researcher - IRIDIA - ULB Brussels, Belgium
To download the manual, click here.
To download the software, click here .
THIS SOFTWARE IS FREELY AVAILABLE FOR EDUCATIONAL AND STRICTLY NON COMMERCIAL AND/OR MILITARY USE
The neuro-fuzzy software for identification and data analysis has been implemented in the MATLAB language ver. 4.2.
The software trains a fuzzy architecture, inspired to Takagi-Sugeno approach, on the basis of a training set of N (single) output-(multi) input
The returned model has the form
1) if input1 is A11 and input 2 is A12 then output =f1(input1,input2)
2) if input1 is A21 and input 2 is A22 then output =f2(input1,input2)
where Aij are parametric membership function.
The program provides a set of structural alternatives in the definition of the fuzzy model: the shape of the membership functions of the antecedents (gaussian or triangular), the parametric form of the consequent (constant or linear f), the combination method of the rules (normalized or not). Further, it is possible to choose between two different clustering policies, K-means or Hyperplane Fuzzy Clustering , to provide the identification algorithm with good initial values of the centers and bases of the membership functions.
The program searchs also for the
'right' complexity (number of rules) of the architecture by adopting a
cross-validation on the available data set. It starts with a minimal
number of rules and at each step increase the number of rules by
restarting the global
procedure, until a maximum number of rules is reached (the user is free
set properly what is the desired range of complexity to range over).
each structure is characterized by its error in generalization,
estimated by a procedure of cross-validation and the optimal number of
rules is searched by comparing the cross validation error obtained at
different levels of complexity. At the end of the global training
phase, the cross validation error is plotted against the number of
rules used and the user is asked to choose the level of complexity at
which the fuzzy system looks to perform better (fig.1): after
this, the fuzzy system of the chosen complexity is identified from
by using the whole data set. The model is now ready to be used for
on new samples.
fig. 1. Cross-validation error vs. complexity diagram
Bersini H., Bontempi G., Decaestecker C. (1995). Comparing RBF and Fuzzy Inference Systems on Theoretical and Practical Basis in F.Fogelman-Soulie', P. Gallinari (Eds.) ICANN '95,International Conference on Artificial Neural Networks, Paris , vol. 1, pp. 169-174
Bersini H., Bontempi G. (1997) Now comes the time to defuzzify neuro-fuzzy models Fuzzy Sets and Systems , 90,2, 161-170.
 Bezdek J.C., Anderson I.M. (1985), An Application of the c-Varieties Clustering Algorithms to Polygonal Curve Fitting, IEEE Trans. Syst., Man Cybern.,vol.SMC-15,no 5. pp 637-641
 Sugeno M. , Yasukawa T.,(1993) A Fuzzy-Logic-Based Approach to Qualitative Modeling, IEEE Trans. Fuzzy Syst., vol.1 no 1
 Bontempi G., Bersini H. (1997) Identification of a sensor model with hybrid neuro-fuzzy methods in A. B. Bulsari, S. Kallio (eds.) Neural Networks in Engineering systems (Proceedings of the 1997 International Conference on Engineering Applications of Neural Networks (EANN '97), Stockolm, Sweden) pp. 325-328.