For a burying depth up to 80cm, we obtain the results given in
the table 1. We can notice that the result of the built RBF
classifier is better than the others, and always without any
specialisation of the construction algorithm.
Figure 5. Representation of the classifier results for the 5
We also notice that the results obtained with the Holdout method
averaged over five different experiments show that the developed
RBF classifier is particularly robust. As a matter of fact, the
difference between the best and the worst level of error
percentage is very small, less than 10% of the average value.
So all these results show that our new algorithm of RBF classifier
permits to obtain a very high performance and robust general
classifier which can be applied on many kinds of pattern
recognition problems with very good results.
4. CODE IDENTIFICATION
The general purpose of our application is to detect and identify
reliably different buried metallic codes with a smart eddy current
sensor . The data are collected by a flat coils metal locator
based on the induction balance principle. This detector is
connected to a mobile measurement system which controls the
A code is built from a succession of different metal pieces
separated by empty spaces. The different codes are obtained by
the combination of different sizes of the metallic parts and empty
Due to the codes similarity and the non linear locator answer
with the burying depth, the classification problem is not very
simple. That is why we have developed intelligent methods to
well solve it. Our first methods was based on the fuzzy logic
theory and the Kohonen SOM. As the SOM algorithm gave
disappointing results, we replace it by the new proposed RBF
The methods based on the fuzzy logic theory are the well-known
Fuzzy Pattern Matching (FPM)  and the distributed rules (DR)
 developed among others by Ishibuchi.
A comparison is made between these different methods and the
proposed RBF classifier.
Table 1. Results of code misclassification for the 4
pattern recognition methods implemented.
The use of incremental RBF networks has been already studied
 but here we have presented a new simple incremental or "selforganised" RBF network algorithm which is able to be used in a
lot of domains without any parameters to set. We have tried with
this algorithm to translate the most simply the RBF network
The results show that the RBF classifier, built simply in the way
we have developed, is very robust and particularly efficient in a
wide range of pattern recognition problems.
 Bishop C.M. "Neural Networks for Pattern Recognition",
Clarendon Press, Oxford, 1995.
 Poggio T. and Girosi F. "Networks for Approximation and
Learning" Proceedings of the IEEE, Vol. 78, pp. 14811497, 1990.
 Hwang Y.-S. and Bang S.-Y. "An Efficient Method to
Construct a Radial Basis Function Neural Network
Classifier" Neural Networks, Vol. 10, No. 8, pp. 1495-1503,
 Bianchini M., Frasconi P. and Gori M. "Learning Without
Local Minima in Radial Basis Function Networks" IEEE
Transaction On Neural Networks, Vol. 6, No. 3, pp. 749756, 1995.
 Guerin-Dugue A. and others "Deliverable R3-B4-P Task
B4 : Benchmarks" Technical Report, ELENA Enhanced
Learning for Evolutive Neural Architecture, ESPRIT Basic
Research Project Number 6891, 1995.
 Belloir F., Klein F. and Billat A. "Pattern Recognition
Methods for Identification of Metallic Codes Detected by
Eddy Current Sensor" Signal and Image Processing
(SIP'97), Proceedings of the IASTED International
Conference, pp. 293-297, 1997.
 Grabisch M. and Sugeno, "A Comparison of some Methods
of Fuzzy Classification on Real Data", Proc. Of IIZUKA'92,
pp. 659-662, Iizuka, Japan, July 1992.
 Ishibuchi H., Nosaki K. and Tanaka H., "Selecting Fuzzy IfThen Rules for Classification Problems Using Genetic
Algorithms", IEEE Tansactions on Fuzzy Systems, vol. 3,
 Fritzke B. "Transforming Hard Problems into Linearly
Separable one with Incremental Radial Basis Function
Networks" In M.J. Vand Der Heyden, J. Mrsic-Flögel and
K. Weigel (eds), HELNET International Workshop on
Neural Networks, Proceedings Volume I/II (1994/1995),
VU University Press, 1996.