An Immuno-Fuzzy Approach to Anomaly Detection
Jonatan Gez

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Other works also have proposed the use of hyper-rectangles
to characterize data in high-dimensional spaces. Simpson [20],
[21] proposed a fuzzy min-max neural network architecture for
classification and clustering of spatial data. In this technique,
the hyper-rectangles represent fuzzy clusters. A deterministic
procedure to place and size the hyper-rectangles was used;
however, its performance was very sensitive to the algorithm
parameters and the order of presentation of the data samples.
Fogel and Simpson [22] used evolutionary programming to
optimize the position of hyper-clusters to cluster data. This
work was extended [23] to support hyper-rectangles not necessarily
aligned with the coordinated axis; however, this work
was restricted to a 2-dimensional space. The main difference
between these approaches and the technique described at the
beginning of this section is that the generated hyper-rectangles
cover the input data (positive space), whereas in the previous
technique the hyper-rectangles cover the negative space.

where

[20] P. Simpson, “Fuzzy min-max neural networks. I. Classification,IEEE
Transactions on Neural Network, vol. 3, pp. 77686, sep 1992.
[21] P. Simpson, “Fuzzy min-max neural networks. II. clustering,IEEE
Transactions on Fuzzy Systems, vol. 1, pp. 32 feb 1993.
[22] D. Fogel and P. Simpson, “Experiments with evolving fuzzy clusters,n
in Proceedings of the Second Annual Conference on Evolutionary
Programming (D. Fogel and W. Atmar, eds.), (La Jolla, California),
pp. 907, 1993.
[23] A. Ghozeil and D. B. Fogel, “Discovering patterns in spatial data using
evolutionary programming,in Genetic Programming 1996: Proceedings
of the First Annual Conference, (Stanford University, CA, USA),
pp. 52127, MIT Press, 281 July 1996.

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