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A Survey on Mini Max Neural Networks

by Akira Imada (October 2004)

In their paper,

Z. Ji and D. Dasgupata (2004) "Augmented Negative Selection Algorithm with Variable-Coverage Detectors." Proceedings of the Congress on Evolutionary Computation,

authors wrote "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...... 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..."

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, 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.

All of these four papers have been resisted to be FTP'ed for free. The bellow are related articles by exploring via google with key words of "simpson" abd "fuzzy-min-max-neural-networks"

Fuzzy Min-Max Neural Network

Here, we see two studys where Fuzzy Logic is used in Data Mining based on Artificial Immune System,

Bogdan Gabrys and Andrzej Bargiela (2000) "General Fuzzy Min-Max Neural Network for Clustering and Classification." IEEE Transactions on Neural Networks Vol. 11 (3) pp. 769--783.

Though this paper describes, as authors wrote, "a general fuzzy min-max (GFMM) which is a generalization and extension of the (original) fuzzy min-max clustering and classification algorithms developed by Simpson", it could be a good introduction to the original Simpson's Fuzzy Min-Max Neural Network, since the original paper by Simpson is not easily available for us, alas. Interesting key phrases are: "New data can be included without the need for retraining;" In supervised learning often referred to as a pattern classification problem,... In unsupervised learning, often re-ferred to as a cluster analysis problem,..."

Bogdan Gabrys (????) Agglomerative Learning Algorithms for General Fuzzy Min-Max Neural Network."

Aristidis Likas and Kvstas Blekas (????) A Reinforcement Learning Approach bsed on the Fuzzy Min-Max Neural Network."

The bellow is not a paper exploring Simpson's Mini-Max-Neural-Networks but an original proposal, and just compared the results with other similar proposals which includes Simpson's. The authors assert their proposal outperfoms all of others being compared.

G. Castellano and A. M. Fanelli(2000) "Fuzzy Inference and Rule Extraction using a Neural Network." Neural Network World Journal Vol. 3, pp. 361--371.

Discovering Patterns in Spatial Data.

Original proposition by Ghozeil and Fogel does not seem to exist in a public domain.

Vladimir Estivill-Castro, and Alan T. Murray (????) "Spatial Clustering for Data Mining with Genetic Algorithms."

This paper cites DBForgel and PKSimpson (1993) Evolving fuzzy clusters Proceedings of the IEEE conference on NN. pp 1829--1834 and AGhozeil and DBForgel (1996) Discovering pattenrs in spatial data using evolutionary programming. Proceedings of the 1st annual conference pp 521-527 MIT PRess. as other attempts to use evolutionary techniques for spatial clustering went on to write are less suitable for spatial data mining applications since they are designed for only small data sets given the delicate encoding and shape restrictions on the clusters. Thoug author wrote Other attemtp