Title

Category regions as new geometrical concepts in Fuzzy-ART and Fuzzy-ARTMAP

Authors

Authors

G. C. Anagnostopoulos;M. Georgiopoulos

Comments

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Abbreviated Journal Title

Neural Netw.

Keywords

adaptive resonance theory; Fuzzy-ART; Fuzzy-ARTMAP; category regions; match region; choice region; claim region; commitment test; NEURAL-NETWORK; CLASSIFICATION; RECOGNITION; FEEDBACK; Computer Science, Artificial Intelligence

Abstract

In this paper we introduce novel geometric concepts, namely category regions, in the original framework of Fuzzy-ART (FA) and Fuzzy-ARTMAP (FAM). The definitions of these regions are based on geometric interpretations of the vigilance test and the F-2 layer competition of committed nodes with uncommitted ones, that we call commitment test. It turns out that not only these regions have the same geometrical shape (polytope structure), but they also share a lot of common and interesting properties that are demonstrated in this paper. One of these properties is the shrinking of the volume that each one of these polytope structures occupies, as training progresses, which alludes to the stability of learning in FA and FAM, a well-known result. Furthermore, properties of learning of FA and FAM are also proven utilizing the geometrical structure and properties that these regions possess; some of these properties were proven before using counterintuitive, algebraic manipulations and are now demonstrated again via intuitive geometrical arguments. One of the results that is worth mentioning as having practical ramifications is the one which states that for certain areas of the vigilance-choice parameter space (p,a), the training and performance (testing) phases of FA and FAM do not depend on the particular choices of the vigilance parameter. Finally, it is worth noting that, although the idea of the category regions has been developed under the premises of FA and FAM, category regions are also meaningful for later developed ART neural network structures, such as ARTEMAP, ARTMAP-IC, Boosted ARTMAP, Micro-ARTMAP, Ellipsoid-ARVARTMAP, among others. (C) 2002 Elsevier Science Ltd. All rights reserved.

Journal Title

Neural Networks

Volume

15

Issue/Number

10

Publication Date

1-1-2002

Document Type

Article

Language

English

First Page

1205

Last Page

1221

WOS Identifier

WOS:000179011600006

ISSN

0893-6080

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