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

    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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