Properties of learning of a Fuzzy ART Variant[taliem.ir]

Properties of learning of a Fuzzy ART Variant

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This paper discusses a variation of the Fuzzy ART algorithm referred to as the Fuzzy ART Variant. The Fuzzy ART Variant is a Fuzzy ART  algorithm that uses a very large choice parameter value. Based on the geometrical interpretation of the weights in Fuzzy ART, useful properties  of learning associated with the Fuzzy ART Variant are presented and proven. One of these properties establishes an upper bound on the number  of list presentations required by the Fuzzy ART Variant to learn an arbitrary list of input patterns. This bound is small and demonstrates  the short-training time property of the Fuzzy ART Variant. Through simulation, it is shown that the Fuzzy ART Variant is as good a clustering  algorithm as a Fuzzy ART algorithm that uses typical (i.e. small) values for the choice parameter. q 1999 Elsevier Science Ltd. All rights reserved

توضیحات محصول

ABSTRACT

This paper discusses a variation of the Fuzzy ART algorithm referred to as the Fuzzy ART Variant. The Fuzzy ART Variant is a Fuzzy ART  algorithm that uses a very large choice parameter value. Based on the geometrical interpretation of the weights in Fuzzy ART, useful properties  of learning associated with the Fuzzy ART Variant are presented and proven. One of these properties establishes an upper bound on the number  of list presentations required by the Fuzzy ART Variant to learn an arbitrary list of input patterns. This bound is small and demonstrates  the short-training time property of the Fuzzy ART Variant. Through simulation, it is shown that the Fuzzy ART Variant is as good a clustering  algorithm as a Fuzzy ART algorithm that uses typical (i.e. small) values for the choice parameter. q 1999 Elsevier Science Ltd. All rights reserved.

INTRODUCTION

Adaptive resonance theory was developed by Grossberg (1976), and a large number of the ART architectures have been introduced in the last  10 years (e.g. Carpenter & Grossberg, 1987a; Carpenter & Grossberg, 1987b; Carpenter & Grossberg, 1990; Carpenter, Grossberg & Reynolds,  1991a; Carpenter, Grossberg & Reynolds, 1991b; Carpenter, Grossberg, Markuzon, Reynolds & Rosen, 1992; Carpenter & Gjaja,  1994; Carpenter & Ross, 1995; Carpenter & Markuzon, 1998; Healy, Caudell & Smith, 1993; Marriott & Harrison, 1995; Tan, 1995; Williamson,  1996) A major separation among all of these architectures is based on whether the learning applied is unsupervised or supervised. Unsupervised  learning is implemented when a collection of input patterns needs to be appropriately clustered into categories, while supervised learning is  utilized when a mapping needs to be learned between inputs and corresponding output patterns. A prominent member of the class of  unsupervised ART architectures is Fuzzy ART (Carpenter et al., 1991b), which is capable of clustering arbitrary collections of arbitrarily complex  analog input patterns. Our focus in this paper is Fuzzy ART and its associated properties of learning. Properties of learning for Fuzzy ART have  already been reported in the literature (Carpenter et al., 1991b; Huang et al., 1995). Most of these properties pertain to a Fuzzy ART network  whose choice parameter is small. In particular, one of our favorite properties of learning in Fuzzy ART (i.e. its short training time) has been  reported only for small values of the choice parameter. The Fuzzy ART algorithm was initially introduced for values of the choice parameter  ranging over the interval (0, ∞) (Carpenter et al., 1991b).

Year: 1999

Publisher : ELSEVIER

By : M. Georgiopoulosa , I. Daghera, G.L. Heilemanb, G. Bebis

File Information: English Language/ 14 Page / size: 119 KB

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سال : 1999

ناشر : ELSEVIER

کاری از : M. Georgiopoulosa, I. Daghera, G.L. Heilemanb, G. Bebis

اطلاعات فایل : زبان انگلیسی / 14 صفحه / حجم : KB 119

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