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.
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).
Publisher : ELSEVIER
By : M. Georgiopoulosa , I. Daghera, G.L. Heilemanb, G. Bebis
File Information: English Language/ 14 Page / size: 119 KB
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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