Fuzzy ART Choice Functions

Adaptive Resonance Theory (ART) models arc real-lime neural networks for category learning, pattern recognition, and prediction. Unsupervised fuzzy ART and supervised fuzzy ARTMAP networks synthesize fuzzy logic and ART by exploiting the formal similarity between tile computations of fuzzy subsethood and the dynamics of ART category choice, search, and learning. Fuzzy ART self-organizes stable recognition categories in response to m·bitrary sequences of analog or binary input patterns. It generalizes the hinm·y ART I model, replacing the set-theoretic intersection (n) with the fuzzy intersection(/\), or component-wise minimum. A normalization procedure called complement coding leads to a symmetric theory in which the fuzzy intersection and the fuzzy union (V), or component-wise maximum, play complementary roles. A geometric interpretation of fuzzy ART represents each category as a box that increases in size as weights decrease. This paper analyzes fuzzy ART models that employ various choice functions for category selection. One such function minimizes total weight change during learning. Benchmark simulations compare pcrl(mnancc of fuzzy ARTMAP systems that use rliJTcrcnt choice functions. ART and ARTMAP Adaptive Resonance Theory (ART) was introduced as a theory of human cognitive information processing (Grossberg, 1976). The theory has led to an evolving series of real-time neural network models for unsupervised and supervised category learning and pattern recognition. These ART models form stable recognition categories in response to arbitrary input sequences with either fast or slow leaming. Unsupervised ART networks include ART I (Carpenter and Grossberg, l9~7a), which stably learns to categorize binary input patterns presented in an arbitrary order; ART 2 (Carpenter and Grossberg, I 9R7b), which stably learns to categorize either analog or binary input patterns presented in an m·bitrary order; and ART 3 (Carpenter and Grossberg, 1990), which carries out parallel search, or hypothesis testing, of distributed recognition codes in a multi-level network hierarchy. Many of the ART papers are collected in the anthology Pattem Recognjfjon by Seli~Org1whjng Neunli Networks (Carpenter and Grossberg, 1991 ). A supervised network architecture, called ARTMAP, self-organizes categorical mappings between m-dimensional input vectors and n-climensional output vectors. ARTMAP's internal control mechanisms create stable recognition categories of optimal size by maximizing code compression while minimizing predictive error in an on-line setting. Binary ART I computations are the foundation of the first ARTMAP network (Carpenter, Grossberg, and Reynolds, I 99 I), which therefore learns binary maps. Fuzzy ART (Carpenter, Grossberg, and Rosen, 1991) generalizes ART I to learn stable recognition categories in response to analog and binary input patterns (Figure I). Th~ domain of fuzzy ART is thus the same as that of ART 2, but fuzzy ART Acknowledgments: This research was supported in part by ARPA (ONR N<XJOI4-92-J-4015), tllc National Science Foundation (NSF lRl 90-00530), ami tllc Orlicc of Naval Research (ONR NOOO 14-91-.l-41 00).