Fuzzy ART: An Adaptive Resonance Algorithm for Rapid, Stable Classification of Analog Patterns

The Fuzzy ART system introduced herein incorporates computations from fuzzy set theory into ART 1. For example, the intersection (n) operator used in ART 1 learning is replaced by the MIN operator (A) of fuzzy set theory. Fuzzy ART reduces to ART 1 in response to binary input vectors, but can also learn stable categories in response to analog input vectors. In particular, the MIN operator reduces to the intersection operator in the binary case. Learning is stable because all adaptive weights can only decrease in time. A preprocessing step, called complement coding, uses on-cell and off-cell responses to prevent category proliferation. Complement coding normalizes input vectors while preserving the amplitudes of individual feature activations.

Fuzzy ART: Fast Stable Learning and Categorization of Analog Patterns by an Adaptive Resonance System

A Fuzzy ART model capable of rapid stable learning of recognition categories in response to arbitrary sequences of analog or binary input patterns is described. Fuzzy ART incorporates computations from fuzzy set theory into the ART 1 neural network, which learns to categorize only binary input patterns. The generalization to learning both analog and binary input patterns is achieved by replacing appearances of the intersection operator (n) in AHT 1 by the MIN operator (Λ) of fuzzy set theory. The MIN operator reduces to the intersection operator in the binary case. Category proliferation is prevented by normalizing input vectors at a preprocessing stage. A normalization procedure called complement coding leads to a symmetric theory in which the MIN operator (Λ) and the MAX operator (v) of fuzzy set theory play complementary roles. Complement coding uses on-cells and off-cells to represent the input pattern, and preserves individual feature amplitudes while normalizing the total on-cell/off-cell vector. Learning is stable because all adaptive weights can only decrease in time. Decreasing weights correspond to increasing sizes of category "boxes". Smaller vigilance values lead to larger category boxes. Learning stops when the input space is covered by boxes. With fast learning and a finite input set of arbitrary size and composition, learning stabilizes after just one presentation of each input pattern. A fast-commit slow-recode option combines fast learning with a forgetting rule that buffers system memory against noise. Using this option, rare events can be rapidly learned, yet previously learned memories are not rapidly erased in response to statistically unreliable input fluctuations.

Fuzzy ART

Adaptive Resonance Theory (ART) models are real-time neural networks for category learning, pattern recognition, and prediction. Unsupervised fuzzy ART and supervised fuzzy ARTMAP synthesize fuzzy logic and ART networks by exploiting the formal similarity between the computations of fuzzy subsethood and the dynamics of ART category choice, search, and learning. Fuzzy ART self-organizes stable recognition categories in response to arbitrary sequences of analog or binary input patterns. It generalizes the binary ART 1 model, replacing the set-theoretic: intersection (∩) with the fuzzy intersection (∧), or component-wise minimum. A normalization procedure called complement coding leads to a symmetric: theory in which the fuzzy inter:>ec:tion and the fuzzy union (∨), or component-wise maximum, play complementary roles. Complement coding preserves individual feature amplitudes while normalizing the input vector, and prevents a potential category proliferation problem. Adaptive weights :otart equal to one and can only decrease in time. A geometric interpretation of fuzzy AHT represents each category as a box that increases in size as weights decrease. A matching criterion controls search, determining how close an input and a learned representation must be for a category to accept the input as a new exemplar. A vigilance parameter (p) sets the matching criterion and determines how finely or coarsely an ART system will partition inputs. High vigilance creates fine categories, represented by small boxes. Learning stops when boxes cover the input space. With fast learning, fixed vigilance, and an arbitrary input set, learning stabilizes after just one presentation of each input. A fast-commit slow-recode option allows rapid learning of rare events yet buffers memories against recoding by noisy inputs. Fuzzy ARTMAP unites two fuzzy ART networks to solve supervised learning and prediction problems. A Minimax Learning Rule controls ARTMAP category structure, conjointly minimizing predictive error and maximizing code compression. Low vigilance maximizes compression but may therefore cause very different inputs to make the same prediction. When this coarse grouping strategy causes a predictive error, an internal match tracking control process increases vigilance just enough to correct the error. ARTMAP automatically constructs a minimal number of recognition categories, or "hidden units," to meet accuracy criteria. An ARTMAP voting strategy improves prediction by training the system several times using different orderings of the input set. Voting assigns confidence estimates to competing predictions given small, noisy, or incomplete training sets. ARPA benchmark simulations illustrate fuzzy ARTMAP dynamics. The chapter also compares fuzzy ARTMAP to Salzberg's Nested Generalized Exemplar (NGE) and to Simpson's Fuzzy Min-Max Classifier (FMMC); and concludes with a summary of ART and ARTMAP applications.

Preattentive Texture Segmentation and Grouping by the Boundary Contour System

An improved Boundary Contour System (BCS) neural network model of preattentive vision is applied to two images that produce strong "pop-out" of emergent groupings in humans. In humans these images generate groupings collinear with or perpendicular to image contrasts. Analogous groupings occur in computer simulations of the model. Long-range cooperative and short-range competitive processes of the BCS dynamically form the stable groupings of texture regions in response to the images.

A Neural Network Model for the Spatial and Temporal Response of Retinal Ganglion Cells

This article introduces a quantitative model of early visual system function. The model is formulated to unify analyses of spatial and temporal information processing by the nervous system. Functional constraints of the model suggest mechanisms analogous to photoreceptors, bipolar cells, and retinal ganglion cells, which can be formally represented with first order differential equations. Preliminary numerical simulations and analytical results show that the same formal mechanisms can explain the behavior of both X (linear) and Y (nonlinear) retinal ganglion cell classes by simple changes in the relative width of the receptive field (RF) center and surround mechanisms. Specifically, an increase in the width of the RF center results in a change from X-like to Y-like response, in agreement with anatomical data on the relationship between α- and

Adaptive Resonance Associative Map: A Hierarchical ART System for Fast Stable Associative Learning

This paper introduces a new class of predictive ART architectures, called Adaptive Resonance Associative Map (ARAM) which performs rapid, yet stable heteroassociative learning in real time environment. ARAM can be visualized as two ART modules sharing a single recognition code layer. The unit for recruiting a recognition code is a pattern pair. Code stabilization is ensured by restricting coding to states where resonances are reached in both modules. Simulation results have shown that ARAM is capable of self-stabilizing association of arbitrary pattern pairs of arbitrary complexity appearing in arbitrary sequence by fast learning in real time environment. Due to the symmetrical network structure, associative recall can be performed in both directions.