Fuzzy ARTMAP: A Neural Network Architecture for Incremental Supervised Learning of Analog Multidimensional Maps

A new neural network architecture is introduced for incremental supervised learning of recognition categories and multidimensional maps in response to arbitrary sequences of analog or binary input vectors. The architecture, called Fuzzy ARTMAP, achieves a synthesis of fuzzy logic and Adaptive Resonance Theory (ART) neural networks by exploiting a close formal similarity between the computations of fuzzy subsethood and ART category choice, resonance, and learning. Fuzzy ARTMAP also realizes a new Minimax Learning Rule that conjointly minimizes predictive error and maximizes code compression, or generalization. This is achieved by a match tracking process that increases the ART vigilance parameter by the minimum amount needed to correct a predictive error. As a result, the system automatically learns a minimal number of recognition categories, or "hidden units", to met accuracy criteria. 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 logic 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. Improved prediction is achieved by training the system several times using different orderings of the input set. This voting strategy can also be used to assign probability estimates to competing predictions given small, noisy, or incomplete training sets. Four classes of simulations illustrate Fuzzy ARTMAP performance as compared to benchmark back propagation and genetic algorithm systems. These simulations include (i) finding points inside vs. outside a circle; (ii) learning to tell two spirals apart; (iii) incremental approximation of a piecewise continuous function; and (iv) a letter recognition database. The Fuzzy ARTMAP system is also compared to Salzberg's NGE system and to Simpson's FMMC system.British Petroleum (89-A-1204); Defense Advanced Research Projects Agency (90-0083); National Science Foundation (IRI 90-00530); Office of Naval Research (N00014-91-J-4100); Air Force Office of Scientific Research (90-0175

Diffuse pattern learning with Fuzzy ARTMAP and PASS

Fuzzy ARTMAP is compared to a classifier system (CS) called PASS (predictive adaptive sequential system). Previously reported results in a benchmark classification task suggest that Fuzzy ARTMAP systems perform better and are more parsimonious than systems based on the CS architecture. The tasks considered here differ from ordinary classificatory tasks in the amount of output uncertainty associated with input categories. To be successful, learning systems must identify not only correct input categories, but also the most likely outputs for those categories. Performance under various types of diffuse patterns is investigated using a simulated scenario

Integrating Symbolic and Neural Processing in a Self-Organizing Architechture for Pattern Recognition and Prediction

British Petroleum (89A-1204); Defense Advanced Research Projects Agency (N00014-92-J-4015); National Science Foundation (IRI-90-00530); Office of Naval Research (N00014-91-J-4100); Air Force Office of Scientific Research (F49620-92-J-0225

A New Oscillating-Error Technique for Classifiers

This paper describes a new method for reducing the error in a classifier. It uses an error correction update that includes the very simple rule of either adding or subtracting the error adjustment, based on whether the variable value is currently larger or smaller than the desired value. While a traditional neuron would sum the inputs together and then apply a function to the total, this new method can change the function decision for each input value. This gives added flexibility to the convergence procedure, where through a series of transpositions, variables that are far away can continue towards the desired value, whereas variables that are originally much closer can oscillate from one side to the other. Tests show that the method can successfully classify some benchmark datasets. It can also work in a batch mode, with reduced training times and can be used as part of a neural network architecture. Some comparisons with an earlier wave shape paper are also made