Analyzing the Fuzzy ARTMAP Matchtracking mechanism with Co-Objective Optimization Theory

In the process of learning a pattern I, the fuzzy ARTMAP algorithm templates (i.e., the weight vectors corresponding to nodes of its category representation layer) compete for the representation of the given pattern. This competition can induce matchtracking: a process that iterates a number of times over the template set searching for a template w* of the correct class that best represents the pattern I. In this paper, we analyze the search for a winning template from the perspective of bi-criterion optimization and prove that it is actually a walk along the Pareto front of an appropriately defined co-objective optimization problem. This observation allows us to propose the basis for an implementation variant of fuzzy ARTMAP that (a) produces exactly the same network as fuzzy ARTMAP, (b) avoids matchtracking by explicitly keeping track of a subset of the Pareto front, (c) finds the correct template to represent an input pattern through a single pass over the template set and (d) eliminates the need for the fuzzy ARTMAP parameter epsiv.