On the match tracking anomaly of the ARTMAP neural network

-This article analyses the match tracking anomaly (MTA ) o f the A R T M A P neural network. The anomaly arises when an input pattern exactly matches its category prototype that the network has previously learned, and the network generates a prediction (through a previously learned associative link) that contradicts the output category that was selected upon presentation o f the corresponding target output. Carpenter et al. claimed that such an anomalous situation will never arise i f the (binary) input vectors have the same number o f ls (Carpenter et al., 1991, Neural Networks, 4, 565-588). This paper shows that such situations can in fact occur. The timing according to which inputs are presented to the network in each learning trial is crucial." i f the target output is presented to the network before the corresponding input pattern, certain pattern sequences will lead the network to the MTA. Two kinds o f M T A are distinguished." one that is independent o f the choice parameter (8) o f the ARTb module, and another that is not. Results o f experiments' that were carried out on a machine learning database demonstrate the existence o f the match tracking anomaly as well as support the analytical results presented here. Keywords---Match tracking, ARTMAP, Adaptive resonance theory, Supervised learning, Self-organization, Hierarchical clustering, Machine learning, Zoo database. 1. I N T R O D U C T I O N The A R T M A P neural network architecture (Carpenter et al., 1991a) is a supervised learning system capable of self-organising stable recognition categories in response to arbitrary sequences of input patterns. I t is built up of a pair of adaptive resonance theory (Carpenter & Grossberg, 1987a) modules (ARTa and ARTb) that are connected through an inter-ART associative memory module. The network has an internal mechanism that conjointly maximises predictive generalisation and minimises predictive error through a self-regulating process called match Acknowledgements: This work was in part supported by Victoria University of Wellington (Research Grant No. RGNT/ 594/371). I am grateful to Peter Andreae, Department of Computer Science, Victoria University of Wellington, New Zealand, for his critical reading of the drafts, valuable suggestions for improving the style and presentation of this article, and even providing further insights into the similarities and differences of the two MTA conditions discussed here. I wish to thank the reviewers for their constructive comments, too. Requests for reprints should be sent to G. Bartfai, Department of Computer Science, Victoria University of Wellington, P.O. Box 600, Wellington, New Zealand. tracking. Whenever the network makes a wrong prediction through a previously learned associative link, the vigilance parameter Pa of the ARTa module will be raised by the minimal amount needed to correct the predictive error at the ARTb module. The ARTa module will then start searching for another category for the current input until it finds a correct prediction, or creates a new ARTa category and its associative link to the corresponding ARTb category. The A R T M A P architecture has been applied to several machine learning benchmark problems (Carpenter et al., 1991a, 1992), and compared favourably with traditional AI learning methods. There are, however, anomalous situations that can occur during training, in which an ARTa input matches its category prototype perfectly and the network makes a wrong prediction (Carpenter et al., 1991a). Raising ARTa vigilance above that (perfect) matching level will prevent the network from finding any other ARTa category, and the wrong prediction will not be corrected. Carpenter et al. claimed that this situation (we shall call it match tracking anomaly, or M T A henceforth) will never arise if the (binary) input patterns have the same number of ls (Carpenter et al., 1991a, pp. 584-585).