OPTIMAL TRAINING OF THRESHOLDED LINEAR CORRELATION CLASSIFIERS

The use of correlation (similarity) matching is common in pattern recognition and can be efficiently implemented in neural hardware. A collection of correlators having common inputs forms a classifier. In his correlation classifier (called the neocognitron), Fukushima uses an iterative procedure to compute the templates and thresholds corresponding to a given set of training patterns. In this paper, we present a closed-form solution to the same training problem, thus trimming the training time to a single epoch (one presentation of each of the training patterns). To expand upon this result, we have also investigated more general classifier models. In a companion paper, we described how generalization can be improved using just the hardware allocated by the original Fukushima model. In this paper, we introduce a more powerful model and derive for it a closed-form training method. We find that its hardware requirements are no greater than those of the neocognitron under certain conditions. Finally, we give a numerical example which demonstrates the superiority of the new model.