Min-max classifiers: Learnability, design and application

Abstract This paper introduces the class of min-max classifiers. These are binary-valued functions that can be used as pattern classifiers of both real-valued and binary-valued feature vectors. They are also lattice-theoretic generalization of Boolean functions and are also related to feed-forward neural networks and morphological signal operators. We studied supervised learning of these classifiers under the Probably Approximately Correct (PAC) model proposed by Valiant. Several subclasses of thresholded min-max functions are shown to be learnable, generalizing the learnability results for the corresponding classes of Boolean functions. We also propose a LMS algorithm for the practical training of these pattern classifiers. Experimental results using the LMS algorithm for handwritten character recognition are promising. For example, in our experiments the min-max classifiers were able to achieve error rates that are comparable or better than those generated using neural networks. The major advantage of min-max classifiers compared to neural networks is their simplicity and the faster convergence of their training algorithm.