Morphological Perceptron Learning

1 Abstract During the last decade, researchers have applied neural networks to a multitude of diicult tasks which would normally require human intelligence. In particular, percep-trons are used to classify patterns into diierent classes. Recently, several researchers introduced a novel class of artiicial neural networks, called morphological neural networks. In this new theory, the rst step in computing the next state of a neuron or in performing the next layer neu-ral network computation involves the nonlinear operation of adding neural values and their synaptic strengths followed by forming the maximum of the results. We have shown in previous papers that the properties of morphological neural networks diier drastically from those of traditional neural network models. In this paper, we introduce a learning algorithm for multilayer morphological percep-trons which is capable of solving arbitrary classiication problems of patterns into two classes. The progress of neurobiology has allowed researchers to build mathematical models of neurons to simulate neural behavior. The model of morphological neural networks presented here is connected with the fundamental question concerning the diierence between biological neural networks and artiicial neural networks: Is the strength of the electric potential of a signal travelling along an axon the result of a multiplicative process and does the mechanism of the postsynaptic membrane of a neuron add the various potentials of electrical impulses, or is the strength of the electric potential an additive process and does the postsynaptic membrane only accept signals of a certain maximum strength? A positive answer to the latter query would provide a strong biological basis for morphological neural networks. The concept of morphological neural networks grew out of the theory of image algebra 12, 13]. It was shown that a subalgebra of image algebra includes the mathematical formulations of currently popular neural network models 7]. Since then, only a few papers involving morphological neural networks have appeared. J.L. Davidson employed morphological neural networks in order to solve template identiication and target classiication problems 3, 2]. C.P. Suarez-Araujo applied morphological neural networks to compute homothetic auditory and visual invariances 15]. Another interesting network consisting of a morphological net and a classical feedforward network used for feature extraction and classiication was designed by P.D. Gader et al. 18, 17, 4]. All of these researchers devised multilayer morphological neural networks for very specialized applications. The most comprehensive and rigorous basis for computing with morphological neural networks appeared in 8]. We need …