Extreme learning machine for a new hybrid morphological/linear perceptron

Abstract

Morphological neural networks (MNNs) can be characterized as a class of artificial neural networks that perform an operation of mathematical morphology at every node, possibly followed by the application of an activation function. Morphological perceptrons (MPs) and (gray-scale) morphological associative memories are among the most widely known MNN models. Since their neuronal aggregation functions are not differentiable, classical methods of non-linear optimization can in principle not be directly applied in order to train these networks. The same observation holds true for hybrid morphological/linear perceptrons and other related models. Circumventing these problems of non-differentiability, this paper introduces an extreme learning machine approach for training a hybrid morphological/linear perceptron, whose morphological components were drawn from previous MP models. We apply the resulting model to a number of well-known classification problems from the literature and compare the performance of our model with the ones of several related models, including some recent MNNs and hybrid morphological/linear neural networks.