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.

中文翻译：

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用于新型混合形态/线性感知器的极限学习机。

形态神经网络（MNN）可以被描述为一类人工神经网络，它们在每个节点上执行数学形态学运算，并可能随后应用激活函数。形态感知器（MPs）和（灰度）形态联想记忆是最广为人知的MNN模型。由于它们的神经元聚合功能不可区分，因此原则上不能直接应用经典的非线性优化方法来训练这些网络。对于混合形态/线性感知器和其他相关模型也是如此。克服这些不可微问题，本文介绍了一种用于训练混合形态学/线性感知器的极限学习机方法，其形态成分取自以前的MP模型。我们将所得模型应用于文献中的许多众所周知的分类问题，并将我们的模型与几种相关模型（包括一些最新的MNN和混合形态/线性神经网络）的性能进行比较。