Ritter G X, Sussner P, Diza-de-Leon J L
University of Florida, Center for Computer Vision and Visualization, Gainesville, FL 32611, USA.
IEEE Trans Neural Netw. 1998;9(2):281-93. doi: 10.1109/72.661123.
The theory of artificial neural networks has been successfully applied to a wide variety of pattern recognition problems. In this theory, the first step in computing the next state of a neuron or in performing the next layer neural network computation involves the linear operation of multiplying neural values by their synaptic strengths and adding the results. A nonlinear activation function usually follows the linear operation in order to provide for nonlinearity of the network and set the next state of the neuron. In this paper we introduce a novel class of artificial neural networks, called morphological neural networks, in which the operations of multiplication and addition are replaced by addition and maximum (or minimum), respectively. By taking the maximum (or minimum) of sums instead of the sum of products, morphological network computation is nonlinear before possible application of a nonlinear activation function. As a consequence, the properties of morphological neural networks are drastically different than those of traditional neural network models. The main emphasis of the research presented here is on morphological associative memories. We examine the computing and storage capabilities of morphological associative memories and discuss differences between morphological models and traditional semilinear models such as the Hopfield net.
人工神经网络理论已成功应用于各种各样的模式识别问题。在该理论中，计算神经元的下一个状态或执行下一层神经网络计算的第一步涉及将神经值与其突触强度相乘并将结果相加的线性运算。通常在该线性运算之后会有一个非线性激活函数，以便为网络提供非线性并设置神经元的下一个状态。在本文中，我们引入了一类新型的人工神经网络，称为形态神经网络，其中乘法和加法运算分别被加法和最大值（或最小值）运算所取代。通过取和的最大值（或最小值）而非乘积的和，形态网络计算在可能应用非线性激活函数之前就是非线性的。因此，形态神经网络的特性与传统神经网络模型的特性截然不同。这里所呈现研究的主要重点是形态联想记忆。我们研究形态联想记忆的计算和存储能力，并讨论形态模型与传统半线性模型（如霍普菲尔德网络）之间的差异。
