一种新的多层感知机隐含层神经元个数上限计算方法

A New Method of Calculating the Upper Limit on Multilayer Perceptron’s Hidden Neuron Number

多层感知机在分类问题中具有广泛的应用。本文针对超平面阈值神经元构成的多层感知机用于分类的情况,求出了输入层神经元最多能把输入空间划分的区域数的解析表达式。该指标在很大程度上说明了感知机输入层的分类能力。本文还对隐含层神经元个数和输入层神经元个数之间的约束关系进行了讨论,得到了更准确的隐含层神经元个数上限。当分类空间的维数远小于输入层神经元个数时,本文得到的隐含层神经元个数上限比现有的结果更小。

Multilayer perceptrons are widely applied in classification. This paper concentrates on the hyperplane multilayer perceptrons for classification. And the maximum number of space cells produced by input neurons is formulated. It shows the classification ability of the input neurons. Based on this, a more accurate upper limit of the hidden layer neuron number is achieved by discussing the restriction between the input neuron number and the hidden neuron number. It is proved that the upper limit of the hidden layer neuron number in this paper is much smaller than the former results when the input space dimension is far smaller than the input layer neuron number.