二进神经网络中的汉明球突及其线性可分性  

Hamming Sphere Dimple in Binary Neural Networks and Its Linear Separability

作　　者：杨娟[1] 陆阳[1] 黄镇谨[1] 王强[1] 

机构地区：[1]合肥工业大学计算机与信息学院,合肥230009

出　　处：《自动化学报》2011年第6期737-745,共9页Acta Automatica Sinica

摘　　要：对于二进神经网络,剖析其神经元的逻辑意义对网络的规则提取是十分重要的,而目前每个神经元所表达的线性结构的逻辑意义仍没有完全解决,一部分线性函数的结构及其逻辑意义尚不明确.本文在寻找线性可分结构的过程中,提出了汉明球突的概念,给出其是否线性可分的判定方法,并得到二进神经元与线性可分的汉明球突等价的充要条件,从而建立了判别线性可分的汉明球突的一般方法,并通过实例验证了该方法的有效性.It is very important to analyze the logical meaning of neurons for extracting rules from binary neural networks （BNNs）.However,the problem is that the logical meaning of linear structure expressed by neurons has not been completely solved and the structure of several linear functions is not clear.To solve this problem,we define a special structure called Hamming sphere dimple and provide the judgment method for linear separability.Furthermore,we obtain the necessary and sufficient condition for the equivalence between the linearly separable Hamming sphere dimple（LSHSD）and the binary neurons.Finally,we propose a general method for judging the LSHSD.This method is validated to be effective to judge the LSHSD through examples.

关 键 词：二进神经网络 线性可分函数 汉明球突 线性分类 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]