二进神经网络中汉明球突的判定及其逻辑意义  

The Judgment for Hamming Sphere Dimple in Binary Neural Networks and Its Logical Meaning

作　　者：杨娟[1] 陆阳[1] 俞磊[1] 方欢[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》2012年第9期1459-1470,共12页Acta Automatica Sinica

摘　　要：在布尔空间中,汉明球突表达了一类结构清晰的布尔函数,由于其特殊的几何特性,存在线性可分与线性不可分两种空间结构.剖析汉明球突的逻辑意义对二进神经网络的规则提取十分重要,然而,从线性可分的汉明球突中提取具有清晰逻辑意义的规则,以及如何判定非线性可分的汉明球突,并得到其逻辑意义,仍然是二进神经网络研究中尚未很好解决的问题.为此,本文首先根据汉明球突在汉明图上的几何特性,采用真节点加权高度排序的方法,提出对于任意布尔函数是否为汉明球突的判定算法;然后,在此基础上利用已知结构的逻辑意义,将汉明球突分解为若干个已知结构的并集,从而得到汉明球突的逻辑意义;最后,通过实例说明判定任意布尔函数是否为汉明球突的过程,并相应得到汉明球突的逻辑表达.In boolean space, Hamming sphere dimple is able to express a kind of boolean function with clear structure. Hamming sphere dimple contains linearly separable and nonlinearly separable structures because of its special geometric characteristic. It is very important to analyze the logical meaning of Hamming sphere dimple for extracting rules from binary neural networks. However, how to extract the rules with explicit logical meaning of the linearly separable and nonlinearly separable Hamming sphere dimples and how to judge whether a nonlinearly separable boolean function is a Hamming sphere dimple have not yet been settled. To solve these problems, we firstly analyze the features of Hamming sphere dimple with Hamming-graph, and then propose an algorithm for judging whether a boolean function is linearly or nonlinearly separable Hamming sphere dimple by sorting the weighted height of the true nodes. Furthermore, we decompose Hamming sphere dimple into two known structures to obtain the logical meaning of Hamming sphere dimple by using the logical meaning of the known structures. Finally, we explain whether an arbitrary boolean function is a Hamming sphere dimple through examples, and obtain the logical meaning of the corresponding Hamming sphere dimple.

关 键 词：二进神经网络 汉明球 汉明球突 笛卡尔球 规则提取 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]