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根据两类线性可分结构笛卡尔积的概念,定义了布尔空间中笛卡尔球的概念,证明了笛卡尔球是一类线性可分结构系.此外,还对以布尔空间中任意样本Ⅹ°为中心,与Ⅹ°之间Hamming距离为1的任意个样本与Ⅹ°组成的集合进行了研究,证明了这是一类笛卡尔球.为了对笛卡尔球进行规则提取,文中还分析了笛卡尔球的逻辑意义,建立了二进神经网络中判别笛卡尔球的一般方法,描述了这种判别方法的具体步骤,并通过一个实例说明了在二进神经网络中判别笛卡尔球的过程.
The concept of Cartesian sphere in Boolean space is defined according to the concept of two types of linear separable Cartesian product, which proves that Cartesian sphere is a class of linear separable structure. In addition, As a center and a set of arbitrary samples and Ⅹ ° whose Hamming distance is 1 between Ⅹ ° has been proved to be a kind of Cartesian sphere.In order to extract the Cartesian sphere regularly, This paper describes the logical meaning of Cartesian ball, establishes the general method of discriminating Cartesian ball in binary neural network, describes the concrete steps of this discriminant method, and illustrates the process of distinguishing Cartesian ball in binary neural network through an example.