二进神经网络中的汉明球突及其线性可分性

杨娟; 陆阳; 黄镇谨; 王强

doi:10.3724/SP.J.1004.2011.00737

二进神经网络中的汉明球突及其线性可分性

doi: 10.3724/SP.J.1004.2011.00737

1.
合肥工业大学计算机与信息学院合肥 230009

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出版历程
- 收稿日期: 2010-12-20
- 修回日期: 2011-02-18
- 刊出日期: 2011-06-20

Hamming Sphere Dimple in Binary Neural Networks and Its Linear Separability

1.
School of Computer and Infomation, Hefei University of Technology, Hefei 230009

摘要

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.
- 二进神经网络 /
- 线性可分函数 /
- 汉明球突 /
- 线性分类
Abstract: 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.
- Binary neural networks /
- linearly separable function /
- Hamming sphere dimple /
- linear classification

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[1]

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