人工神经网络学习的代数方法

Algebraic Learning Procedures for Artificial Neural Networks

介绍了具有自环和无自环的神经网络利用 Ｍｏｏｒｓ－Ｐｅｎｒｏｓｅ伪逆的学习方法，分析 了这种方法获得的权重所具有的优点，如权重方均根值最小等．使得网络具有较好与较 均匀的鲁捧性。找到了具有自环和无自环网络在权重方均根最小条件下权重之间的关 系，从而使无自环网络的学习过程与有自环的网络同样简单。通过伪逆方法找到了确定 阈值的优化办法，使网络鲁棒性有不同程度的提高。

The learning procedures using Moors-Penrose Pseudo-inverse method for neural networks with and without self-feedback connections and the relation between these two kinds of networks are presented. It is demonstrated that the networks trained by these procedures work well and show better and even robustness for they have minimal mean-square-root connection weights. It is proven that the parameters of the network without self-feedback connections can be obtained directly from the parameters of the network with self-feedback connections, provided that both of them have minimal mean-square-root connection weights. The optimal threshold value of a network is also derived using pseuds-inverse method, which will enhance the robustness of the network.