简单Perceptron学习算法的收敛性

A Discussion of the Learning in a Simple Perceptron

当输入是无穷集或区域时，通过构造一个上鞅，本文证明了简单Ｐｅｒｃｅｐｔｒｏｎ学习算法的收敛性。

In this paper,we extend the convergence of the simple perceptron learning rule to the case that the set of inputs is infinity or a region。 When the set of inputs is linearly separable,we prove that a simple perceptron always improves its performance。As the set of the inputs is ‘strong’linearly separable,then within finite time the connections among units converge to a limit which separates the inputs.The convergence rate is also estimated。