多元插值、多模式现象和无关信息的认定

Multivariable Interpolation, Multi Pattern and the Identification of Irrelevant Information

本文给出了Ｌａｇｒａｎｇｅ插值多项式在多元情况下的一个推广。讨论了多元插值问题在三层ＢＰ神经网络上的实现。得出了与径向基方法基本平行的结果。根据这些结果，指出了神经网络学习过程中可能出现的多模式现象。并举例说明，由于存在这种多模式现象，仅根据神经网络的学习权值的分布来判定输入因素是否重要，可能导致错误的结论。

A kind of multivariable pattern of Lagrange interpolation polynomial and the way to realize it by neural network which parallels the RBF is given. The phenomenon of multi pattern is discussed. For example, we point out that identifying the irrelevant information only by the set of weights of the trained neural network is incredible.