改进的链接超平面逼近算法

Improving algorithm of hinging hyperplanes for function approximation

提出了一种新的链接超平面逼近算法。“链接超平面”算法作为非线性逼近方法以链接函数为基函数 ;由于基函数的局限性 ,使“链接超平面”算法不可能达到最佳逼近。论文在二维空间上将双层 maxim in函数扩充为逼近中的基函数 ,经扩充后的模型可表示二维空间上所有的分片线性函数 ,从而其逼近能力强于仅用单层 maximin函数作为基函数的算法。仿真实验表明 ,在参数个数相同的情况下 。

A new algorithm for hinging hyperplanes is presented based on double layer maximum minimum functions and one layer maximum minimum functions. The analysis showed that any piecewise linear function could be represented by double layer maximum minimum functions and one layer maximum minimum functions. New algorithm has better approximation efficiency than Breiman's algorithm that is based on one layer maximum minimum function. A simulation shows that with the same number of parameters, the new model has better approximation precision and the least predicted error than Breiman's algorithm.