构造性分片线性神经网络逼近

Constructive PWL neural network approximation

针对非线性系统建模中用标准连续分片线性神经网络(SCPLNN)模型拟合二维平面上离散点的问题,依据逼近误差最小化的原则,提出了一种优化的三角形剖分算法进行区域划分。采用特征点代替采样点进行剖分,并给出了基于这种区域划分的SCPLNN模型逼近算法。将此逼近算法与基于Delaunay剖分SCPLNN模型逼近算法、典范分片线性表示的链接超平面逼近算法进行比较。实验结果表明,基于最优三角形剖分SCPLNN模型逼近算法可以有效和快速提高拟合精确度。

For the problem of approximating two dimensional scattered data with standard continuous piecewise linear neural networks （SCPLNN） model in modeling of nonlinear system, an optimal triangulation algorithm is proposed to subdivide the domain by the standard of minimizing error. During this process, feature points were used in place of sample data to do triangulation, then an algorithm of piece- wise- linear neural networks approximation based on optimal triangulation was given. This algorithm was compared with that based on Delaunay triangulation and that of hinging hyperplanes for canonical piece- wise -linear representation. Results show that fitting precision is improved efficiently and quickly by it.