多项式感知器的非线性映射性能分析及其格型实现

Nonlinear Mapping Performance Analysis of Polynomial Perceptron and Its Lattice Realization

本文详细分析了多项式感知器的非线性映射性能，证明了满足Ｓｔｏｎｅ－Ｗｅｉｅｒｓｔｒａｓｓ定理的多项式感知器可以逼近任一连续函数，并具有与四层神经网络相一致的非线性映射能力。导出了便于ＶＬＳＩ实现的多项式感知器的格型实现算法，进行了计算机模拟，并给出了相应的数值结果。

The nonlinear mapping ability of polynomial perceptron (PP)is analyzed in this paper,which shows that any continuous functions can be approximated with any given accuracy by the polynomial perceptron satisfying Stone-Weierstrass Theorem and the nonlinear mapping ability of the polynomial perceptron is the same as that of multilayer perceptron (MLP). A new lattice polynomial perceptron (LPP) model is derived, which is very suitable for VLSI implementation. Computer simulations have been carried out and the experimental results are given.