The Normalized Radial Basis Function Neural Network and its Relation to the Perceptron

The normalized radial basis function neural network emerges in the statistical modeling of natural laws that relate components of multivariate data. The modeling is based on the kernel estimator of the joint probability density function pertaining to given data. From this function a governing law is extracted by the conditional average estimator. The corresponding nonparametric regression represents a normalized radial basis function neural network and can be related with the multi-layer perceptron equation. In this article an exact equivalence of both paradigms is demonstrated for a one-dimensional case with symmetric triangular basis functions. The transformation provides for a simple interpretation of perceptron parameters in terms of statistical samples of multivariate data.