Sensitivity of Spatial Analysis Neural Network Training and Interpolation to Structural Parameters

Abstract

A Spatial Analysis Neural Network (SANN) algorithm was applied for the analysis of geospatial data, on the basis of nonparametric statistical analysis and the concepts of traditional Artificial Neural Networks. SANN consists of a number of layers in which the neurons or nodes between layers are interconnected successively in a feed-forward direction. The Gaussian Kernel Function layer has several nodes, and each node has a transfer or an activation function that only responds (or activates) when the input pattern falls within its receptive field, which is defined by its smoothing parameter or width. The activation widths are functions of the model structural parameters, including the number of the nearest neighbor points P and a control factor F. The estimation method is based on two operational modes, namely, a training-validation mode in which the model structure is constructed and validated, and an interpolation mode. In this paper we discuss the effect of varying F and P upon the accuracy of the estimation in a two-dimensional domain for different input field sizes, using spatial data of wheat crop yield from Eastern Colorado. Crop yield is estimated as a function of the two-dimensional Cartesian coordinates (easting and northing). The results of the research led to the conclusion that optimal values of F and P depend on the sample size, i.e., for small data sets F=1.5 and P=7 while for large data sets F=2.5 and P=9. In addition, the accuracy of the interpolated field varies with the sample size. As expected for small sample sizes, the interpolated field and its variability may be significantly underestimated.