Abstract
Artificial neural network (ANN) is a computational model of biological nervous system. The major advantage of this system is that it can process the data having nonlinear behavior and classify appropriately complex and noisy image. The most widely used technique for modifying the connection weights in ANN is termed error back-propagation, which minimizes the error between the output from the network and the desired output using the steepest descent method.However, an ideal modifying rule should also consider the characteristics of spatial correlation of data.
We propose a new modifying rule of the connection weights of network, ESV criteria, which considers both error and semivariogram. The semivariogram expresses the spatial correlation of data by a relationship between the distance of data pair and difference of their values. Typical interpolation method using the semivariogram is Kriging, a weighting average method. The proposed method based on the ESV criteria is called Neural Kriging (NK) .
In order to evaluate the effectiveness of NK, it was applied to a reconstruction problem of a defined data-distribution model from randomly selected discrete data. Two kinds of model, isotropie spherical model and orthogonal anisotropic Gaussian model, were examined. It was revealed that the interpolation errors of NK are smaller than those of ANN and Ordinary Kriging for both models. Therefore, NK is regarded as an interpolation method of high accuracy which can be used for randomly distributed data with any structure of spatial correlation.
Furthermore, NK was applied to the distribution analysis of temperature and pH of water sampled from hot springs and geothermal investigation wells in the Hohi area, northeastern Kyushu, Japan. The result made it clear that the trend of their distributions is harmony with thedirection of principal fracture system in this area.
