Spatial interpolation using MLP-RBFN hybrid networks

It is easy for a multi-layered perception (MLP) to fit a stratified spatial interpolation pattern whose form is close to open surface; while it is easy for a radial basis function network (RBFN) to fit a pocket (radial) spatial interpolation pattern whose form is close to closed surface. However, in the real world, the spatial interpolation pattern may consist of stratified and pocket patterns. Neither MLP nor RBFN can fit the pattern easily. To combine their advantages to fit the complex hybrid spatial interpolation patterns, in this article we propose a novel neural network, MLP-RBFN hybrid network (MRHN), whose hidden layer contains sigmoid and Gaussian units at the same time. Although there are two kinds of processing units in MRHN, in this study we used the principle of minimizing the error sum of squares to derive the supervised learning rules for all the network parameters. This research took rainfall distribution in Taiwan as a case study. The results show that (1) the prediction error of the testing dataset outside the training dataset demonstrated that MRHN was the most accurate among the three networks, RBFN was the next best, and MLP was the worst; (2) the MLP model seriously underestimated the values of high observed rainfall; (3) over-learning may be a serious shortcoming of using RBFN in spatial interpolation applications; (4) MRHN may have better generalization learning capacity than RBFN in spatial interpolation applications.