Data transformation for neural network models in water resources applications

Abstract

A step that should be considered when developing artificial neural network (ANN) models for water resources applications is the selection of an appropriate transformation of the data. In general, the primary motivations for data transformation are: (1) to scale the data so as to be commensurate with the transfer function in the output layer; (2) to standardise each of the variables; (3) to provide a suitable initialization of the ANN; and (4) to modify the distribution of the input variables to provide a better mapping to the outputs. In this paper, five different transformations are investigated in an attempt to improve the ANN's forecasting ability. These are: linear transformation, logarithmic transformation, histogram equalization, seasonal transformation and a transformation to normality. A case study is presented in which each of the ANN models developed using the different transformation techniques is used to forecast salinity in the River Murray at Murray Bridge (South Australia) 14 days in advance. When tested on a validation set from July 1992 to March 1998, the model developed using the linear transformation resulted in the lowest root mean squared forecasting error. This finding further strengthens the claim that the probability distribution of the data does not need to be known to develop effective ANN models. No improvement in the ANN model's forecasting ability was made using the logarithmic, seasonal and normality transformations. The model developed using histogram equalization produced good results for data within the training domain but was not robust on new patterns outside of the calibration range.