Sparse grids: a new predictive modelling method for the analysis of geographic data

Abstract

We introduce in this paper a new predictive modelling method to analyse geographic data known as sparse grids. The sparse grids method has been developed for data-mining applications. It is a machine-learning approach to data analysis and has great applicability to the analysis and understanding of geographic data and processes. Sparse grids are a subset of grid-based predictive modelling approaches. The advantages they have over other grid-based methods are that they use fewer parameters and are less susceptible to the curse of dimensionality. These mean that they can be applied to many geographic problems and are readily adapted to the analysis of geographically local samples. We demonstrate the utility of the sparse grids system using a large and spatially extensive data set of regolith samples from Weipa, Australia. We apply both global and local analyses to find relationships between the regolith data and a set of geomorphometric, hydrologic and spectral variables. The results of the global analyses are much better than those generated using an artificial neural network, and the local analysis results are better than those generated using moving window regression for the same analysis window size. The sparse grids system provides a potentially powerful tool for the analysis and understanding of geographic processes and relationships.