Abstract
We describe in this paper a new data mining approach for the analysis of spatial data for environmental modelling. The sparse grids analysis system models the functional relationship between a set of predictor variables and a response variable by using a combination of easily computable functions defined on grids of varying mesh sizes in attribute space. The approach circumvents the so-called “curse of dimensionality” by using, instead of a costly high-dimensional grid a with a fine mesh size in every dimension, a collection of grids that are coarse along some dimensions but fine along others. Adaptive sparse grid regression and classification methods select combinations of grids that suit a particular data set. One advantage of the sparse grids approach from an environmental analysis perspective is that it uses machine learning approaches, and so can deal with correlated data, as are common in environmental problems. One advantage of the sparse grids approach from an environmental analysis perspective is that it uses machine learning approaches, and so can deal with correlated data, as is commonly the case with geographic data. They also require fewer degrees of freedom than do full grid models, allowing them to be applied to more datasets. The parameters defining the adaptive sparse grids can be used to interpret relationships in terms of scale and resolution. For example, the distribution of mesh points used in the set of lattices describes the complexity of the relationships present. It can be used to understand if the system is responding to fine scale variations (many mesh points used) or to gross patterns (few mesh points used). This is valuable information for environmental modelling.