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

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.

[1]  Chris Brunsdon,et al.  Is ‘Statistix Inferens’ Still the Geographical Name for a Wild Goose? , 2001, Trans. GIS.

[2]  R. Itami,et al.  GIS-based habitat modeling using logistic multiple regression : a study of the Mt. Graham red squirrel , 1991 .

[3]  B. Lees,et al.  Reconnaissance Thermoluminescence Dating of Northern Australian Coastal Dune Systems , 1990, Quaternary Research.

[4]  Markus Hegland,et al.  Additive sparse grid fitting , 2003 .

[5]  Simon E. Cook,et al.  A Rule-based System to Map Soil Properties , 1996 .

[6]  Michael Griebel,et al.  Data Mining with Sparse Grids , 2001, Computing.

[7]  J. Franklin.  Predictive vegetation mapping: geographic modelling of biospatial patterns in relation to environmental gradients , 1995 .

[8]  R. Abrahart,et al.  Detection of conceptual model rainfall—runoff processes inside an artificial neural network , 2003 .

[9]  Chris Brunsdon,et al.  Geographically Weighted Regression: The Analysis of Spatially Varying Relationships , 2002 .

[10]  B. Lees.  Geomorphological evidence for late Holocene climatic change in northern Australia , 1992 .

[11]  Mark Gahegan,et al.  Is inductive machine learning just another wild goose (or might it lay the golden egg)? , 2003, Int. J. Geogr. Inf. Sci..

[12]  Shawn W. Laffan,et al.  Endemism in the Australian flora , 2001 .

[13]  H. Bungartz,et al.  Sparse grids , 2004, Acta Numerica.

[14]  J. Franklin,et al.  The elements of statistical learning: data mining, inference and prediction , 2005 .

[15]  Philippe G. Ciarlet,et al.  The finite element method for elliptic problems , 2002, Classics in applied mathematics.

[16]  N. Zimmermann,et al.  Predictive mapping of alpine grasslands in Switzerland: Species versus community approach , 1999 .

[17]  Mark Gahegan,et al.  Improving neural network performance on the classification of complex geographic datasets , 1999, J. Geogr. Syst..

[18]  Hans-Joachim Bungartz,et al.  Dünne Gitter und deren Anwendung bei der adaptiven Lösung der dreidimensionalen Poisson-Gleichung , 1992 .

[19]  Antoine Guisan,et al.  Predictive habitat distribution models in ecology , 2000 .

[20]  Michael Griebel,et al.  A combination technique for the solution of sparse grid problems , 1990, Forschungsberichte, TU Munich.

[21]  W. Tobler.  A Computer Movie Simulating Urban Growth in the Detroit Region , 1970 .

[22]  Grace Wahba,et al.  Spatial-Temporal Analysis of Temperature Using Smoothing Spline ANOVA , 1998 .

[23]  Brian G. Lees,et al.  Decision-tree and rule-induction approach to integration of remotely sensed and GIS data in mapping vegetation in disturbed or hilly environments , 1991 .

[24]  Samy Bengio,et al.  Local Machine Learning Models for Spatial Data Analysis , 2000 .

[25]  Brian G. Lees,et al.  Neural network applications in the geosciences: An introduction , 1996 .

[26]  P. Gould.  Is Statistix Inferens the Geographical Name for A Wild Goose , 1970 .

[27]  Shawn W. Laffan,et al.  Using process models to improve spatial analysis , 2002, Int. J. Geogr. Inf. Sci..

[28]  J. Freidman,et al.  Multivariate adaptive regression splines , 1991 .

[29]  S. Laffan,et al.  Inferring the Spatial Distribution of Regolith Properties Using Surface Measurable Features , 2001 .

[30]  Ian T. Foster,et al.  The anatomy of the grid: enabling scalable virtual organizations , 2001, Proceedings First IEEE/ACM International Symposium on Cluster Computing and the Grid.

[31]  Gary A. Peterson,et al.  Soil Attribute Prediction Using Terrain Analysis , 1993 .

[32]  Shawn W. Laffan,et al.  Predicting regolith properties using environmental correlation: a comparison of spatially global and spatially local approaches , 2004 .

[33]  B. Lees,et al.  Marine transgression and dune initiation on western Cape York, northern Australia , 1993 .

[34]  A. Lehmann,et al.  Predicting species spatial distributions using presence-only data: a case study of native New Zealand ferns , 2002 .

[35]  T. G. Freeman,et al.  Calculating catchment area with divergent flow based on a regular grid , 1991 .

[36]  Michael Griebel,et al.  Classification with sparse grids using simplicial basis functions , 2002, Intell. Data Anal..

[37]  Robert A. Schowengerdt,et al.  A review and analysis of backpropagation neural networks for classification of remotely-sensed multi-spectral imagery , 1995 .