Fast algorithms for automatic mapping with space-limited covariance functions


In this paper we discuss a fast Bayesian extension to kriging algorithms which has been used successfully for fast, automatic mapping in emergency conditions in the Spatial Interpolation Comparison 2004 (SIC2004) exercise. The application of kriging to automatic mapping raises several issues such as robustness, scalability, speed and parameter estimation. Various ad-hoc solutions have been proposed and used extensively but they lack a sound theoretical basis. In this paper we show how observations can be projected onto a representative subset of the data, without losing significant information. This allows the complexity of the algorithm to grow as O(n m 2), where n is the total number of observations and m is the size of the subset of the observations retained for prediction. The main contribution of this paper is to further extend this projective method through the application of space-limited covariance functions, which can be used as an alternative to the commonly used covariance models. In many real world applications the correlation between observations essentially vanishes beyond a certain separation distance. Thus it makes sense to use a covariance model that encompasses this belief since this leads to sparse covariance matrices for which optimised sparse matrix techniques can be used. In the presence of extreme values we show that space-limited covariance functions offer an additional benefit, they maintain the smoothness locally but at the same time lead to a more robust, and compact, global model. We show the performance of this technique coupled with the sparse extension to the kriging algorithm on synthetic data and outline a number of computational benefits such an approach brings. To test the relevance to automatic mapping we apply the method to the data used in a recent comparison of interpolation techniques (SIC2004) to map the levels of background ambient gamma radiation. © Springer-Verlag 2007.

Publication DOI:
Divisions: ?? 50811700Jl ??
College of Engineering & Physical Sciences > Systems analytics research institute (SARI)
Additional Information: The original publication is available at
Uncontrolled Keywords: fast Bayesian extension,kriging algorithms,automatic mapping,emergency conditions,Spatial Interpolation Comparison 2004,space–limited covariance functions,covariance models,interpolation techniques,background ambient gamma radiation,Environmental Engineering,Environmental Chemistry,Water Science and Technology,Statistics and Probability,Civil and Structural Engineering
Publication ISSN: 1436-3259
Last Modified: 26 Mar 2024 08:08
Date Deposited: 23 Nov 2010 15:18
Full Text Link: http://www.spri ... 4t1x6561j28l16/
Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
PURE Output Type: Article
Published Date: 2008-08
Published Online Date: 2007-07-13
Authors: Ingram, Benjamin R.
Cornford, Dan (ORCID Profile 0000-0001-8787-6758)
Evans, David J.


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