Support vector machines and gradient boosting for graphical estimation of a slate deposit
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Critical for an efficient and effective exploitation of a slate mine is to obtain information on its technical quality, in other words, on the exploitability potential of the deposit. We applied support vector machines (SVM) and LS-Boosting to the assessment of the technical quality of a new unexploited area of a mine, and compared the results to those obtained for kriging and neural networks. Firstly we analyzed the relationship between kriging and semi-parametric SVM in a regularization framework and explored the different alternatives for training these networks. Subsequently, in an attempt to combine both radial and projection structures, we formulated a boosting technique for radial basis function (RBF) networks defined over projections in the input space (RBFPP). The application of these techniques to our test drilling data demonstrated a similar level of performance for all the estimators examined, with the main difference occurring in the shape of the respective deposit reconstructions. Therefore, in choosing between the different techniques, an essential aspect will be their ability to reproduce the morphological characteristics of the true process. In this paper we also evaluate the benefits of using the estimated covariogram as the kernel of the SVMs and compare the sparsity of the different solutions. The results obtained show that the selection of a standard kernel that ignores the variability structure of the problem produces poorer results than when the estimated covariogram is used as the kernel.
KeywordsBoosting Kernels Slate Spatial statistics SVM
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The research of J. Taboada was supported by the European Union, FEDER program, Project 1FD97-0091. The research of W. González-Manteiga was supported by Ministerio de Ciencia y Tecnología of the Spanish Government, Project BFM2002-03213. The authors wish to thank the associate editor and an anonymous referee for stimulating comments.