Creating a quality map of a slate deposit using support vector machines

In this work, we create a quality map of a slate deposit, using the results of an investigation based on surface geology and continuous core borehole sampling. Once the quality of the slate and the location of the sampling points have been defined, different kinds of support vector machines (SVMs)-SVM classification (multiclass one-against-all), ordinal SVM and SVM regression-are used to draw up the quality map. The results are also compared with those for kriging. The results obtained demonstrate that SVM regression and ordinal SVM are perfectly comparable to kriging and possess some additional advantages, namely, their interpretability and control of outliers in terms of the support vectors. Likewise, the benefits of using the covariogram as the kernel of the SVM are evaluated, with a view to incorporating the problem association structure in the feature space geometry. In our problem, this strategy not only improved our results but also implied substantial computational savings.

[1]  Noel A Cressie,et al.  Statistics for Spatial Data. , 1992 .

[2]  Alexander J. Smola,et al.  Support Vector Regression Machines , 1996, NIPS.

[3]  V. Vapnik Estimation of Dependences Based on Empirical Data , 2006 .

[4]  Nello Cristianini,et al.  An introduction to Support Vector Machines , 2000 .

[5]  Stéphane Canu,et al.  Environmental data mining and modeling based on machine learning algorithms and geostatistics , 2004, Environ. Model. Softw..

[6]  Bernhard Schölkopf,et al.  Learning with kernels , 2001 .

[7]  J. Taboada,et al.  Mineralogía y microestructura de la pizarra de techar: comportamiento termoóptico y fisibilidad , 1998 .

[8]  Nello Cristianini,et al.  An Introduction to Support Vector Machines and Other Kernel-based Learning Methods , 2000 .

[9]  Timothy C. Coburn,et al.  Geostatistics for Natural Resources Evaluation , 2000, Technometrics.

[10]  Mike Rees,et al.  5. Statistics for Spatial Data , 1993 .

[11]  Javier García-Guinea,et al.  SPANISH ROOFING SLATE DEPOSITS , 1997 .

[12]  Vladimir Vapnik,et al.  Statistical learning theory , 1998 .

[13]  W. González-Manteiga,et al.  Support vector machines and gradient boosting for graphical estimation of a slate deposit , 2004 .

[14]  Ángeles Saavedra,et al.  Quality index for ornamental slate deposits , 1998 .

[15]  Alexander J. Smola,et al.  Hyperkernels , 2002, NIPS.

[16]  Corinna Cortes,et al.  Support-Vector Networks , 1995, Machine Learning.

[17]  Ángeles Saavedra,et al.  Evaluation of a slate extraction bank , 2001 .

[18]  W. González-Manteiga,et al.  Comparison of Kriging and Neural Networks With Application to the Exploitation of a Slate Mine , 2004 .

[19]  Javier Taboada,et al.  Application of geostatistical techniques to exploitation planning in slate quarries , 1997 .

[20]  Bernhard E. Boser,et al.  A training algorithm for optimal margin classifiers , 1992, COLT '92.

[21]  Nello Cristianini,et al.  Learning the Kernel Matrix with Semidefinite Programming , 2002, J. Mach. Learn. Res..

[22]  Vladimir N. Vapnik,et al.  The Nature of Statistical Learning Theory , 2000, Statistics for Engineering and Information Science.

[23]  J. Taboada Castro,et al.  Optimizing of stripping in a slate bank , 1994 .

[24]  Yi Lin,et al.  Support Vector Machines and the Bayes Rule in Classification , 2002, Data Mining and Knowledge Discovery.

[25]  Ralf Herbrich,et al.  Large margin rank boundaries for ordinal regression , 2000 .