Support Vector Machines for Classification and Mapping of Reservoir Data
Support vector machines (SVM) is a new machine learning approach based on statistical learning theory (Vapnik-Chervonenkis theory). VC theory has a solid mathematical background for dependencies estimation and predictive learning from finite data sets. SVM is based on the structural risk minimisation principle, aiming to minimise both the empirical risk and the complexity of the model, thereby providing high generalisation abilities. SVM provides non-linear classification and regression by mapping the input space into a higher-dimensional feature space using kernel functions, where the optimal solutions are constructed. This paper presents a review on the use of SVM for the analysis and modelling of spatially distributed information. The methodology developed here combines the power of SVM with well known geostatistical approaches such as exploratory data analysis and exploratory variography. A case study (classification and regression) based on reservoir data with 294 vertically averaged porosity values and 2D seismic velocity and amplitude is presented. Such results are also compared with geostatistical models.
KeywordsSupport Vector Machine Support Vector Regression Ordinary Kriging Radial Basis Function Neural Network General Regression Neural Network
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- Burgess, C. A Tutorial on Support Vector Machines for Pattern Recognition. Data mining and knowledge discovery, 1998.Google Scholar
- Deutsch, C.V., and Journel, A.G. GSLIB. Geostatistical Software Library and User’s Guide. Oxford University Press, New York, 1997.Google Scholar
- Gilardi, N., Kanevski, M., Mayoraz, E. and Maignan, M. Spatial Data Classification with Support Vector Machines. Geostat 2000 Congress. South Africa, April 2000.Google Scholar
- Haykin, S. Neural Networks. A Comprehensive Foundation. Second Edition. Macmillan College Publishing Company. N.Y., 1999.Google Scholar
- Kanevski, M. Spatial Predictions of Soil Contamination Using General Regression Neural Networks. Int. J. on Systems Research and Information Systems, 8(4), 241–256, 1999.Google Scholar
- Kanevski, M. and Canu, S. Spatial Data Mapping with Support Vector Regression. IDIAP Reasearch Report, RR-00–09, 2000.Google Scholar
- Kanevski, M, Demyanov, V., Chernov, S., Savelieva, E., Serov, A., Timonin, V. and Maignan, M. Geostat Office for Environmental and Pollution Spatial Data Analysis. Mathematische Geologie, N3, April, 73–83, 1999.Google Scholar
- Kanevski, M., Pozdnukhov, A., Canu, S. and Maignan, M. Advanced Spatial Data Analysis and Modelling with Support Vector Machines. IDIAP Research Report, RR-00–31, 2000a.Google Scholar
- Kanevski, M., Wong, P.M. and Canu, C. Spatial Data Mapping with Support Vector Regression and Geostatistics. Intl. Conf. on Neural Information Processing, Taejon, November, 1307–1311, 2000b.Google Scholar
- Mayoraz, E. and Alpaydin, E. Support Vector Machine for Multiclass Classification, IDIAP-RR 98–06, 1998.Google Scholar
- Weston, J. and Watkins, C. Multi-class Support Vector Machines. Technical Report CSD-TR-98–04, 9 pp., 1998.Google Scholar
- Vapnik, V. Statistical Learning Theory. John Wiley & Sons, 1998.Google Scholar
- Wong, P.M. and Shibli, S.A.R. Combining Multiple Seismic Attributes with Linguistic Reservoir Qualities for Scenario-based Reservoir Modelling. SPE Asia Pacific Oil and Gas Conference and Exhibition, Brisbane, October, 2000.Google Scholar
- WWW.kernel-machines.org, 2001.