Advertisement

Mathematical Geosciences

, Volume 42, Issue 4, pp 433–446 | Cite as

Applicability of Statistical Learning Algorithms for Spatial Variability of Rock Depth

  • Pijush Samui
  • T. G. Sitharam
Case Study

Abstract

Two algorithms are outlined, each of which has interesting features for modeling of spatial variability of rock depth. In this paper, reduced level of rock at Bangalore, India, is arrived from the 652 boreholes data in the area covering 220 sq⋅km. Support vector machine (SVM) and relevance vector machine (RVM) have been utilized to predict the reduced level of rock in the subsurface of Bangalore and to study the spatial variability of the rock depth. The support vector machine (SVM) that is firmly based on the theory of statistical learning theory uses regression technique by introducing ε-insensitive loss function has been adopted. RVM is a probabilistic model similar to the widespread SVM, but where the training takes place in a Bayesian framework. Prediction results show the ability of learning machine to build accurate models for spatial variability of rock depth with strong predictive capabilities. The paper also highlights the capability of RVM over the SVM model.

Keywords

Support vector machine Relevance vector machine Rock depth Spatial variability 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Berger JO (1985) Statistical decision theory and Bayesian analysis. Springer, New York Google Scholar
  2. Boser BE, Guyon IM, Vapnik VN (1992) A training algorithm for optimal margin classifiers. In: Haussler D (ed) 5th annual ACM workshop on COLT. ACM Press, Pittsburgh, pp 144–152 Google Scholar
  3. Cristianini N, Shawe-Taylor J (2000) An introduction to support vector machine. Cambridge University Press, Cambridge. www.support-vector.net Google Scholar
  4. Kanevski, Maignan (2004) Analysis and modelling of spatial environmental data. PPUR Google Scholar
  5. Kanevski M (ed) (2008) Advanced mapping of environmental data. Geostatistics, machine learning and Bayesian maximum entropy. iSTE and Wiley, New York Google Scholar
  6. Li Y, Campbell C, Tipping M (2002) Bayesian automatic relevance determination algorithms for classifying gene expression data. Bioinformatics 18(10):1332–1339 CrossRefGoogle Scholar
  7. MacKay DJ (1992) Bayesian methods for adaptive models. PhD thesis, Dep of Comput and Neural Syst. Calif Inst of Technol, Pasadena, CA Google Scholar
  8. MathWork, Inc. (1999) Matlab user’s manual, Version 5.3. Natick, The MathWorks, Inc Google Scholar
  9. Mukherjee S, Osuna E, Girosi F (1997) Nonlinear prediction of chaotic time series using support vector machine. In: Proc IEEE workshop on neural networks for signal processing, vol 7. Institute of Electrical and Electronics Engineers, New York, pp 511–519 Google Scholar
  10. Muller KR, Smola A, Ratsch G, Scholkopf B, Kohlmorgen J, Vapnik V (1997) Predicting time series with support vector machines. In: Proc int conf on artificial neural networks. Springer, Berlin, p 999 Google Scholar
  11. Radhakrishna BP, Vaidyanadhan R (1997) Geology of Karnataka. Geological Society of India, Bangalore Google Scholar
  12. Scholkopf B (1997) Support vector learning. R. Oldenbourg, Munich Google Scholar
  13. Sincero AP (2003) Predicting mixing power using artificial neural network. EWRI world water and environmental Google Scholar
  14. Tipping M (2000) The relevance vector machine. Adv Neural Inf Process Syst 12:652–658 Google Scholar
  15. Tipping ME (2001) Sparse Bayesian learning and the relevance vector machine. J Mach Learn 1:211–244 CrossRefGoogle Scholar
  16. Vapnik V (1995) The nature of statistical learning theory. Springer, New York Google Scholar
  17. Vapnik V (1998) The nature of statistical learning theory. Wiley, New York Google Scholar
  18. Vapnik V, Golowich S, Smola A (1997) Support method for function approximation regression estimation and signal processing. In: Mozer M, Petsch T (eds) Advance in neural information processing system, vol 9. MIT Press, Cambridge Google Scholar
  19. Wahba G (1985) A comparison of GCV and GML for choosing the smoothing parameter in the generalized spline-smoothing problem. Ann Stat 4:1378–1402 CrossRefGoogle Scholar

Copyright information

© International Association for Mathematical Geosciences 2010

Authors and Affiliations

  1. 1.Center for Disaster Mitigation and ManagementVITVelloreIndia
  2. 2.Department of Civil EngineeringIndian Institute of ScienceBangaloreIndia

Personalised recommendations