Skip to main content

Advertisement

Log in

Applicability of Statistical Learning Algorithms for Spatial Variability of Rock Depth

  • Case Study
  • Published:
Mathematical Geosciences Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Berger JO (1985) Statistical decision theory and Bayesian analysis. Springer, New York

    Google Scholar 

  • 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 

  • Cristianini N, Shawe-Taylor J (2000) An introduction to support vector machine. Cambridge University Press, Cambridge. www.support-vector.net

    Google Scholar 

  • Kanevski, Maignan (2004) Analysis and modelling of spatial environmental data. PPUR

  • Kanevski M (ed) (2008) Advanced mapping of environmental data. Geostatistics, machine learning and Bayesian maximum entropy. iSTE and Wiley, New York

    Google Scholar 

  • Li Y, Campbell C, Tipping M (2002) Bayesian automatic relevance determination algorithms for classifying gene expression data. Bioinformatics 18(10):1332–1339

    Article  Google Scholar 

  • MacKay DJ (1992) Bayesian methods for adaptive models. PhD thesis, Dep of Comput and Neural Syst. Calif Inst of Technol, Pasadena, CA

  • MathWork, Inc. (1999) Matlab user’s manual, Version 5.3. Natick, The MathWorks, Inc

    Google Scholar 

  • 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 

  • 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 

  • Radhakrishna BP, Vaidyanadhan R (1997) Geology of Karnataka. Geological Society of India, Bangalore

    Google Scholar 

  • Scholkopf B (1997) Support vector learning. R. Oldenbourg, Munich

  • Sincero AP (2003) Predicting mixing power using artificial neural network. EWRI world water and environmental

  • Tipping M (2000) The relevance vector machine. Adv Neural Inf Process Syst 12:652–658

    Google Scholar 

  • Tipping ME (2001) Sparse Bayesian learning and the relevance vector machine. J Mach Learn 1:211–244

    Article  Google Scholar 

  • Vapnik V (1995) The nature of statistical learning theory. Springer, New York

    Google Scholar 

  • Vapnik V (1998) The nature of statistical learning theory. Wiley, New York

    Google Scholar 

  • 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 

  • 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

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Pijush Samui.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Samui, P., Sitharam, T.G. Applicability of Statistical Learning Algorithms for Spatial Variability of Rock Depth. Math Geosci 42, 433–446 (2010). https://doi.org/10.1007/s11004-010-9268-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11004-010-9268-7

Keywords

Navigation