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Principal Component Analysis

  • Y. Z. Ma
Chapter

Abstract

Multivariate statistical methods beyond the correlation and covariance analysis include principal component analysis (PCA), factor analysis, discriminant analysis, classification, and various regression methods. Because of the increasing use of neural networks in the recent decades, some classical statistical methods are now less frequently used. However, PCA has been continuously used in both statistical data analysis and machine learning because of its versatility. At the same time, PCA has had several extensions, including nonlinear PCA, kernel PCA, and PCA for discrete data.

This chapter presents an overview of PCA and its applications to geosciences. The mathematical formulation of PCA is reduced to a minimum; instead, the presentation emphasizes the data analytics and innovative uses of PCA for geosciences. More applications of PCA are presented in Chap.  10.

References

  1. Abdi, H., & Williams, L. J. (2010). Principal component analysis (Statistics & data mining series) (Vol. 2, pp. 433–459). Wiley.Google Scholar
  2. Ferguson, J. (1994). Introduction to linear algebra in geology. London, UK: Chapman & Hall.Google Scholar
  3. Hindlet, F., Ma, Y. Z., & Hass, A. (1991). Statistical analysis on AVO data. In Proceeding of EAEG, C028:264-265, Florence, Italy.Google Scholar
  4. Jolliffe, I. T. (2002). Principal component analysis (2nd ed.). New York: Springer.zbMATHGoogle Scholar
  5. Ma, Y. Z. (2011). Lithofacies clustering using principal component analysis and neural network: applications to wireline logs. Mathematical Geosciences, 43(4), 401–419.CrossRefGoogle Scholar
  6. Ma, Y. Z., & Gomez, E. (2015). Uses and abuses in applying neural networks for predicting reservoir properties. Journal of Petroleum Science and Engineering, 133, 66–65.  https://doi.org/10.1016/j.petrol.2015.05.006.CrossRefGoogle Scholar
  7. Ma, Y. Z., & Zhang, Y. (2014). Resolution of happiness-income paradox. Social Indicators Research, 119(2), 705–721.  https://doi.org/10.1007/s11205-013-0502-9.CrossRefGoogle Scholar
  8. Ma Y. Z. et al. (2014, April). Identifying hydrocarbon zones in unconventional formations by discerning Simpson’s paradox. Paper SPE 169496 presented at the SPE Western and Rocky Regional Conference.Google Scholar
  9. Ma, Y. Z., Moore, W. R., Gomez, E., Luneau, B., Kaufman, P., Gurpinar, O., & Handwerger, D. (2015). Wireline log signatures of organic matters and lithofacies classifications for shale and tight carbonate reservoirs. In Y. Z. Ma & S. Holditch (Eds.), Handbook of unconventional resource (pp. 151–171). Waltham: Gulf Professional Publishing/Elsevier.Google Scholar
  10. Prensky, S. E. (1984). A Gamma-ray log anomaly associated with the Cretaceous-Tertiary boundary in the Northern Green River Basin, Wyoming. In B. E. Law (Ed.), Geological characteristics of low-permeability Upper Cretaceous and Lower Tertiary Rocks in the Pinedale Anticline Area, Sublette County, Wyoming, USGS Open-File 84-753, pp. 22–35. https://pubs.usgs.gov/of/1984/0753/report.pdf. Accessed 6 Aug 2017.
  11. Richman, M. (1986). Rotation of principal components. International Journal of Climatology, 6(3), 293–335.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Y. Z. Ma
    • 1
  1. 1.SchlumbergerDenverUSA

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