Skip to main content

Interesting Projections of Multidimensional Data by Means of Generalized Principal Component Analyses

  • Conference paper
Compstat

Summary

Principal Component Analysis can produce several interesting projections of a point cloud if suitable inner products are chosen for measuring the distances between the units. We discuss two examples of such choices. The first one allows us to display outliers, while the second is expected to display clusters. Doing so we introduce a robust estimate of a covariance matrix and we investigate some of its properties.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Dempster, A.P. (1969): Continuous multivariate analysis. Addison-Wesley.

    Google Scholar 

  2. Friedman, J.H. and Tukey, J.W. (1974) A projection pursuit algorithm for exploratory data analysis. IEEE Trans. Comp., C. 23, 9,881–890.

    Article  Google Scholar 

  3. Gnanadesikan, R. and Kettenring, J.R. (1972) Robust estimates, residuals and outlier detection with multiresponse data. Biometrics,28,81–124.

    Article  Google Scholar 

  4. Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J. and Stahel, W.A. (1986) Robust Statistics; the Approach based on Influence Functions. Wiley, New York.

    Google Scholar 

  5. Huber, P.J. (1981) Robust Statistics. Wiley, New York.

    Book  Google Scholar 

  6. Huber, P.J. (1985): Projection Pursuit. Ann. Statist., 13, 435–525.

    Article  Google Scholar 

  7. Jones, M. C. and Sibson, R. (1987) What is Projection Pursuit? J.R. Stat. Soc., A, 150 1, 1–36.

    Article  Google Scholar 

  8. Marazzi, A. (1985): Robust affine invariant covariances in ROBETH. ROBETH-85, Doc. N°6. Lausanne, Institut universitaire de medecine sociale et preventive.

    Google Scholar 

  9. Seber, G.A.F. (1984): Multivariate observations. Wiley, New York.

    Book  Google Scholar 

  10. Yenyukov, I.S. (1988) Projection Pursuit. Heidelberg. Detecting structures by means of Compstat88, 47–58. Physica-Verlag, Heidelberg

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Physica-Verlag Heidelberg

About this paper

Cite this paper

Caussinus, H., Ruiz, A. (1990). Interesting Projections of Multidimensional Data by Means of Generalized Principal Component Analyses. In: Momirović, K., Mildner, V. (eds) Compstat. Physica-Verlag HD. https://doi.org/10.1007/978-3-642-50096-1_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-50096-1_19

  • Publisher Name: Physica-Verlag HD

  • Print ISBN: 978-3-7908-0475-1

  • Online ISBN: 978-3-642-50096-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics