4. Canonical Variate Analysis Biplots

  1. John Gower1,
  2. Sugnet Lubbe2 and
  3. Niël le Roux3

Published Online: 3 NOV 2010

DOI: 10.1002/9780470973196.ch4

Understanding Biplots

Understanding Biplots

How to Cite

Gower, J., Lubbe, S. and Roux, N. l. (2011) Canonical Variate Analysis Biplots, in Understanding Biplots, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470973196.ch4

Author Information

  1. 1

    The Open University, UK

  2. 2

    University of Cape Town, South Africa

  3. 3

    University of Stellenbosch, South Africa

Publication History

  1. Published Online: 3 NOV 2010
  2. Published Print: 7 JAN 2011

ISBN Information

Print ISBN: 9780470012550

Online ISBN: 9780470973196

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Keywords:

  • canonical variate analysis (CVA) biplots;
  • Mahalanobis distances

Summary

The main tool of canonical variate analysis (CVA) is to transform the observed variables into what are termed canonical variables that have the property that the squared distances between the means of the groups are given by Mahalanobis distance. Mahalanobis distance is monotonically related to the probability of misclassification when assigning a sample to one of two groups each with a multinormal distribution with the same covariance matrix but with different means. The main function for constructing CVA biplots is the function CVAbipl. CVA is one of the most useful multivariate methods; its independence from the effects of measurement scales is a major advantage. The basic methodology has been known in applied mathematics and in statistics for many decades. This chapter discusses three ways of centring the points representing the canonical means.

Controlled Vocabulary Terms

multiple discriminant analysis