1. Introduction

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

Published Online: 3 NOV 2010

DOI: 10.1002/9780470973196.ch1

Understanding Biplots

Understanding Biplots

How to Cite

Gower, J., Lubbe, S. and Roux, N. l. (2011) Introduction, in Understanding Biplots, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470973196.ch1

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



  • asymmetric biplot;
  • biplot;
  • canonical variate analysis (CVA);
  • multidimensional scaling (MDS);
  • multiple correspondence analysis (MCA);
  • principal components analysis (PCA);
  • samples;
  • symmetric biplot;
  • variables


This introductory chapter presents an overview of how the other chapters of the book are organised. It discusses about biplots that can be classified into asymmetric (biplots giving information on sample units and variables of a data matrix) and symmetric (biplots giving information on rows and columns of a two-way table). In symmetric biplots, rows and columns may be interchanged without loss of information, while in asymmetric biplots variables and sample units are different kinds of object that may not be interchanged. Distances between samples, relationships between variables and inner products between samples and variables are represented in the asymmetric biplot. Matrices are used extensively to enable the mathematically inclined reader to understand the algebra behind the different biplots. The chapter presents some notations used in biplots such as correspondence analysis (CA), multiple correspondence analysis (MCA), canonical variate analysis (CVA), multidimensional scaling (MDS) and principal component analysis (PCA).

Controlled Vocabulary Terms

biplot; multidimensional scaling; multiple correspondence analysis; multiple discriminant analysis; principal components analysis; quantitative variables