Biplot

A biplot simultaneously plots information on the observations and the variables in a multidimensional dataset.

A biplot can optimally represent any two of the following characteristics:
  • distances between observations
  • relationships between variables
  • inner products between observations and variables
There are 3 types of biplot based on which of these characteristics they represent:
Type Characteristics
PCA Distances between the observations and also the inner products between observations and variables.
Covariance / Correlation Relationships between the variables and the inner products between observations and variables.
Joint Distances between observations and also the relationship between variables.

A 2-dimensional biplot represents the information contained in two of the principal components. It is an approximation of the original multidimensional space.

Classic biplot

The classical biplot (Gabriel 1971) plots points representing the observations and vectors representing the variables.

PCA biplot

A more recent innovation, the PCA biplot (Gower & Hand 1996), represents the variables with calibrated axes and observations as points allowing you to project the observations onto the axes to make an approximation of the original values of the variables.