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2.5. Biplots: Plotting Observations and Variables Together

The biplot, introduced by Gabriel (1971) and discussed extensively in Gower and Hand (1996), is a graphical representation of a data matrix by means of two sets of markers representing its rows and columns respectively. These graphs describe relationships between the observations, by helping to form groups and clusters, as well as between the variables.

Suppose we have a set of n observations on p variables. A biplot describes the relationships among the p variables and the n observations. It is based on the fact (commonly referred to as a QR decomposition) that any n by p matrix Y of rank r can be expressed as

Y = GH′, (2,1)

where G and H respectively are n by r and p by r matrices ...

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