Information Technology Reference
In-Depth Information
2.11 Summary
In this chapter we have concentrated on assymmetric biplots as defined in Chapter 1. As
with an ordinary scatterplot, we have seen that such a biplot consists of
•
a set of points representing samples;
•
labelled axes representing variables.
We have also studied how to calibrate the axes for prediction or interpolation. Our
illustrations have used linear axes, but we have already discussed the possibility of using
irregular calibrations, nonlinear axes and convex regions for categorical variables. We
have pointed out the advantages of being able to shift axes and to rotate plots as an aid
to making more readable biplots. The possibilities for scaling axes have been addressed.
The size of a data set is a potential challenge to the usefulness of a biplot. We have
discussed some measures for handling data sets containing many data points as well as
data sets with many variables. Especially when there are a large number of points, there
is a need to simplify the display by using various strategies for representing density and
variability.
In this chapter, the focus has been on understanding the basics of biplot construction
by analogy with properties of ordinary scatterplots for approximating a
p
-variable data
matrix. We have also discussed in some detail R code for implementing all procedures.
This we did for two reasons: firstly, we believe that programming a procedure leads
to a better understanding of the procedure; and secondly, we would like to provide the
reader with the necessary computer software to produce all the biplot material discussed
in the topic. An important issue has been avoided thus far: how good is the overall
biplot approximation? How trustworthy are the biplot axes for predicting the values of
the variables they represent? How accurate are the positions occupied by the individual
samples in the biplot approximations? These and other topics have been deferred to
chapters dealing with the specific types of biplots. In the next chapter, we give the
algebraic and geometric basis of PCA biplots and discuss several interesting applications
of PCA biplots.
