Principal component analysis biplots - Understanding Biplots - page 144

Ta b l e 3 . 2 7 Predictions for samples s416 and s56 .

Var s416 s56

X1 33 . 23 31 . 53

X2 6469 . 34 7735 . 64

X3 438 . 91 277 . 49

X4 − 5 . 36 − 5 . 33

X5 15 . 41 11 . 45

X6 − 13 . 40 − 10 . 30

X7 10494 . 21 16423 . 32

X8 0 . 98 1 . 18

The annotations in the biplot in the bottom panel of Figure 3.45 were added using
the function calls

> draw.arrow(length = 0.15, angle = 15) (twice)
> draw.text(string = "Sample #56", cex = 0.7)
> draw.text(string = "Sample #416", cex = 0.7)

and making the appropriate selections on the biplot.

3.9 Conclusion

In this chapter we have discussed PCA as a method for approximating a centred (and
scaled if needed) data matrix. This allowed us to find the scaffolding upon which to
construct a PCA biplot in one, two or three dimensions as an extension of an ordinary
scatterplot. Understanding the basics of a PCA biplot is essential for its interpretation.
However, understanding the basics and constructing the initial PCA biplot are but the
first steps in a biplot analysis of a data matrix. The final stage is not only a matter of
understanding but is also an art: fine-tuning and adding enhancements to come up with
a final biplot highlighting the secrets of a data matrix. Therefore, we urge the reader to
experiment with the various functions provided in UBbipl and use their creativity to
enable novel extensions.
Several of the examples encountered in Chapter 3 contain information regarding some
predefined grouping or class structure. Although this information can be included in a
PCA biplot by, for example, interpolating group means into the biplot, the procedure of
finding the scaffolding underpinning the PCA biplot does not utilize this information.
This deficiency is remedied in the next chapter.