Information Technology Reference
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. P
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Figure 5.21 Circular prediction of the point P for the example data set: a circle with
diameter the dotted line extending from O to P is drawn and the intersection of each
of the biplot axes with the circle gives the predictions for point P. Note the differ-
ence in the positions of the rectangle indicating the Y -prediction of point P for (a)
circular prediction and (b) normal prediction (Figure 5.15). Since the X -axis is almost
linear the rectangles indicating the circular and normal X -predictions of P are nearly
identical.
With the standard assumption that our data matrix X for PCA is centred, x = 0 , it follows
that B = XX . This is of the same form as B = YY , showing that the representation
in Euclidean space is already obtained from the matrix X and no embedding needs
to be applied. Alternatively, the embedding step can be viewed as a linear identity
transformation. Once the Euclidean representation X (or Y ) is obtained, the principal
axes are computed for optimal representation in r dimensions (see Section 5.6.1).
5.6 Constructing nonlinear biplots
Our main function for constructing nonlinear biplots is the function Nonlinbipl .Inthis
section we provide details of its usage and capabilities. Nonlinbipl has many features
in common with those of PCAbipl and CVAbipl as discussed in Chapters 3 and 4. Thus,
in this section we concentrate on what is specific to Nonlinbipl .
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