Graphics Programs Reference
In-Depth Information
tween variables and replaces groups of correlated variables by new uncorre-
lated variables, the
principal components
(PC). The performance of the PCA
is better illustrated with help of a bivariate data set than a multivariate one.
Figure 9.1 shows a bivariate data set that exhibits strong linear correlation
between the two variables
x
and
y
in an orthogonal
xy
coordinate system.
The two variables have their univariate means and variances (Chapter 3).
The bivariate data set can be described by a bivariate sample mean and a co-
variance (Chapter 4). The
xy
coordinate system can be replaced by a new or-
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First variable x
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Fig. 9.1
Principal component analysis (PCA) illustrated on a bivariate scatter. The original
xy
coordinate system is replaced by a new orthogonal system, where the fi rst axis passes through
the long axis of the data scatter and the new origin is the bivariate mean. We can now reduce
dimensionality by dropping the second axis without losing much information.
