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Principal Components

​
random seed
212
graph
1
2
3
n
10
100
999
ρ
0.6
The construction of principal components is illustrated. This Demonstration considers the case for two variables
X
1
and
X
2
that are simulated as multivariate normal with zero means, unit variances, and theoretical correlation
ρ
. The sample size
n
can be 10, 100, or 999, and there are three graphs.
Graph 1: the data is plotted along with the Karhunen–Loeve directions
Graph 2: the data is shown projected on each of the two Karhunen–Loeve directions; note that there are
2n
data points
Graph 3: the principal components are plotted corresponding to each direction; visually, the principal components are the coordinates of the projected points in each of the directions
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