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