# Principal Components

Principal Components

The construction of principal components is illustrated. This Demonstration considers the case for two variables and that are simulated as multivariate normal with zero means, unit variances, and theoretical correlation . The sample size can be 10, 100, or 999, and there are three graphs.

X

1

X

2

ρ

n

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 data points

2n

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