1. Techniques for studying correlation and covariance structure
Principle Components Analysis (PCA)
Factor Analysis

2. Principle Component Analysis

3. Let
Assume

4. Let
have a p-variate Normal distribution
with mean vector
Definition:
The linear combination
is called the first principle component if
is chosen to maximize
subject to

5. Consider maximizing
subject to
Using the Lagrange multiplier technique
Let

6. Now
and

7. Summary
is the first principle component if
is the eigenvector (length 1)of S associated with the largest eigenvalue l1 of S.