Principal Component Analysis (PCA)

To summarize:
• The eigenvectors v 1 , v 2 , …, v n of the covariance matrix have
corresponding eigenvalues λ 1 ≥ λ 2 ≥ … ≥ λ n . They can be found
with standard algorithms.
• λ 1 is the variance of the projection in the v 1 direction, λ 2 is
the variance of the projection in the v 2 direction, and so on.
• The largest eigenvalue λ 1 corresponds to the principal
component with the greatest variance, the next largest
eigenvalue corresponds to the principal component with the
next greatest variance, etc.
• So, which eigenvector (green or red) corresponds to the
smaller eigenvalue in this example?
Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch 10