Principal Component Analysis (PCA)

• Let x 1 , x 2 , …, x p be the p sample images (n-dimensional).
• Find the mean image, m, and subtract it from each
image: z i = x i – m
• Let A be the matrix whose columns are the
mean-subtracted sample images.
⎡ ↑ ↑ ↑ ⎤
⎢
⎥
A = ⎢z1
z 2 L z p ⎥ n ×
⎢
⎥
⎣ ↓ ↓ ↓ ⎦
• Estimate the covariance matrix:
Σ
=
1
Cov( A)
= A A
p −1
What are the dimensions of Σ ?
matrix
Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch 22
T
p