PCA review

• computes covariance matrix in reduced dimensions
• compute principal components from eigenvalues
• Choose dimensionality \(r\) relevant to \(\alpha\)
• \(\Sigma = U \Delta U^T = \sum^d_{i=1}\lambda_i u_i u_i^T\)
• \(\Sigma\) is just a combination of these rank one matricies

SVD

• \(\Sigma = V \Delta V^T \)
• \(X = U \Delta V^T\)