Principal component analysis

Questions/things to explain

• Analogously to the covariance matrix one can define a correlation matrix. What happens if you run SVD on the correlation matrix?
• multiple ways to look at PCA:
  • SVD on the covariance matrix (this is probably the same as one of the other interpretations)
  • maximum variance (see Bishop)
  • minimum-error (see Bishop)
  • the best linear compression-recovery of data to a lower dimension (see Shalev-Shwartz and Ben-David). Is this the same as minimum-error interpretation?