Principal component analysis: Difference between revisions
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* multiple ways to look at PCA: | * multiple ways to look at PCA: | ||
** SVD on the covariance matrix (this is probably the same as one of the other interpretations) | ** SVD on the covariance matrix (this is probably the same as one of the other interpretations) | ||
** maximum variance (see Bishop) | ** maximum variance (see Bishop). This one uses the Lagrange multiplier and [[derivative of a quadratic form]]. | ||
** minimum-error (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? | ** 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? | ||
Revision as of 03:38, 14 July 2018
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). This one uses the Lagrange multiplier and derivative of a quadratic form.
- 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?