Principal component analysis: Difference between revisions
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* Analogously to the [[covariance matrix]] one can define a correlation matrix. What happens if you run SVD on the correlation matrix? | * 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: | * multiple ways to look at PCA: | ||
** SVD on the covariance matrix (this is probably the same as | ** SVD on the covariance matrix (this is probably the same as the maximum variance interpretation, or rather a sub-interpretation of that; if you view the covariance matrix as a transformation that takes white noise to your data set, then the principal components = axes of the ellipsoid = the views that maximize variance) | ||
** maximum variance (see Bishop). This one uses the Lagrange multiplier and [[derivative of a quadratic form]]. | ** 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 03:44, 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 the maximum variance interpretation, or rather a sub-interpretation of that; if you view the covariance matrix as a transformation that takes white noise to your data set, then the principal components = axes of the ellipsoid = the views that maximize variance)
- 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?