difference between CCA (canonical correlation analysis) and partial least squares(PLS)

difference between CCA (canonical correlation analysis) and partial least squares(partial least squares)

Hi As there are two comprehensive comparison between CCA and PLS:

1 Eigenproblems in Pattern Recognition, by Tijl De Bie et.al.

2 A unifiedl appraoch to PCA, PLS, MLR and CCA by Borga(he also has a previous version called CCA tutorial, which is less comprehensive, yet still very good)

So the major difference is that CCA is maximizing the correlation (to be precise, Pearson correlation), wherein PLS maximizes covariance. Looks like CCA is just like normalized version of PLS considering the relation between correlation and covariance. Is there any other "big" difference? Like application scenarios, etc? Thanks!

asked Feb 15 '14 at 12:40

BO LIU
21●6●6●8

edited Feb 15 '14 at 12:42

2 Answers:

oldest newest most voted

There are several important differences:

Unlike CCA, PLS does not directly optimize a particular criterion; however, it tends to converge to solutions very close to Inter Batteries Analysis, i.e., something between CCA and PCR (Principal Component Regression),
PLS is an iterative method,
PLS can handle missing values,
In CCA the number of components is limited to the min of the number of explanatory and response variables.

Due to the last difference, PLS is useful in applications where the number of explanatory variables (p) is much greater than the number of response variables (q). In such cases CCA can only produce min(p, q) (more precisely min(rank(X), rank(Y)) components, while PLS is not limited to the rank of the explanatory (X) and response (Y) matrices.

answered Feb 15 '14 at 16:43

Martin SAVESKI
156●3●4

0	thanks for your expert answer! answered Sep 29 '14 at 22:54 BO LIU 21●6●6●8

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Tags:

dimensionality-reduction ×31
least-squares ×6
distance-based-learning ×5
canonical-component-analysis ×2
partial ×2

Asked: Feb 15 '14 at 12:40

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Last updated: Sep 29 '14 at 22:54

difference between CCA (canonical correlation analysis) and partial least squares(PLS)

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