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Seems like a trivial question but one for which I can't seem to find an answer.

Are PLS-DA (partial least squares discriminant analysis) and PLS-LDA (partial least squares followed by linear discriminant analysis) the same?

If not, how does PLS-DA differ from standard PLSR (partial least squares regression)? As far as I understand it PLS-DA is just substituting the classes/factors for numbers.

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No, they are not the same.

In PLS-DA, the Y matrix consists of categorical variables of 0 and 1 where each column represents a class. To illusturate, let's assume you have 6 samples where each 2 samples belongs to a group your Y matrix would look something like this:

G1 G2 G3
-- -- --
1  0  0
1  0  0
0  1  0
0  1  0
0  0  1
0  0  1

The results obtained from PLS-DA is in the same form of the Y matrix regardless of the number of latent variables used.

In PLS-LDA, however, the scores of X(with desired number of latent variables) obtained from PLS is used for LDA. It is very similar to PCA-LDA where PCA is used as a dimension reduction prior to LDA while same logic is exploited with PLS scores in PLS-LDA.

  • Reference: Chemometrics for Pattern Recognition, Richard G. Brereton
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