It seems that LDA's components are bounded by the number of classes ([1], [2]).
Is it the same for Canonical Correlation Analysis (CCA) or can I use more components than classes?
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No you can't extract more discriminants than number if classes minus 1. LDA indeed can be seen a special case of CCA. There is a number threads here about it. – ttnphns Apr 22 '21 at 17:50