Is that correct that LDA/FDA can only generate 2 outputs as a dimensional reduction method?
Suppose I have 100 features, I want to reduce to 5 features. Is LDA/FDA not usable?
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Also, note that you need labels to perform LDA, which is not always available (or relevant). That's why PCA is usually preferred because it's class-agnostic.
The number of output dimensions in LDA is linked to the number of degrees of freedom in the dataset, which is linked to the number of classes $c$: eigenvalues above $c$ will be zero and bear no information (same as with PCA and explained variance).