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I'm trying to understand what LDA exactly does when used as a classifier. I've understood how the dimensionality reduction works and I've understood that the classification task is carried out with the application of Bayes' theorem, but I still can't figure out if LDA executes both operations when used as a classification algorithm.

Is it correct to say that LDA, as a classifier, executes by itself dimensionality reduction and then applies Bayes' theorem for classification?

If that makes any difference, I've used LDA in Python from the sklearn library.

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