Perhaps i am wrong but i feel that there is two meaning behind linear discriminant analysis. In French we have two methods called:
- Analyse discriminante linéaire (https://fr.wikipedia.org/wiki/Analyse_discriminante_lin%C3%A9aire) wich lays on a gaussian joint distribution assumption
- Analyse factorielle discriminante (http://cedric.cnam.fr/vertigo/Cours/RCP216/coursReductionVolume.html#analyse-factorielle-discriminante): wich lays on geometric assumption trying to both maximize the interclass variance and to minimize the intraclass variance. This approach conduct to maximize the rayleigh quotient.
Is there only one terminologie in English for theses two approach ? If yes what is the reason, how theses two methods are correlated (the second one seems more generic and seems a good way to reduce dimension before running a classification method such an svm)?
Edit: I think (from Wikipedia) that the generative method is called LDA and the geometric one is called Fisher discriminant analysis.