I know that there are topics about this question but in my view, the answers are not clear enough. I don't understand the main difference between Linear Discriminant Analysis (LDA) and Gaussian Mixture Models (GMM).
Both have the same purpose : determine the posteriori $P(G=j|X=x)$, and maximize it for a certain $j$ in order to attribute class $j$ to $x$. I have the feeling that in GMM the way we estimate our parameters (EM algorithm) is the difference. Or, I don't know maybe the difference is that in LDA we want to draw an hyperplane in order to classify after any data ?
Because we agree that basically, LDA data correspond to a gaussian mixture model. It's just the way parameters are estimated that differs no?
Well as you can see, I'm a bit confused. I hope someone could explain me.