Are Fisher's linear discriminant and logistic regression related? I have some experience with both FLD and LR for classification. 
On most data sets, I get very similar results, which raises the question - are FLD and LR related in some why? 
An idea, for example, if I assume a normal distribution on the likelihood function instead a of a logistic function, does the maximization come down to the FLD criteria?
Please note that I'm asking about FLD and NOT LDA.
Also, I'm looking for a mathematical way to show that FLD and LR are equivalent under some constraints. I had some ideas but nothing worked out. I'm sure it holds some way.
 A: For many reasons, classification is not a good goal for most problems; prediction is.  Logistic regression (LR) is a more direct probability model to use for prediction, with fewer assumptions.  Linear discriminant analysis (LDA) assumes that X has a multivariate normal distribution given Y.  Using Bayes' rule to get Prob(Y|X) you get a logistic model.  So if assumptions of LDA hold, assumptions of LR automatically hold.  The reverse is not true, hence LR is more robust (e.g., X's can be dichotomous, far from normal).  It is interesting that logistic regression is, in a sense, more related to the normal distribution that is probit regression.
A: Just (maybe redundant) elaborate on Frank's answer. LDA is based on assumptions of multivariate normality and equality of covariance matrices of the 2 groups (in population); it is also  irritable to outliers and to unbalanced n's; the predictors should normally be interval scale. All that is not required by LR which is therefore more universally robust. Probability of classification is estimated in LDA indirectly by formulas such as Bayes' but directly in LR. Still, when all assumptions for LDA are nicely met LDA is somewhat superior to LR from a statistical perspective.
