If I understand correctly, a Linear Discriminant Analysis (LDA) assumes normal distributed data, independent features, and identical covariances for every class for the optimality criterion.
Since the mean and variance is estimated from the training data, isn't it already a violation?
I found a quotation in an article (Li, Tao, Shenghuo Zhu, and Mitsunori Ogihara. “Using Discriminant Analysis for Multi-Class Classification: An Experimental Investigation.” Knowledge and Information Systems 10, no. 4 (2006): 453–72. )
"linear discriminant analysis frequently achieves good performances in the tasks of face and object recognition, even though the assumptions of common covariance matrix among groups and normality are often violated (Duda, et al., 2001)"
-- unfortunately, I couldn't find the corresponding section in Duda et. al. "Pattern Classification".
Any experiences or thoughts about using LDA (vs. Regularized LDA or QDA) for non-normal data in context of dimensionality reduction?