I have a question about the relationship between the result of Eigenface and Fisherface on face recognition. (Eigenface and Fisherface is the topic of Computer Vision. Those are related with PCA and LDA, respectively.)
Suppose that we have two sets of faces denoted by $S_{x} = \{x_{i}\mid i=1, ... , N \}$ and $S_{y} = \{ {y}_{i}\mid i=1, ... , N \}$.
And the mean and covariance matrices of the sets are given by $ ( \mu_{x} , C_x )$ and $ ( \mu_{y} , C_y )$, respectively.
If the covariance matrices $C_x$ and $C_y$ are identical, what is the relationship between Eigenface and Fisherface of $S_{x} \bigcup S_{y}$?
From here, each mean $\mu_x $ and $ \mu_y$ are completely unknown.