# How to understand that MANOVA and discriminant analysis are special cases of canonical correlation analysis?

I am reading a statistical book which writes,

Canonical correlation represents one way in which we can examine the relationship between multiple dependent variables ($\bf{Y}$) and multiple independent variables ($\bf{X}$).

Based on my understanding, in canonical correlation analysis (CCA) the independent variables are treated as continuous variables, and in MANOVA and discriminant analysis (LDA) $\bf{X}$ are discrete variables, or "groups". Is this the reason that makes the latter two special cases of canonical correlation?

Are there any other reasons for this "special case" statement?

Do MANOVA and discriminant analysis have some mathematical connection with canonical correlation? I have basic understanding of the background mechanism but I have not got time to dive deep into.

• One of possible answers: stats.stackexchange.com/a/31468/3277. – ttnphns May 21 '15 at 14:47
• LDA on X is equivalent to CCA between X and the class indicator matrix G. And MANOVA and LDA are essentially the same model. If I have some time, I will try to post an answer providing some details. – amoeba Nov 29 '15 at 1:28