Title: A Probabilistic Interpretation of Canonical Correlation Analysis
Author: Francis R. Bach and Michael I. Jordan
Date: April 2005
Pub: PDF
Url: http://www.stat.berkeley.edu/~jordan/688.pdf

Abstract:
We give a probabilistic interpretation of canonical correlation
(CCA) analysis as a latent variable model for two Gaussian random
vectors. Our interpretation is similar to the probabilistic
interpretation of principal component analysis (Tipping and 
Bishop, 1999; Roweis, 1998). In addition, we cast Fisher linear 
discriminant analysis (LDA) within the CCA framework.