A Probabilistic Interpretation of Canonical Correlation Analysis

April, 2005
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Francis R. Bach and Michael I. Jordan

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.

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