A Latent Variable Implementation of Canonical Correlation Analysis for Data Visualisation

Recently a probabilistic method of performing principal component analysis based on latent variables has been created. Previous methods integrated out the latent variables and optimised the parameters. However [2] integrates out the parameters and optimises the positions of the latent points. We apply the same technique to create a latent variable model of canonical correlation analysis. We show with artificial data that this technique is especially suitable for data visualisation and then apply the method on a standard problem with real data from [4]. We also investigate how to envisage multiple correlations. Finally we investigate the identification of nonlinear relationships between two data sets and show how these may be easily sparsified in order to speed up computation.