Manymachine learning task are involvedwith the transfer of information fromone representation to a corresponding representation or tasks where several different observations represent the same underlying phenomenon. A classical algorithm for feature selection using information from multiple sources or representations is Canonical Correlation Analysis (CCA). In CCA the objective is to select features in each observation space that are maximally correlated compared to dimensionality reduction where the objective is to re-represent the data in a more efficient form. We suggest a dimensionality reduction technique that builds on CCA. By extending the latent space with two additional spaces, each specific to a partition of the data, the model is capable of representing the full variance of the data. In this paper we suggest a generative model for shared dimensionality reduction analogous to that of CCA.