Shared Gaussian Process Latent Variables Models

A fundamental task is machine learning is modeling the relationship between different observation spaces. Dimensionality reduction is the task reducing the number of dimensions in a parameterization of a data-set. In this thesis we are interested in the cross-road between these two tasks: shared dimensionality reduction. Shared dimensionality reduction aims to represent multiple observation spaces within the same model. Previously suggested models have been limited to the scenarios where the observations have been generated from the same manifold. In this paper we present a Gaussian process Latent Variable Model (GP-LVM) [33] for shared dimensionality reduction without making assumptions about the relationship between the observations. Further we suggest an extension to Canonical Correlation Analysis (CCA) called Non Consolidating Component Analysis (NCCA). The proposed algorithm extends classical CCA to represent the full variance of the data opposed to only the correlated. We compare the suggested GP-LVM model to existing models and show results on real-world problems exemplifying the advantages of our approach.