Bayesian Sparse Factor Analysis with Kernelized Observations

Latent variable models for multi-view learning attempt to find low-dimensional projections that fairly capture the correlations among multiple views that characterise each datum. High-dimensional views in medium-sized datasets and non-linear problems are traditionally handled by kernel methods, inducing a (non)-linear function between the latent projection and the data itself. However, they usually come with scalability issues and exposition to overfitting. To overcome these limitations, instead of imposing a kernel function, here we propose an alternative method. In particular, we combine probabilistic factor analysis with what we refer to as kernelized observations, in which the model focuses on reconstructing not the data itself, but its correlation with other data points measured by a kernel function. This model can combine several types of views (kernelized or not), can handle heterogeneous data and work in semi-supervised settings. Additionally, by including adequate priors, it can provide compact solutions for the kernelized observations (based in a automatic selection of bayesian support vectors) and can include feature selection capabilities. Using several public databases, we demonstrate the potential of our approach (and its extensions) w.r.t. common multi-view learning models such as kernel canonical correlation analysis or manifold relevance determination gaussian processes latent variable models.