Bayesian Sparse Factor Analysis with Kernelized Observations

Abstract

Multi-view problems can be faced with latent variable models since they are able to find low-dimensional projections that fairly capture the correlations among the multiple views that characterise each datum. On the other hand, high-dimensionality and non-linear issues 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. Here, we propose merging both approaches into single model so that we can exploit the best features of multi-view latent models and kernel methods and, moreover, overcome their limitations. 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 relationship with other data points measured by a kernel function. This model can combine several types of views (kernelized or not), and it 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 Relevance Vectors (RVs) -- 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.