  A simple framework Probabilistic Multi-view Graph Embedding (PMvGE) is
proposed for multi-view feature learning with many-to-many associations so that
it generalizes various existing multi-view methods. PMvGE is a probabilistic
model for predicting new associations via graph embedding of the nodes of data
vectors with links of their associations. Multi-view data vectors with
many-to-many associations are transformed by neural networks to feature vectors
in a shared space, and the probability of new association between two data
vectors is modeled by the inner product of their feature vectors. While
existing multi-view feature learning techniques can treat only either of
many-to-many association or non-linear transformation, PMvGE can treat both
simultaneously. By combining Mercer's theorem and the universal approximation
theorem, we prove that PMvGE learns a wide class of similarity measures across
views. Our likelihood-based estimator enables efficient computation of
non-linear transformations of data vectors in large-scale datasets by minibatch
SGD, and numerical experiments illustrate that PMvGE outperforms existing
multi-view methods.
