A probabilistic framework for multi-view feature learning with many-to-many associations via neural networks
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A simple framework Probabilistic Multi-view Graph Embedding (PMvGE) is proposed for multi-view feature learning with many-to-many associations. 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. PMvGE generalizes various existing multi-view methods such as Multiset Canonical Correlation Analysis (MCCA) and Cross-view Graph Embedding (CvGE). Our likelihood-based estimator enables efficient computation of non-linear transformations of data vectors in large-scale datasets by minibatch SGD. Numerical experiments illustrate that PMvGE outperforms existing multi-view methods.
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