  Multiview analysis aims at extracting shared latent components from data
samples that are acquired in different domains, e.g., image, text, and audio.
Classic multiview analysis, e.g., canonical correlation analysis (CCA), tackles
this problem via matching the linearly transformed views in a certain latent
domain. More recently, powerful nonlinear learning tools such as kernel methods
and neural networks are utilized for enhancing the classic CCA. However, unlike
linear CCA whose theoretical aspects are clearly understood, nonlinear CCA
approaches are largely intuition-driven. In particular, it is unclear under
what conditions the shared latent components across the views can be
identified---while identifiability plays an essential role in many
applications. In this work, we revisit nonlinear multiview analysis and address
both the theoretical and computational aspects. Our work leverages a useful
nonlinear model, namely, the post-nonlinear model, from the nonlinear mixture
separation literature. Combining with multiview data, we take a nonlinear
multiview mixture learning viewpoint, which is a natural extension of the
classic generative models for linear CCA. From there, we derive a learning
criterion. We show that minimizing this criterion leads to identification of
the latent shared components up to certain ambiguities, under reasonable
conditions. Our derivation and formulation also offer new insights and
interpretations to existing deep neural network-based CCA formulations. On the
computation side, we propose an effective algorithm with simple and scalable
update rules. A series of simulations and real-data experiments corroborate our
theoretical analysis.
