Nonlinear Multiview Analysis: Identifiability and Neural Network-based Implementation

Multiview analysis aims to extract common information from data entities across different domains (e.g., acoustic, visual, text). Canonical correlation analysis (CCA) is one of the classic tools for this problem, which estimates the shared latent information via linear transforming the different views of data. CCA has also been generalized to the nonlinear regime, where kernel methods and neural networks are introduced to replace the linear transforms. While the theoretical aspects of linear CCA are relatively well understood, nonlinear multiview analysis is still largely intuition-driven. In this work, our interest lies in the identifiability of shared latent information under a nonlinear multiview analysis framework. We propose a model identification criterion for learning latent information from multiview data, under a reasonable data generating model. We show that minimizing this criterion leads to identification of the latent shared information up to certain indeterminacy. We also propose a neural network based implementation and an efficient algorithm to realize the criterion. Our analysis is backed by experiments on both synthetic and real data.