Neural Network-Assisted Nonlinear Multiview Component Analysis: Identifiability and Algorithm

--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 veiws 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. 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 nonlinear multiview analysis criteron. We show that minimizing this criterion leads to identification of the latent shared components up to certain ambiguities, under reasonable conditions. 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. Multiview analysis has been an indispensable tool in statistical signal processing, machine learning, and data analytics. In the context of multiview learning, a view can be understood as measurements of data entities (e.g., a cat) in a certain domain (e.g., text, image, and audio). Most data entities naturally appear in different domains. Multiview analysis aims at extracting essential and common information from different views. Compared with single-view analysis tools like principal component analysis (PCA), independent component analysis (ICA) [1], and nonnegative matrix factorization (NMF) [2], multiview analysis tools such as canonical correlation analysis (CCA) [3] have an array of unique features. For example, CCA has been shown to be more robust to noise and view-specific strong interference [4], [5]. The classic CCA has been extensively studied in the literature, ever since its proposal in statistics in the 1930s [3], [6]. Q. Lyu and X. Fu are with the School of Electrical Engineering and Computer Science, Oregon State University, Corvallis, OR 97331, United States. The transformations are supposed to'project' the views to a domain where the views share similar representations. Interestingly, the formulated optimization problem, although being nonconvex, can be recast into a generalized eigende-composition problem and solved efficiently [3], [7].