Learning Canonical F-Correlation Projection for Compact Multiview Representation

Abstract

Canonical correlation analysis (CCA) matters in multiview representation learning. But, CCA and its most variants are essentially based on explicit or implicit covariance matrices. It means that they have no ability to model the nonlinear relationship among features due to intrinsic linearity of covariance. In this paper, we address the preceding problem and propose a novel canonical F-correlation framework by exploring and exploiting the nonlinear relationship between different features. The framework projects each feature rather than observation into a certain new space by an arbitrary nonlinear mapping, thus resulting in more flexibility in real applications. With this framework as a tool, we propose a correlative covariation projection (CCP) method by using an explicit nonlinear mapping. Moreover, we further propose a multiset version of CCP dubbed MCCP for learning compact representation of more than two views. The proposed MCCP is solved by an iterative method, and we prove the convergence of this iteration. A series of experimental results on six benchmark datasets demonstrate the effectiveness of our proposed CCP and MCCP methods.