Deep Canonical Correlation Analysis

Abstract

We introduce Deep Canonical Correlation Analysis (DCCA), a method to learn com-plex nonlinear transformations of two views of data such that the resulting representations are highly linearly correlated. Parameters of both transformations are jointly learned to maximize the (regularized) total correlation. It can be viewed as a nonlinear extension of the linear method canonical correlation analy-sis (CCA). It is an alternative to the nonpara-metric method kernel canonical correlation analysis (KCCA) for learning correlated non-linear transformations. Unlike KCCA, DCCA does not require an inner product, and has the advantages of a parametric method: train-ing time scales well with data size and the training data need not be referenced when computing the representations of unseen in-stances. In experiments on two real-world datasets, we find that DCCA learns represen-tations with significantly higher correlation than those learned by CCA and KCCA. We also introduce a novel non-saturating sigmoid function based on the cube root that may be useful more generally in feedforward neural networks.