Nonlinear canonical correlation analysis by neural networks.

Canonical correlation analysis (CCA) is widely used to extract the correlated patterns between two sets of variables. A nonlinear canonical correlation analysis (NLCCA) method is formulated here using three feedforward neural networks. The first network has a double-barreled architecture, and an unconventional cost function, which maximizes the correlation between the two output neurons (the canonical variates). The remaining two networks map from the canonical variates back to the original two sets of variables. Tested on data sets with correlated nonlinear structures, NLCCA showed that the underlying nonlinear structures could be retrieved accurately under moderately noisy conditions. After a mode had been retrieved, NLCCA was applied to the residual to successfully retrieve the next mode. When tested for prediction skills, the NLCCA outperformed the CCA when the two sets of variables contained correlated nonlinear structures.