Nonlinear canonical correlation analysis by neural networks

Canonical correlation analysis (CCA) is widely used to extract the correlat ed patterns between two sets of variables. A nonlinear canonical correlatio n analysis (NLCCA) method is formulated here using three feedforward neural networks. The first network has a double-barreled architecture, and an unc onventional cost function, which maximizes the correlation between the two output neurons (the canonical variates). The remaining two networks map fro m the canonical variates back to the original two sets of variables. Tested on data sets with correlated nonlinear structures, NLCCA showed that the u nderlying nonlinear structures could be retrieved accurately under moderate ly noisy conditions. After a mode had been retrieved, NLCCA was applied to the residual to successfully retrieve the next mode. When tested for predic tion skills, the NLCCA outperformed the CCA when the two sets of variables contained correlated nonlinear structures. (C) 2000 Elsevier Science Ltd. A ll rights reserved.