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Robust variants of nonlinear canonical correlation analysis (NLCCA) are introduced to improve performance on datasets with low signal-to-noise ratios, for example those encountered when making seasonal climate forecasts. The neural network model architecture of standard NLCCA is kept intact, but the cost functions used to set the model pa- rameters are replaced with more robust variants. The Pearson product-moment correlation in the double-barreled network is replaced by the biweight midcorrelation, and the mean squared error (mse) in the inverse mapping networks can be replaced by the mean absolute error (mae). Robust variants of NLCCA are demonstrated on a syn- thetic dataset and are used to forecast sea surface temper- atures in the tropical Pacific Ocean based on the sea level pressure field. Results suggest that adoption of the bi- weight midcorrelation can lead to improved performance, es- pecially when a strong, common event exists in both predic- tor/predictand datasets. Replacing the mse by the mae leads to improved performance on the synthetic dataset, but not on the climate dataset except at the longest lead time, which sug- gests that the appropriate cost function for the inverse map- ping networks is more problem dependent.

Robust nonlinear canonical correlation analysis: application to seasonal climate forecasting