Nonlinear multivariate statistical models, such as nonlinear principal component analysis (NLPCA) and nonlinear canonical correlation analysis (NLCCA), have been used in place of linear models for analysis and prediction in climatology. Datasets encountered in climatology are, however, often short and noisy, making the identification of robust nonlinear models a particularly challenging task. This can be attributed, in part, to the practice of setting model parameters by minimizing the mean squared error (mse), which is not robust in the presence of outliers.

Robust versions of NLPCA and NLCCA are developed to help mitigate overfitting on short, noisy datasets. Robust NLPCA replaces the mse cost function with the mean absolute error (mae), while robust NLCCA replaces the Pearson product-moment correlation with the Spearman rank correlation and the mse with the mae. Robust NLPCA and NLCCA models are evaluated on synthetic and real-world climate datasets and are compared against standard NLPCA and NLCCA models. Robust models are better able to extract the signal from noisy datasets than their non-robust counterparts.