Nonlinear Principal Predictor Analysis: Application to the Lorenz System

Abstract

Principal predictor analysis is a multivariate linear technique that fits between regression and canonical correlation analysis in terms of the complexity of its architecture. This study introduces a new neural network approach for performing nonlinear principal predictor analysis (NLPPA). NLPPA is applied to the Lorenz system of equations and is compared with nonlinear canonical correlation analysis (NLCCA) and linear multivariate models. Results suggest that NLPPA is capable of performing better than NLCCA when datasets are corrupted with noise. Also, NLPPA modes may be extracted in less time than NLCCA modes. NLPPA is recommended for prediction problems where a clear set of predictors and a clear set of predictands can be easily defined.