Reduction of the multlvariate input dimension using principal component analysis

Abstract

There are limitations for the existing methods to model multivariate time series because that defining the input components is highly difficult. The main purpose of this paper is to expand the principal components analysis (PCA) method to extract the joint information of multiple variables. First, both the linear correlations and the nonlinear correlations are detected to initialize an embedding delay window, which contains enough information for prediction. Then, the PCA method is expanded to extract the joint information of multiple variables in a complex system. Finally, neural network makes predictions on the basis of approximating both the functional relationship between different variables and the map between current state and future state. © Springer-Verlag Berlin Heidelberg 2006.