ABSTRACT
This structure may consist of a number of irrelevant and redundant variables even though a suitable pair of embedding dimension m and time delay τ are appropriately selected when performing the phase space reconstruction. The fact of equidistance time-delayed variables in the phase space reconstruction might also induce some redundancies. We propose the phase space dimensionality reduction based on principal component analysis (PCA) to solve these issues by creating a compact and lower dimensional phase space of a dynamical system which can improve the accuracy of chaotic model predictions. Similar researches have been done, such as an attractor reconstruction from univariate time series with a distortion functional comparison of singular system and redundancy criteria studied by Fraser (1989). While Han et al. (2006) extracted the feature components of noisy multivariate time series based on singular value decomposition (SVD) and applied ANN for predicting a dynamical system. Yet, to the best of our knowledge, none of papers concentrated on the phase space dimensionality reduction on improving univariate and multivariate chaotic model predictions. For testing how phase space dimensionality reduction may improve predictive chaotic model performance, both the sea water level and surge time series data along the Dutch coast were considered.
