State-space reconstruction and prediction of chaotic time series based on fuzzy clustering

Selecting the embedding dimension of a dynamic system is a key step toward the analysis and prediction of nonlinear and chaotic time-series. This paper proposes a clustering-based algorithm for this purpose. The clustering is applied in the reconstructed space defined by the lagged output variables. The intrinsic dimension of the reconstructed space is then estimated based on the analysis of the eigenvalues of the fuzzy cluster covariance matrices, while the correct embedding dimension is inferred from the prediction performance of the local models of the clusters. The main advantage of the proposed solution is that three tasks are simultaneously solved during clustering: selection of the embedding dimension, estimation of the intrinsic dimension, and identification of a model that can be used for prediction.