Manifold Analysis in Reconstructed State Space for Nonlinear Signal Classification

Abstract

A framework based on manifold learning in reconstructed state space is proposed as feature extraction means for nonlinear signal classification. On one hand, manifolds are of importance in characterizing chaotic attractors. On the other hand, there are a large number of toolkits in the context of manifold learning. These motivate us to apply manifold learning in reconstructed state space as feature extraction means for nonlinear signal classification, which bridges the gap between nonlinear science and manifold learning and enables a new viewpoint to study nonlinear signals. In this study, the nonlinear signal analysis is performed as follows. First, we embed the time series of interest into a high-dimensional space via state space reconstruction. Then, we employ locally linear embedding (LLE) to obtain the local manifold characteristics around every point in the reconstructed state space. Finally, we summarize all the local features into a global representation via principal component analysis (PCA). Two case studies of oceanic and EEG signal classification were carried out with the proposed scheme. As confirmed by the experiments, the proposed methodology is effective for such applications. This paper puts forward not only a feature extraction method but also a new direction in which a large number of toolkits are available for nonlinear signal analysis for the sake of signal classification.