Nonlinear Signal Classification in the Framework of High-Dimensional Shape Analysis in Reconstructed State Space

A new framework is proposed as a feature extraction means for nonlinear signal classification. It contains two core ideas: 1) use a set of PoincarÉ surfaces to cut the trajectory that is reconstructed from the nonlinear time series of interest by means of state space reconstruction in order that the structural characteristics in different local regions can be highlighted, respectively, and 2) use shape analyzers in terms of computer vision to characterize the geometric structure of the trajectory. The experiments show that: 1) the geometric structures of reconstructed trajectories contain useful information for nonlinear signal classification; 2) shape analyzers in terms of computer vision are able to capture such information; and 3) the proposed framework provides a means to access the rich information contained in the geometric structures of reconstructed trajectories.