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Title: Determining the minimum embedding dimension for state space reconstruction through recurrence networks
Authors: Harikrishnan, K. P.
Jacob, Rinku
Misra, R.
Dept. of Physics
Keywords: Nonlinear time series analysis
Recurrence networks
State space reconstruction
Kullback Leibler measure
Issue Date: Dec-2017
Publisher: Indian Academy of Sciences
Citation: Indian Academy of Sciences Conference Series, 1(1), 43-49.
Abstract: The analysis of observed time series from nonlinear systems is usually done by making a time-delay reconstruction to unfold the dynamics on a multidimensional state space. An important aspect of the analysis is the choice of the correct embedding dimension. The conventional procedure used for this is either the method of false nearest neighbors or the saturation of some invariant measure, such as, correlation dimension. Here we examine this issue from a complex network perspective and propose a recurrence network based measure to determine the acceptable minimum embedding dimension to be used for such analysis. The measure proposed here is based on the well known Kullback-Leibler divergence commonly used in information theory. We show that the measure is simple and direct to compute and give accurate result for short time series. To show the significance of the measure in the analysis of practical data, we present the analysis of two EEG signals as examples.
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