Abstract
A novel visualization scheme for permutation entropy is presented in this paper. The proposed scheme is based on non-uniform attractor embedding of the investigated time series. A single digital image of permutation entropy is produced by averaging all possible plain projections of the permutation entropy measure in the multi-dimensional delay coordinate space. Computational experiments with artificially-generated and real-world time series are used to demonstrate the advantages of the proposed visualization scheme.
Highlights
Real-world time series and experimental data are usually contaminated with noise
A novel visualization scheme for permutation entropy is presented in this paper
The proposed scheme is based on non-uniform attractor embedding and uses different time delays, but results in a single digital image
Summary
Real-world time series and experimental data are usually contaminated with noise. System states of such time series are usually complex, nonstationary and difficult to identify. PE is based on one-dimensional time series reconstruction into a D-dimensional space with the embedding delay τ. The time series embedding scheme into the higher dimension space was first presented by Packard, Crutchfield, Farmer and Shaw [19,20]. This embedding scheme represents the optimal properties of a dynamical system if the embedding dimension Dand time delay τ (the difference between consecutive observations) are estimated adequately. The selection of the optimal vector of time delays for non-uniform embedding is a difficult optimization problem that requires massive computational resources. The main objective of this paper is to employ non-uniform time series embedding for the construction of a visualization scheme for PE. A discussion and concluding remarks are given in the last section
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