The Experts below are selected from a list of 6195 Experts worldwide ranked by ideXlab platform
J C Sprott - One of the best experts on this subject based on the ideXlab platform.
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neural network method for determining Embedding Dimension of a time series
Communications in Nonlinear Science and Numerical Simulation, 2011Co-Authors: A Maus, J C SprottAbstract:A method is described for determining the optimal short-term prediction time-delay Embedding Dimension for a scalar time series by training an artificial neural network on the data and then determining the sensitivity of the output of the network to each time lag averaged over the data set. As a byproduct, the method identifies any intermediate time lags that do not influence the dynamics, thus permitting a possible further reduction in the required Embedding Dimension. The method is tested on four sample data sets and compares favorably with more conventional methods including false nearest neighbors and the ‘plateau Dimension’ determined by saturation of the estimated correlation Dimension. The proposed method is especially advantageous when the data set is small or contaminated by noise. The trained network could be used for noise reduction, forecasting, and estimating the dynamical and geometrical properties of the system that produced the data, such as the Lyapunov exponent, entropy, and attractor Dimension.
Henry D I Abarbanel - One of the best experts on this subject based on the ideXlab platform.
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false neighbors and false strands a reliable minimum Embedding Dimension algorithm
Physical Review E, 2002Co-Authors: Matthew B Kennel, Henry D I AbarbanelAbstract:The time-delay reconstruction of the state space of a system from observed scalar data requires a time lag and an integer Embedding Dimension. We demonstrate a reliable method to estimate the minimum necessary Embedding Dimension that improves upon previous methods by correcting for systematic effects due to temporal oversampling, autocorrelation, and changing time lag. The method gives a sharp and reliable indication of the proper Dimension. With little computational cost, the method also distinguish easily between infinite-Dimensional colored noise-including noisy periodicity-and low-Dimensional dynamics.
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determining Embedding Dimension for phase space reconstruction using a geometrical construction
Physical Review A, 1992Co-Authors: Matthew B Kennel, Reggie Brown, Henry D I AbarbanelAbstract:We examine the issue of determining an acceptable minimum Embedding Dimension by looking at the behavior of near neighbors under changes in the Embedding Dimension from d\ensuremath{\rightarrow}d+1. When the number of nearest neighbors arising through projection is zero in Dimension ${\mathit{d}}_{\mathit{E}}$, the attractor has been unfolded in this Dimension. The precise determination of ${\mathit{d}}_{\mathit{E}}$ is clouded by ``noise,'' and we examine the manner in which noise changes the determination of ${\mathit{d}}_{\mathit{E}}$. Our criterion also indicates the error one makes by choosing an Embedding Dimension smaller than ${\mathit{d}}_{\mathit{E}}$. This knowledge may be useful in the practical analysis of observed time series.
Masahide Watanabe - One of the best experts on this subject based on the ideXlab platform.
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Embedding Dimension estimation of chaotic time series using self generating radial basis function network
Fuzzy Sets and Systems, 1995Co-Authors: Ryu Katayama, Kaihei Kuwata, Yuji Kajitani, Masahide WatanabeAbstract:Abstract In this paper, we apply the self-generating radial basis function network (SGRBF) to the Dimension analysis of the nonlinear dynamical systems including chaotic time series. Firstly, we formulate a nonlinear time series identification problem with a nonlinear autoregressive moving average (NARMAX) model. Secondly, we propose an identification algorithm using SGRBF, which is regarded as both a three-layer network or a fuzzy model of class C∞ with Gaussian membership function. We apply this method to the estimation of Embedding Dimension for chaotic time series, since the Embedding Dimension plays an essential role for the identification and the prediction of nonlinear dynamical systems including chaos. In this estimation method, identification problems with gradually increasing Embedding Dimension are solved, and the identified result is used for computing correlation coefficients between the predicted time series and the observed one. We apply this method to the Embedding Dimension estimation of a Henon map and a chaotic pulsation time series in a finger's capillary vessels.
A Maus - One of the best experts on this subject based on the ideXlab platform.
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neural network method for determining Embedding Dimension of a time series
Communications in Nonlinear Science and Numerical Simulation, 2011Co-Authors: A Maus, J C SprottAbstract:A method is described for determining the optimal short-term prediction time-delay Embedding Dimension for a scalar time series by training an artificial neural network on the data and then determining the sensitivity of the output of the network to each time lag averaged over the data set. As a byproduct, the method identifies any intermediate time lags that do not influence the dynamics, thus permitting a possible further reduction in the required Embedding Dimension. The method is tested on four sample data sets and compares favorably with more conventional methods including false nearest neighbors and the ‘plateau Dimension’ determined by saturation of the estimated correlation Dimension. The proposed method is especially advantageous when the data set is small or contaminated by noise. The trained network could be used for noise reduction, forecasting, and estimating the dynamical and geometrical properties of the system that produced the data, such as the Lyapunov exponent, entropy, and attractor Dimension.
Matthew B Kennel - One of the best experts on this subject based on the ideXlab platform.
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false neighbors and false strands a reliable minimum Embedding Dimension algorithm
Physical Review E, 2002Co-Authors: Matthew B Kennel, Henry D I AbarbanelAbstract:The time-delay reconstruction of the state space of a system from observed scalar data requires a time lag and an integer Embedding Dimension. We demonstrate a reliable method to estimate the minimum necessary Embedding Dimension that improves upon previous methods by correcting for systematic effects due to temporal oversampling, autocorrelation, and changing time lag. The method gives a sharp and reliable indication of the proper Dimension. With little computational cost, the method also distinguish easily between infinite-Dimensional colored noise-including noisy periodicity-and low-Dimensional dynamics.
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determining Embedding Dimension for phase space reconstruction using a geometrical construction
Physical Review A, 1992Co-Authors: Matthew B Kennel, Reggie Brown, Henry D I AbarbanelAbstract:We examine the issue of determining an acceptable minimum Embedding Dimension by looking at the behavior of near neighbors under changes in the Embedding Dimension from d\ensuremath{\rightarrow}d+1. When the number of nearest neighbors arising through projection is zero in Dimension ${\mathit{d}}_{\mathit{E}}$, the attractor has been unfolded in this Dimension. The precise determination of ${\mathit{d}}_{\mathit{E}}$ is clouded by ``noise,'' and we examine the manner in which noise changes the determination of ${\mathit{d}}_{\mathit{E}}$. Our criterion also indicates the error one makes by choosing an Embedding Dimension smaller than ${\mathit{d}}_{\mathit{E}}$. This knowledge may be useful in the practical analysis of observed time series.
