Neural Network Method for Determining Embedding Dimension of a Time
A. Maus and J.
Physics Department, University
of Wisconsin, 1150 University Ave., Madison, WI 53706, USA
Received 3 June 2010; Accepted 20 October 2010; Available online 26
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
Ref: A. Maus and J. C. Sprott, Commun.
Nonlinear Sci. Numer. Simulat. 16, 3294-3302 (2011)
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