On the validity of estimating EEG correlation dimension from a spatial embedding.

We demonstrate by using simulations that spatial embedding of single-variable time series data does not reliably reconstruct state-space dynamics. Instead, correlation dimension estimated from spatially embedded data is largely a measure of linear cross-correlation in the data set. For actual electroencephalographic (EEG) data, we demonstrate a high negative correlation between spatial correlation dimension and the average amount of lag-zero cross-correlation between "nearest-neighbor" embedding channels (the greater the cross-correlation, the lower the dimension). We also show that the essential results obtained from spatially embedding EEG data are also obtained when one spatially embeds across a set of highly cross-correlated stochastic (second-order autoregressive) processes. Although, with appropriate surrogate data, correlation dimension estimated from spatially embedded data detects nonlinearity, its use is not recommended because correlation dimension estimated from temporally embedded data both reconstructs state-space dynamics and, with appropriate surrogate data, detects nonlinearity as well.

[1]  R Jouvent,et al.  Decrease of complexity in EEG as a symptom of depression. , 1994, Neuroreport.

[2]  James Theiler,et al.  Testing for nonlinearity in time series: the method of surrogate data , 1992 .

[3]  L Pezard,et al.  Non-linear forecasting measurements of multichannel EEG dynamics. , 1994, Electroencephalography and clinical neurophysiology.

[4]  Floris Takens,et al.  On the numerical determination of the dimension of an attractor , 1985 .

[5]  W. Pritchard,et al.  Measuring chaos in the brain: a tutorial review of nonlinear dynamical EEG analysis. , 1992, The International journal of neuroscience.

[6]  Spatio-temporal dynamics of human EEG , 1992 .

[7]  S. Ellner.  Estimating attractor dimensions from limited data: A new method, with error estimates , 1988 .

[8]  Theiler,et al.  Generating surrogate data for time series with several simultaneously measured variables. , 1994, Physical review letters.

[9]  D. Lehmann,et al.  From Mapping to the Analysis and Interpretation of EEG/EP Maps , 1989 .

[10]  D. Ruelle,et al.  Ergodic theory of chaos and strange attractors , 1985 .

[11]  A. Provenzale,et al.  Finite correlation dimension for stochastic systems with power-law spectra , 1989 .

[12]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[13]  W. Pritchard,et al.  Dimensional analysis of no-task human EEG using the Grassberger-Procaccia method. , 1992, Psychophysiology.

[14]  F. Takens.  Detecting strange attractors in turbulence , 1981 .

[15]  F. H. Lopes da Silva,et al.  Chaos or noise in EEG signals; dependence on state and brain site. , 1991, Electroencephalography and clinical neurophysiology.

[16]  J.C. de Munck,et al.  A random dipole model for spontaneous brain activity , 1992, IEEE Transactions on Biomedical Engineering.

[17]  I. Dvořák,et al.  Takens versus multichannel reconstruction in EEG correlation exponent estimates , 1990 .

[18]  Ramesh Srinivasan,et al.  Implications of recording strategy for estimates of neocortical dynamics with electroencephalography. , 1993, Chaos.

[19]  Agnessa Babloyantz,et al.  A comparative study of the experimental quantification of deterministic chaos , 1988 .

[20]  C M Michel,et al.  Global dimensional complexity of multi-channel EEG indicates change of human brain functional state after a single dose of a nootropic drug. , 1993, Electroencephalography and clinical neurophysiology.

[21]  J. Theiler.  Some Comments on the Correlation Dimension of 1/fαNoise , 1991 .

[22]  R. Mañé,et al.  On the dimension of the compact invariant sets of certain non-linear maps , 1981 .

[23]  W. Pritchard,et al.  Dimensional analysis of resting human EEG. II: Surrogate-data testing indicates nonlinearity but not low-dimensional chaos. , 1995, Psychophysiology.

[24]  J Wackermann,et al.  Global dimensional complexity of the EEG in healthy volunteers. , 1995, Neuropsychobiology.

[25]  K. Coburn,et al.  EEG-based, neural-net predictive classification of Alzheimer's disease versus control subjects is augmented by non-linear EEG measures. , 1994, Electroencephalography and clinical neurophysiology.

[26]  Pezard,et al.  Nonlinear Forecasting And Correlation Dimension Of Brain Dynamics : A Multichannel Study Nonlinear Forecasting And Correlation Dimension Of Brain Dynamics : A Multichannel Study. , 1992 .