ON THE VALIDITY OF ESTIMATING EEC CORRELATION DIMENSION FROM A SPATIAL EMBEDDING

We demonstrate by using simulations that spatial embedding of single-v ariable time series data does not reliably reconstruct state-space dyn amics. Instead, correlation dimension estimated from spatially embedde d data is largely a measure of linear cross-correlation in the data se t. For actual electroencephalographic (EEC) data, we demonstrate a hig h negative correlation between spatial correlation dimension and the a verage amount of lag-zero crosscorrelation between ''nearest-neighbor' ' embedding channels (the greater the cross-correlation, the lower the dimension). We also show that the essential results obtained from spa tially embedding EEG data are also obtained when one spatially embeds across a set of highly cross-correlated stochastic (second-order autor egressive) processes. Although, with appropriate surrogate data, corre lation dimension estimated from spatially embedded data detects nonlin earity, its use is not recommended because correlation dimension estim ated from temporally embedded data both reconstructs state-spate dynam ics and, with appropriate surrogate data, detects nonlinearity as well .