On the validity of spatial embedding: A reply to Pezard et al.

Careful consideration of the issues raised by Pezard and colleagues (in thi s issue of Psychophysiology) allows for the conclusion that spatial embeddi ng may be valid as a method of dynamical reconstruction. However, two probl ems with the technique cannot be ignored. First, spatial embedding of EEG i nvariably involves linear cross-correlation among channels, which distorts the dynamical reconstruction due to compression toward the main state-space diagonal. Further, before spatially embedding across a set of channels, on e must first check for at least "similar" dynamics among them, using, for e xample, a measure such as estimated mutual dimension. Measuring a "whole co rtex" state via spatial embedding may also be possible in principle, except for the nontrivial obstacle of separating local dynamics that are heteroge neous across the cortex from activity reflecting the "unified field" of the cortex as a whole.