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

Careful consideration of the issues raised by Pezard and colleagues (in this issue of Psychophysiology) allows for the conclusion that spatial embedding may be valid as a method of dynamical reconstruction. However, two problems with the technique cannot be ignored. First, spatial embedding of EEG invariably 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, one must first check for at least "similar" dynamics among them, using, for example, a measure such as estimated mutual dimension. Measuring a "whole cortex" state via spatial embedding may also be possible in principle, except for the nontrivial obstacle of separating local dynamics that are heterogeneous across the cortex from activity reflecting the "unified field" of the cortex as a whole.