[Eeglablist] average reference and connectivity

[Roy Cox]

Hi all,

I would like to get some expert opinions on the use of the average
reference when investigating phase-based connectivity (e.g., PLV, PLI,
etc), and a potential problem when using this approach.

While no referencing scheme is optimal, it is often argued that the average
reference offers "the best" solution given a sufficient amount of
electrodes (we use 60). The reference can be interpreted as the "height"
from which the topographical landscape of voltage amplitudes is viewed.
While any perspective is valid, average referencing places the viewpoint at
the average of all electrodes, which is declared zero. Importantly, this is
done on a sample-by-sample basis, meaning that the average is always zero.

Enter widespread synchronous oscillations. I've often noticed that when
strong in-phase alpha activity is present over posterior cortex, the
average reference results in equally strong and anti-phase alpha
oscillations over anterior regions (with a small region in between where
alpha activity is relatively absent). Similarly, during deep sleep there
are very strong frontal slow oscillations that are inverted in polarity
over posterior regions.

Now, any phase-based metric will return beautiful long-range (anti-phase)
connectivity, which is entirely (or at least largely) an artefact of the
referencing.

When using average mastoids as a reference (also not perfect - I know), it
is evident that there is no phase reversal from anterior to posterior
areas: alpha activity is (visually) absent from frontal regions, and sleep
oscillations are synchronous (in-phase) across most of cortex (but, by
necessity, relatively small close to the sites used for referencing).

In sum, while I'm sure the average reference is valid on a sample-by-sample
basis, problems seem to arise when time enters the equation and widespread
large negativities have to be matched by widespread positivities to keep
the average zero.

I imagine amplitude-envelope correlations could also suffer from spurious,
average reference-induced, oscillations.

This is all terribly hand-wavy and non-mathematical, so it would be great
if someone could comment on this to support or disprove my reasoning.

Roy
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