Re-referencing

After this module you should be able to:

• explain why there is no such thing as the voltage "at" one electrode;
• describe average, linked-mastoid, Cz and bipolar references, and say which ones the course headsets allow;
• predict what a reference change will and will not do to a channel's alpha power;
• explain why average-referenced data loses one dimension, and what that means for ICA.

Every channel is a difference #

A voltmeter needs two leads. Each EEG channel is the voltage at one electrode minus the voltage at a reference point. If the reference picks up brain activity, blinks or noise, that activity appears, upside down, in every channel that uses it.

There is no electrically silent place on the head, so every choice of reference is a compromise. Re-referencing means recomputing all channels against a different reference after recording. Because subtraction is linear, you can do it at any time, as long as the original reference's channels were recorded or the new reference can be built from channels you have.

flowchart LR
    E["electrode O1"] --> D(("O1 − ref"))
    R["reference<br/>(ear, mastoid, Cz,<br/>or the average)"] --> D
    D --> C["the channel<br/>you see as 'O1'"]

The common references #

See the same three seconds four ways #

Three seconds of s01_rest_eyes-closed_19ch.edf (from 60 s) under four references.

What changes:

• Cz reference: Cz becomes a perfectly flat line, by definition. O1 alpha changes a little, because Cz's own activity is now mixed into every other channel.
• Average reference: posterior alpha now shows up, smaller and inverted, at the front of the head. Average reference forces the channels to sum to zero at every instant, so a big positive signal at the back must be balanced by negative signal somewhere else.
• Bipolar chain: P3-O1 and C3-P3 keep strong alpha because O1 and P3 differ; Fp1-F3 shows almost none, because neither site has much.

What does not change: the underlying brain activity, and the times at which things happen. A reference changes how the activity is distributed across channels, not when it occurs.

You can put numbers on this with the median-Welch alpha power (8-13 Hz, µV²/Hz) of s01 from 10 to 300 s:

The bipolar P3-O1 pair gives 38.1 µV²/Hz. O1 stays the highest-alpha site under every reference, which is why the Lab 2 check "is alpha highest at the back?" is robust. Absolute values change by 30% or more, which is why you can only compare band power between recordings that share a reference.

Average reference and rank #

After average referencing, the channels always sum to zero. For s01 the largest absolute sum across all 19 channels after set_eeg_reference("average") is about 6 × 10⁻¹³ µV, i.e. zero to rounding error. That means any one channel can be computed from the other 18: the data has 18 independent dimensions, not 19. MNE reports this as rank:

import mne
from eeg101 import load_sample

raw = load_sample("rest_ec").filter(1, 40)
print(mne.compute_rank(raw))                                   # {'eeg': 19}
print(mne.compute_rank(raw.copy().set_eeg_reference("average")))  # {'eeg': 18}
print(mne.compute_rank(raw.copy().set_eeg_reference(["Cz"])))     # {'eeg': 18}

Why you care: ICA cannot find more components than the data has dimensions. On average-referenced 19-channel data, ask for at most 18 components (ICA(n_components=18) or fewer; the labs use 15). MNE handles this with a PCA step and warns you if you ask for too many. Interpolating a bad channel or re-referencing to a single channel also removes a dimension. EEGLAB users meet the same problem as "rank deficiency" warnings.

Doing it in MNE #

import mne
from eeg101 import load_sample

raw = load_sample("rest_ec").filter(1.0, 40.0)

avg = raw.copy().set_eeg_reference("average")      # average reference
cz = raw.copy().set_eeg_reference(["Cz"])          # single channel
bip = mne.set_bipolar_reference(raw.copy(), anode=["Fp1", "F3", "C3", "P3"],
                                cathode=["F3", "C3", "P3", "O1"])  # bipolar chain

# With mastoid channels you would write: raw.set_eeg_reference(["M1", "M2"])
# The course files have no M1/M2, so this line would raise an error here.

avg.plot(duration=5)

Notes:

• set_eeg_reference modifies the object in place and returns it; use .copy() to keep the original.
• Mark bad channels (raw.info["bads"] = ["T3"]) before average referencing, so the bad channel is left out of the average.
• In MNE, projection=True adds the average reference as a projector instead of applying it immediately. You will see this in older tutorials.

Read MNE's Setting the EEG reference tutorial next; it shows the same comparisons on a 60-channel dataset.

Check yourself #