mne_connectivity.envelope_correlation

Hello
I’m a person who is studying brain waves.

I have a question about the envelope_correlation() function of mne_connectivity.
use this function with (orthogonalize=“pairwise”, log=True, absolute=True)

def envelope_correlation(data, names=None,
                         orthogonalize="pairwise",
                         log=False, absolute=True, verbose=None):
    for ei, epoch_data in enumerate(data):
        data_mag = np.abs(epoch_data)
        data_conj_scaled = epoch_data.conj()
        data_conj_scaled /= data_mag
        if log:
            data_mag *= data_mag
            np.log(data_mag, out=data_mag)

        # subtract means
        data_mag_nomean = data_mag - np.mean(data_mag, axis=-1, keepdims=True)

        # compute variances using linalg.norm (square, sum, sqrt) since mean=0
        data_mag_std = np.linalg.norm(data_mag_nomean, axis=-1)
        data_mag_std[data_mag_std == 0] = 1
        corr = np.empty((n_nodes, n_nodes))

        # loop over each signal in this specific epoch
        # which is now (n_signals, n_times) and compute envelope
        for li, label_data in enumerate(epoch_data):
            if orthogonalize is False:  # the new code
                label_data_orth = data_mag[li]
                label_data_orth_std = data_mag_std[li]
            else:
                label_data_orth = (label_data * data_conj_scaled).imag
                np.abs(label_data_orth, out=label_data_orth)
                # protect against invalid value -- this will be zero
                # after (log and) mean subtraction
                label_data_orth[li] = 1.
                if log:
                    label_data_orth *= label_data_orth
                    np.log(label_data_orth, out=label_data_orth)
                label_data_orth -= np.mean(label_data_orth, axis=-1,
                                           keepdims=True)
                label_data_orth_std = np.linalg.norm(label_data_orth, axis=-1)
                label_data_orth_std[label_data_orth_std == 0] = 1

            # correlation is dot product divided by variances
            corr[li] = np.sum(label_data_orth * data_mag_nomean, axis=1)
            corr[li] /= data_mag_std
            corr[li] /= label_data_orth_std
        if orthogonalize:
            # Make it symmetric (it isn't at this point)
            if absolute:
                corr = np.abs(corr)
            corr = (corr.T + corr) / 2.

What I’m curious about in the code above is the variable assigned to the corr[li] in the label data for statement.

corr[li] = np.sum(label_data_orth * data_mag_nomean, axis=1)

For example, let’s say the shape of input data is (30,19,5000). (epoch, node, time)

Then, the epoch data variable has shape (19,5000).
and data_mag , data_mag_nomean, data_mag_std also has shape (19,5000).

for li, label_data in enumerate(epoch_data):

And after this code,
label_data_orth is an orthogonal signal of 19 channels for label_data.

What I’m curious about here is
In this code, to calculate the Pearson correlation,
np.sum(label_data_orth * data_mag_nomean, axis=1) was used.

I wonder why data_mag_nomean is included instead of data_mag_nomean[li].
Shouldn’t corr[li] contain 19 orthologized signals of label_data and label_data?

If there’s anything I misunderstood, please tell me.

Thank you.

ping @adam2392 . The line in question is here:

Additionally, if I’m right,

corr[li] = np.sum(label_data_orth * data_mag_nomean, axis=1)
corr[li] /= data_mag_std

I think this code should be modified as follows

corr[li] = np.sum(label_data_orth * data_mag_nomean[li], axis=1)
corr[li] /= data_mag_std[li]

Pinging @larsoner I remember you contributing the orthogonalize portion of the code(?). Do you happen to know the right answer. I’m going to re-read this a few times to see if I can spot the issue…

@Junseok726 apologies, I didn’t work on the original code. I was just involved in refactoring. So from what I can tell, I tried your change, but it broke a unit test.

In mne-connectivity/test_envelope.py at main · mne-tools/mne-connectivity · GitHub, there seems to be a unit test that was copied over from testing against the output of FieldTrip.

The resulting error shows:

mne_connectivity/tests/test_envelope.py:85: in test_envelope_correlation
    assert_allclose(
E   AssertionError: 
E   Not equal to tolerance rtol=1e-07, atol=0
E   
E   Mismatched elements: 6 / 10 (60%)
E   Max absolute difference: 0.6672455
E   Max relative difference: 8.65513432
E    x: array([0.      , 0.796435, 0.744338, 0.774606, 0.      , 0.70164 ,
E          0.734013, 0.      , 0.698528, 0.      ])
E    y: array([0.      , 0.195495, 0.077092, 0.252088, 0.      , 0.098989,
E          0.099146, 0.      , 0.073179, 0.      ])

so it seems that if you apply your proposed fix, then there is an issue. If you end up figuring out the source of your confusion, I would love to know!

Seems like perhaps we can at the very least make some extra in-line comments, or documentation to the function to explain what’s happening.

Hello
Thank you for your answer.

Thank you for letting me know even though I didn’t know that I would verify it through the test code.

After reviewing it, I think I misunderstood.

I thought the label_data_orth variable contained the orthogonal vector of n_label channels for label_data vector.

However, we found that the label_data_orth variable contained an orthogonal vector for each channel in label_data.

Thank you for noticing my mistake.

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