[Mne_analysis] Global field power

[Phillip Alday]

        External Email - Use Caution        

RMS is indeed the same as SD *when* the mean is zero. But I'm not sure
that's always the case in EEG, depending on which `picks` you have and
what the reference is.

There is also one more bit of fine print: the denominator for RMS is
pretty clear, but the denominator for SD may have a degrees of freedom
correction. So even if the case of zero mean, computing the RMS by hand
vs. calling a library function for SD may yield different results
depending on the library defaults for df. If I recall correctly,
scipy.stats actually uses a different default than numpy....


On a related topic: the R function scale() has a big note on this in its
documentation, because it allows for centering (subtracting the mean)
and/or scaling (RMS) and the combination of these two flags creates
straight centering, RMS, SD, or the identity transform.

Phillip

On 23/7/20 12:17 pm, José C. García Alanis wrote:
>
>         External Email - Use Caution        
>
> Hey everybody, hey Christoph,
>
> I believe, in this case the result of the standard deviation (SD) and
> root mean square (RMS) approach should be roughly the same (if not the
> same).
> You are right, that the RMS computation makes no subtraction of the
> mean across channels as it would be the case for the standard
> deviation. However, if the mean is zero, then the difference of a
> value to the mean it's just the value itself (the mean of the signal
> evoked.data should be pretty close to zero). Thus, the results of the
> calculations should be equivalent. But I'm open for discussion if this
> assumption is wrong.
>
> A quick snipped to test this assumption:
>
> D = np.random.normal(0, 1, 1000)
> D.std()
> 0.9586524583070871
>
> np.sqrt((D * D).mean())
> 0.9586667427413401
>
> Roughly the same. The results should vary if you assume a mean != 0.
>
> Best,
> José
>
>
>
> Am Do., 23. Juli 2020 um 10:53 Uhr schrieb Christoph Huber-Huber
> <christoph at huber-huber.at <mailto:christoph at huber-huber.at>>:
>
>             External Email - Use Caution        
>
>     Hi list,
>
>     I recently came across that mne python uses 3 different formulas
>     for calculating global field power (GFP). I’m wondering why.
>     They are:
>
>     - The spatial standard deviation
>     line 1492 of /mne/viz/utils.py
>     gfp = evoked.data.std(axis=0)
>     This is the original version as e.g. in Lehmann & Skrandies
>     (1980) dx.doi.org/10.1016/0013-4694(80)90419-8
>     <http://dx.doi.org/10.1016/0013-4694(80)90419-8>
>     Note that the fieldtrip folks write about global field power “The
>     naming implies a squared measure but this is not the case.” (see
>     help text of the FT_GLOBALMEANFIELD function of the fieldtrip
>     toolbox).
>
>     - Root mean square
>     line 2988 of /mne/viz/utils.py
>     combine_dict['gfp'] = lambda data: np.sqrt((data ** 2).mean(axis=1))
>     There is no subtraction of the mean across channels as would be
>     the case for standard deviation.
>
>     - Again, root mean square
>     line 466 of /mne/viz/evoked.py
>     this_gfp = np.sqrt((D * D).mean(axis=0))
>
>     - Sum of squares
>     line 131 of
>     /examples/time_frequency/plot_time_frequency_global_field_power.py
>     gfp = np.sum(average.data ** 2, axis=0)
>     Here, we’re dealing with power values of a time-frequency
>     decomposition, so that’s perhaps the reason for the missing mean
>     and sqrt?
>
>     The mne python glossary at /doc/glossary.rst describes GFP as “the
>     standard deviation of the sensor values at each time point”,
>     consistent with Lehmann & Skrandies. That seems to be correct only
>     for the first formula mentioned here.
>
>     Any suggestions for the reasons of when to use which version and
>     educated guesses of whether these differences matter in practice
>     are highly welcome.
>
>     Thank you very much,
>     Christoph
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