[Mne_analysis] [Freesurfer] question about how to calculate COV for MNE
Joseph Dien
jdien07 at mac.com
Mon Apr 7 17:26:28 EDT 2014
This is helpful, thanks!
Some further thoughts and questions:
1) Given how whitening is conducted, the reference choice would be critical. I want to make sure that when my software writes out the COV information to the -cov.fif file, that it is doing it correctly. How is referencing being handled? For example, is the COV info always average referenced even if the data accompanying it has not been average referenced yet? Or is it always in the current referencing scheme with the reference info sent along separately so it can be taken into account later? Or what?
2) I also see part of what was confusing me. It sounded as though 4.17 was for when one is averaging data together whereas 6.3 is for when one is subtracting or summing. So when combining subject averages together into a grand average, one would use the 4.17 procedure, which quite rightly made no sense to me. Instead, 4.17 is intended for the situation where ideally only noise is present and the goal is to just weight the estimates of noise according to their quality (the number of observations used to generate them) when combining them, which in the case of two perfect COV estimates of noise will not change when combined together (still perfect).
So I understand 4.17 now. I am still wrestling with how 6.3 is to be applied. My understanding is that when one adds or subtracts two epochs with nothing but random noise, the noise level does not change. If anything the noise level (variance over the epoch) increases as I just demonstrated to myself with an Excel spreadsheet. The noise level improvement only occurs when one takes the average of the epochs and is well known in the EEG field to occur following a square root of the number of observations involved.
So what situation is 6.3 intended for? It seems to indicate that if one takes a difference wave (say ERP to incongruent word minus congruent word) then one should calculate Leff as described and then obtain the new COV by dividing the original COV (C-zero) by Leff. Given the previous paragraph, this procedure doesn’t make sense to me since the noise level (as measured by COV) should not be decreasing. So I’m clearly still missing something.
From a practical perspective, I’m asking because I want to make sure my software generates the correct COV for difference waves.
Respectfully,
Joe
On Apr 7, 2014, at 10:01 AM, Hari Bharadwaj <hari at nmr.mgh.harvard.edu> wrote:
> Hi Joe,
> Thought I'll mention a couple of things that might help understand the scaling etc.
>
> (1) the noise cov that is computed and stored in the -cov.fif files corresponds to the covariance of the measurement noise in the *raw* data and hence when using it to localize multitrial *averaged* evoked responses, it is scaled by the number of trials in the average (based on the assumption that noise is independent from trial to trial and hence scales that way).. Look for the "nave" input when generating "stc" files.
>
> (2) whether you add or subtract two *average* evoked responses, the resulting noise distribution is the same (i.e., still mean zero and variance depending on the numbers of trials in each condition).. More generally when you take an arbitrary linear combination of two or more averaged responses, the mean is still zero for the noise and the variance scales depending of the weights for each condition and numbers of trials that went into the corresponding averages.
>
> (3) based on (2), considering the common special case of a difference response of two (separately averaged) conditions, if the number of trials in each of the two conditions that went in were not the same and are instead L1 and L2 respectively, then the effective scaling of the noise (from raw to the difference waveform) variance is what is calculated as Leff.
>
> HTH,
> Hari
>
>
> Hari Bharadwaj
> PhD Candidate, Biomedical Engineering,
> Auditory Neuroscience Laboratory
> Boston University, Boston, MA 02215
>
> Martinos Center for Biomedical Imaging,
> Massachusetts General Hospital
> Charlestown, MA 02129
>
> hari at nmr.mgh.harvard.edu
> Ph: 734-883-5954
>
> On Apr 6, 2014, at 11:40 PM, Joseph Dien <jdien07 at mac.com> wrote:
>
>> I should say Python, not C++…
>>
>> On Apr 6, 2014, at 11:31 PM, Joseph Dien <jdien07 at mac.com> wrote:
>>
>>> Fair enough! Just trying to understand what Section 6.3 is trying to communicate. So let me try another possible interpretation:
>>>
>>> Compute the COV for the two conditions. When subtracting the two conditions, the accompanying COV matrix (same for both conditions since they were pooled when computing it) is divided by Leff. Likewise the accompanying degrees of freedom (used if it is subsequently averaged together with another COV matrix per Section 4.17) is set equal to Leff.
>>>
>>> Not saying this is a procedure that makes sense to me either, just asking what the intent is of the MNE developers. Based on your response, this is currently my best guess, although it doesn’t make sense to me either since dividing the COV matrix by a single scalar (however computed) shouldn’t affect computations about relative noise levels in the channels. Basically, I’m not sure what is being done with COV so it’s hard for me to judge what is a reasonable interpretation of Section 6.3.
>>>
>>> I appreciate the link to the code, but since I’m a Matlab programmer not a C++ programmer, it’s very hard for me to parse the code. If someone could just tell me what is to be done according to 6.3 when computing a difference wave rather than just what not to do, this would be greatly appreciated. I’m trying to add support for FIFF file format to my Matlab EEG software analysis suite (http://sourceforge.net/projects/erppcatoolkit/) and want to make sure I’m doing it in a manner that would be acceptable to the MNE developers, for the benefit of the users of my package.
>>>
>>> Thanks for taking the time to read my question!
>>>
>>> Joe
>>>
>>>
>>>
>>> On Apr 5, 2014, at 5:51 AM, Alexandre Gramfort <alexandre.gramfort at telecom-paristech.fr> wrote:
>>>
>>>> hi joe,
>>>>
>>>>>> I have a question about how to calculate the COV for the MNE software.
>>>>>> As I understand it from Section 4.17 of the 2.7.3 MNE manual, if one is
>>>>>> averaging together COV matrices, one weights them by the number of
>>>>>> observations going into each one. I also see from Section 4.17.2 that these
>>>>>> are technically not covariance matrices so much as sum-of-squares matrices
>>>>>> where the epochs going into each variable has been baseline corrected.
>>>>>>
>>>>>> Assuming my understanding so far is correct, my question is about how to
>>>>>> proceed when making linear combinations of COV matrices, as in a difference
>>>>>> wave, as discussed in Section 6.3. Would the following be the correct
>>>>>> procedure?
>>>>>>
>>>>>> Compute the COV separately for the two conditions (say standard and rare
>>>>>> oddballs). Subtract the two COV matrices to obtain C0.
>>>>
>>>> Subtracting two COV matrices is a bad idea. You can make the new cov
>>>> non positive.
>>>>
>>>> basically the noise cov is just to estimate the noise so any sample you use
>>>> to get a better estimate the better. There is no condition or contrast
>>>> at this stage.
>>>>
>>>> for source reconstruction you should use the same noise cov for the two
>>>> conditions to have the same inverse operator.
>>>>
>>>> you can look at this file to know more about the internals:
>>>>
>>>> https://github.com/mne-tools/mne-python/blob/master/mne/cov.py
>>>>
>>>> HTH
>>>> Alex
>>>>
>>>>
>>>>>> Then calculate C by
>>>>>> dividing by Leff, which in turn is calculated as Leff= (L1*L2)/(L1+L2) where
>>>>>> L1 is the number of observations in the first COV matrix and L2 is for the
>>>>>> second.
>>>>>>
>>>>>> But if done in this way, the two COV matrices would not be weighted by
>>>>>> their relative sample sizes. So would I also weight them by L1 and L2
>>>>>> during the subtraction, as done for averaging per 4.17? But then what is
>>>>>> the purpose of the Leff calculation? Or is the idea that one would calculate
>>>>>> a single COV based on both conditions and then one would modify COV by Leff
>>>>>> to reflect that the signal-to-noise ratio has been reduced by combining two
>>>>>> averages with differing sample sizes? But in the case where both samples
>>>>>> equal, say, 10, Leff would end up equalling 100/20=5. Dividing C by 5 seems
>>>>>> like too much. Anyway, very confused. Any guidance would be appreciated.
>>>>>>
>>>>>> Respectfully,
>>>>>>
>>>>>> Joe
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>> --------------------------------------------------------------------------------
>>>>>>
>>>>>> Joseph Dien,
>>>>>> Senior Research Scientist
>>>>>> Maryland Neuroimaging Center
>>>>>> University of Maryland
>>>>>>
>>>>>> E-mail: jdien07 at mac.com
>>>>>> Phone: 202-297-8117
>>>>>> http://joedien.com
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>
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>>>
>>> --------------------------------------------------------------------------------
>>>
>>> Joseph Dien,
>>> Senior Research Scientist
>>> Maryland Neuroimaging Center
>>> University of Maryland
>>>
>>> E-mail: jdien07 at mac.com
>>> Phone: 202-297-8117
>>> http://joedien.com
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>
>>
>> --------------------------------------------------------------------------------
>>
>> Joseph Dien,
>> Senior Research Scientist
>> Maryland Neuroimaging Center
>> University of Maryland
>>
>> E-mail: jdien07 at mac.com
>> Phone: 202-297-8117
>> http://joedien.com
>>
>>
>>
>>
>>
>>
>>
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--------------------------------------------------------------------------------
Joseph Dien,
Senior Research Scientist
Maryland Neuroimaging Center
University of Maryland
E-mail: jdien07 at mac.com
Phone: 202-297-8117
http://joedien.com
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