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Sep 14, 2012  03:09 PM
MVPA analysis questions
Alfonso

I have a number of questions about this analysis. Sorry for so many but I figured I would fit them in all at once.

1) Do you have any references for the MVPA analysis? I didn't see anything listed in the brain connectivity paper.  I'm a bit puzzled by it as I can't tell what it is doing under the hood. Is it just a PCA?I read through your advice on the forum but I'm not quite sure about looking at the contrasts and the results.I have 15 subjects. They are studied before and after a medication.2) From the comments in the forum I guess you would suggest 64 first level and 2 or at most 3 second level dimensions?3) In the second level window would I do the following - Subject level: 1 - Conditions: Select both conditions: Can I set the contrast to [1 -1] or should it be eye(2)?  You mention looking at f-tests or 2 sided t-tests, but I wasn't sure where to set that up. I'm guessing that eye(2) does an F-test, while [-1 1] could be a two-sided t-test when the results window comes up. - Measures: Would I select all the connectome-MVPA dimensions or can they be examined 1 at a time?4) Once the results window comes up, a lot of the brain is significant! Unless I use a very low height threshold (0.000001) it looks like one big blob. Is this usual? 5) I'm not sure how to explore the results further. You mention looking at it in SPM. What images should I forward to SPM or how is this done? You also mention using the regional results in a seed-to-voxel analysis, however, with so much of the brain "lighting up" this seems difficult. 6) If I want to look at pre and post separately is it appropriate to just select one of them and look at the maps for just pre or just post? 7)  When I look at the conditions separately I notice that pre is negative (blue) and post is positive (red). I understand that positive and negative are not absolute with these types of analyses, but would it be fair to say that the opposite response is seen between conditions?8) I notice when I click on the results table different parts of the glass brain are colored yellow corresponding to the voxels associated with a particular cluster. Is there an image where these results are all available that is coded by a different value for each network? This would make is easy to overlay the image and color it by the value, or how is this information stored (i.e., how are the different networks of voxels selected)?
Thanks,
Darren
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Sep 18, 2012  11:09 AM
RE: MVPA analysis questions
Dear Darren,
I have also been playing with conn and voxel-to-voxel conectum maps. I was interested to test how connectivity maps for different experimental conditions vary.
First, conn automatically creates folders with SPM file and beta images, which we can then explore and do statistics as normal with SPM results function.
Second, The apparent view that the whole brain lights up is partly a result of the fact the view is transparent, but it is common.
To explore the results of each eigenimage in the conn contrast window: select the relevant things yon want to explore and enter - between subject [1] between condition[1] and between measure [1] depending on how many component you estimated. then click voxel-to-voxel result explore. In the window you get, on the right corner, you can choose to see negative, positive or both etc.

Finally, similar to your point 7, we have also found that the results of comparing across the conditions are also driven by opposite signs in eth components (positive in two condition while negative in a third). Interestingly, the two conditions that are positive are similar while the negative condition is different psychologically. But we are not sure how to interpret the results. 

I am debating with my colleagues what is the meaning of a negative value in PCA? is it de-activation? is it less synchronization? or is it simply different networks than the one that are positive, hence we really should ignore the signs when comparing across eigenimages and maybe use only absolute values.

thanks and looking forward hearing your and Alfonso thought
Alla (&Pia)
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Sep 18, 2012  11:09 AM
RE: MVPA analysis questions
Dear Alla and list

I received the following very detailed and helpful reply from Alfonso, which I think answers some of your questions as well. In brief, exploring individual eigen components or individual conditions is not advised. Also as a consequence of how the calculation is done the conditions are demeaned and this appears to force one to be negative and the other positive, so not much can be made of this difference. Details below.

Darren

On Wed, Sep 12, 2012 at 11:21 PM, Darren Gitelman <[url=mailto:d-gitelman@northwestern.edu]d-gitelman@northwestern.edu[/url]> wrote:
AlfonsoSusan suggested I contact you about the MVPA analysis. Sorry for so many questions. 1) Do you have any references for this type of analysis? I didn't see anything listed in the brain connectivity paper.  I'm a bit puzzled by it as I can't tell what it is doing under the hood. Is it just a PCA?
We are currently working on a manuscript describing this type of analysis (I am hoping it will be ready in a few weeks and I will be happy to send you an preliminary copy when it is ready if you would like), the analyses are relatively straightforward, they simply perform a PCA (separately for each voxel) characterizing the functional connectivity between this voxel and the rest of the brain, and then store the resulting component scores as functional maps that can be entered into standard second-level analyses for between-group or between-condition tests. 
 
I read through your advice on the forum but I'm not quite sure about looking at the contrasts and the results.I have 15 subjects. They are studied before and after a medication.2) From the comments in the forum I guess you would suggest 64 first level and 2 or at most 3 second level dimensionsA?
Yes, that sounds perfectly reasonable 
3) In the second level window would I do the following - Subject level: 1 - Conditions: Select both conditions: Can I set the contrast to [1 -1] or should it be eye(2)?  You mention looking at f-tests or 2 sided t-tests, but I wasn't sure where to set that. I'm guessing that eye(2) does an F-test, while [-1 1] could be a two-sided t-test when the results window comes up.
 - Measures: Would I select all the connectome-MVPA dimensions or can they be examined 1 at a time?
Typically you would select both conditions and set the between-conditions contrast vector to [1 -1]. Then you would select all of your MVPA dimensions (e.g. 3) and set the between-measures contrast to 'eye(3)'. This will perform an f-test that compares (for each voxel) the 3 component scores across the two conditions (so that significant results for any given voxel mean that the functional connectivity pattern between this voxel and the rest of the brain differs across conditions).  
 
4) Once the results window comes up, a lot of the brain is significant! Unless I use a very low height threshold (0.000001) it looks like one big blob. Is this usual?
That is unusual, could you please let me know more details about what specific contrast you are specifying in this case? (also please be sure to be using the latest version of the software -currently version 13L-, if I recall correctly an earlier release contained a bug in the MVPA computation across multiple conditions that may be affecting your results)
 
 5) I'm not sure how to explore the results further. You mention looking at it in SPM. What images should I forward to SPM or how is this done? You also mention using the regional results in a seed-to-voxel analysis, however, with so much of the brain "lighting up" this seems difficult.
We are currently collecting users feedback and working to automate the process of performing this sort of post-hoc analyses in the software, but you are right that one typically finds at most a few areas rather than most of the brain "lighting up". The standard post hoc analyses typically involve creating a mask with the areas that 'light up', and then using these areas as seeds in seed-to-voxel analyses. 
 
 6) If I want to look at pre and post separately is it appropriate to just select one of them and look at the maps for just pre or just post?
Not really, these analyses are designed for detecting differences in connectivity between groups or between conditions. The results are not particularly meaningful if you simply select a single condition (e.g. in this case, because the PCA decomposition removes the mean across all subjects and conditions, the principal-component-score maps for each individual condition are implicitly centered, so effectively a contrast of [1,0] is equivalent to a contrast [0.5 -0.5])
 
 7)  When I look at the conditions separately I notice that pre is negative (blue) and post is positive (red). I understand that positive and negative are not absolute with these types of analyses, but would it be fair to say that the opposite response is seen between conditions?
No, the individual score maps should not be used to interpret any potential between-group or between-condition differences. In particular in this case, and for the same reasons as above (the maps are effectively 'centered' by the PCA decomposition step), it is always the case that you should get exactly opposite signs for each voxel when looking at the individual conditions separately (when looking at the first condition you are effectively entering a contrast of the form [0.5 -0.5], while when looking at the second condition you are then effectively entering a contrast of the form [-0.5 0.5]), so one should not interpret those results as 'opposite responses' across conditions. The appropriate test here is to simply use a [1,-1] between-conditions contrast, which will indicate which areas show between-condition differences in connectivity, and then performing post-hoc analyses to characterize these differences. 
8) I notice when I click on the results table different parts of the glass brain are colored corresponding to the voxels associated with a particular cluster. Is there an image where these results are all available that is coded by a different value for each network? This would make is easy to overlay the image and color it by the value, or how is this information stored?
If you click on the 'export mask' button and create a file with the supra-threshold voxels, you can then type the following in matlab to create a volume with a different value for each cluster:
rex(filename,filename,'level','clusters','output_type','save','output_files',{'roi.img'},'gui',0);
(where filename is the name of the mask file). This will create a new file where each suprathreshold voxel is labeled with a number identifying each cluster (e.g. you can then enter this file as a seed in the conn toolbox to perform post hoc seed-to-voxel analyses)
Hope this helps!
Best
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Sep 18, 2012  06:09 PM
RE: MVPA analysis questions

Dear Darren,

Thank you for your reply. Possible the coming
manuscript will highlight some questions that i have after Alfonso's answers:

1. Why conditions are dependent on each other in some
way? i.e., why one condition forces others to be negative? If I do understand
correctly, computing SVD (=PCA when M voxel separately assumes that the SVD is performed on a matrix MxN where M - a
number of scans and N - correlation values between this one particular voxel
and the rest of the brain. After all standard procedures (mean normalisation,
defining eigenvectors in space and time and eigenvalues) normally we will get a
Principal Component (say, we are interested in only first one) that consists of
different values and can be positive and negative (please, see any papers on
SVD).  After an arbitrary thresholding highly correlated voxels (! highly
correlated with our particular voxel) with positive and negative values will
compose our first Principal component. Right? In previous studies (e.g.,
Worsley et al., 2005) the positive and negative signs were interpreted as:
(citing:
In non-mathematical terms, SVD seeks to express the
correlation structure by a small number of “principal components” multiplied by
random weights that vary randomly over time or subject. Voxels with high
principal component values clearly co- vary together and are therefore
positively correlated; voxels with high opposite signed components co-vary in
opposite senses and are therefore negatively correlated. In practice we extract
the first few principal components, then threshold these components at an arbitrary
level (since there is as yet no P-value results for local maxima of principal
or independent components). These regions are then our estimate of the
connected voxels).
 

My question is: how the negative and positive signs
are treated in conn? Does conn takes only the absolute value (if so - why?
Rotation-invariant explanation is does not solve the problem with
interpretation and mathematical meaning of the components of SVD).

2. How the principal components for each voxel are
mapped in the brain? Say, we have got that principal component for voxel 1
included some highly correlated voxels, e.g. voxels 10, 11, 12. For voxel 2 we
have got highly correlated voxels 10, 11, 15, 17. So how the overlapped
components are mapped? Logically, in some cumulative manner.

I have some questions more, but these two above are
crucial for understanding conn.

Darren and Alfonso, may I ask your opinion? Thank you
in advance.






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Sep 18, 2012  09:09 PM
RE: MVPA analysis questions
Dear Alla,

Regarding your questions let me first try to clarify in a bit more detail what these 'principal component scores' in the voxel-to-voxel MVPA analysis mean to see if this helps.

Let's say that for a single voxel of interest we have computed the functional connectivity between this voxel and the rest of the brain for every subject/condition in our experiment (let's say we have 15 subjects and 2 conditions, so we end up with 30 'seed-to-voxel' maps using our original voxel of interest as 'seed'), and we were to stack those maps into a MxN matrix (where M is the number of subjects*conditions -30 in our example- and N is the number of voxels in the brain). We are interested in representing this matrix using a lower-dimensional representation that would capture most of the between-subjects/conditions variability in functional connectivity patterns between our voxel of interest and the rest of the brain, so we perform a principal component decomposition of this matrix and obtain a set of K 'principal components' (a NxK matrix of 'spatial' components) as well as a set of K 'principal component scores' (a MxK matrix of component scores).
Let's say for simplicity that we are only interested in the first component. The first 'spatial component' would be a Nx1 vector (a spatial map), and the 'principal component scores' of interest are a simple Mx1 vector (a single number for each subject/condition). These latter numbers are the ones that we are going to be later entering into a second-level analysis. By definition these numbers have maximal between-subjects/conditions variance (there is no other normed linear combination of the columns of our original MxN matrix that results in a set of numbers with higher variance than our first principal component scores), and they have zero mean.

To use a particular example, let's say that we visually explore the functional connectivity patterns between our original voxel of interest and the rest of the brain and we notice that most of the between-subjects/conditions variability seems to dominated by some subjects/conditions showing markedly higher connectivity between our original voxel of interest and some particular brain area, while other subjects/conditions show markedly lower connectivity between our voxel of interest and this same brain area. In this case the first 'spatial component' would be characterized by having positive (/negative) values over this particular area and values closer to zero otherwise. Similarly the first 'component score' values would be characterized by having positive (/negative) values for those subjects/conditions that showed higher connectivity with this particular area, and negative (/positive) values for those subjects/conditions that showed lower connectivity with this particular area.

We can then enter these 'principal component score' values into a standard between-subjects/conditions analysis to find out whether these values are associated with our conditions of interest (e.g. is it the case that the the data from condition 1 shows significantly different 'principal component score' values than those coming from condition 2). A significant result in these analyses indicates that the functional connectivity patterns between our original voxel of interest and the rest of the brain seem to be modulated by the experimental condition. Note that because the 'principal component scores' have zero mean, if we take any arbitrary split of our data into two sets, it will always be the case that the average scores within the first set will have opposite sign than the average scores within the second set (e.g. the averages add up to zero for equal-sized sets). The question that these second-level analyses address is whether the *size* of this difference (when splitting the data using our two experimental conditions) is large enough to be considered statistically significant (compared to the total between-subjects/conditions variability).

Last, note that in our example we have always considered an original voxel of interest. The voxel-to-voxel MVPA analyses effectively repeat this exact process for *every* voxel in the brain (so instead of having 30 'principal component score' values, one for each subject/condition, we end up having 30 'principal component score' maps, where the value at any specific voxel represents the principal component score value as discussed above), and perform the second-level analyses jointly across all voxels simply entering these maps into our desired between-subjects/conditions analyses. When you find in your results any particular voxel as significant (let's say in our example we find the original voxel of interest as significant because the functional connectivity between this voxel and the other particular brain area that we discussed in our example above was modulated by the experimental condition), one could theoretically then go and look at the 'spatial principal components' associated with the specific between-subjects/conditions difference in scores found in order to better characterize what this difference 'means' (find out that the culprit was the level of association between this voxel and that other particular brain area), but due to storage limitations those 'spatial principal component' maps are not actually being saved anywhere (they would require storing K spatial maps *for each voxel*, which is an incredible amount of storage space) so the easiest approach is to simply use those supra-threshold voxels as seeds in standard seed-to-voxel analyses as post-hoc analyses, and that will show you how specifically the connectivity between this voxel and the rest of the brain is being modulated by your experimental condition.

Let me know if this helps clarify the interpretation a bit.

Best
Alfonso


Originally posted by alla yankovskaya:

Dear Darren,

Thank you for your reply. Possible the coming
manuscript will highlight some questions that i have after Alfonso's answers:

1. Why conditions are dependent on each other in some
way? i.e., why one condition forces others to be negative? If I do understand
correctly, computing SVD (=PCA when M voxel separately assumes that the SVD is performed on a matrix MxN where M - a
number of scans and N - correlation values between this one particular voxel
and the rest of the brain. After all standard procedures (mean normalisation,
defining eigenvectors in space and time and eigenvalues) normally we will get a
Principal Component (say, we are interested in only first one) that consists of
different values and can be positive and negative (please, see any papers on
SVD).  After an arbitrary thresholding highly correlated voxels (! highly
correlated with our particular voxel) with positive and negative values will
compose our first Principal component. Right? In previous studies (e.g.,
Worsley et al., 2005) the positive and negative signs were interpreted as:
(citing:
In non-mathematical terms, SVD seeks to express the
correlation structure by a small number of “principal components” multiplied by
random weights that vary randomly over time or subject. Voxels with high
principal component values clearly co- vary together and are therefore
positively correlated; voxels with high opposite signed components co-vary in
opposite senses and are therefore negatively correlated. In practice we extract
the first few principal components, then threshold these components at an arbitrary
level (since there is as yet no P-value results for local maxima of principal
or independent components). These regions are then our estimate of the
connected voxels).
 

My question is: how the negative and positive signs
are treated in conn? Does conn takes only the absolute value (if so - why?
Rotation-invariant explanation is does not solve the problem with
interpretation and mathematical meaning of the components of SVD).

2. How the principal components for each voxel are
mapped in the brain? Say, we have got that principal component for voxel 1
included some highly correlated voxels, e.g. voxels 10, 11, 12. For voxel 2 we
have got highly correlated voxels 10, 11, 15, 17. So how the overlapped
components are mapped? Logically, in some cumulative manner.

I have some questions more, but these two above are
crucial for understanding conn.

Darren and Alfonso, may I ask your opinion? Thank you
in advance.






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Sep 19, 2012  06:09 AM
RE: MVPA analysis questions
Hi Alfonso,
Thank you for your explanation. Now the MVPA in conn does make a sense for me. Sorry for bombarding the forum. However, I think this will be helpful for everyone who is going to do MVPA with conn.
alla
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