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<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black">Eelke<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black">Thanks for your response. It’s a good answer and helps to elucidate my question, but part of the question remains. Your description of a) b) and c) were implicit in my
question, so maybe this is the crux:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black">The 1) and 2) below are probably identical. Doing this in the leadfield results in the 1 x nvoxel LF coefficients; then applying a filter (eLORETA, sLORETA) to the 1
x nv LF coefficients, is probably the same as first doing the filter and then the max orientation SVD (e.g., 2).<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black">I guess the critical question is what 3) is doing? What does it mean “the data covariance is projected through the filters”?<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black">I have not tried 1) (leadfield step), but have done 2) and 3) and they give different results. I presume this is because the orientation of the filters in 2) is not the
same as the orientation of the filters modified by the data in 3).<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black">Also, re your note below… If I have X and Y datasets, and do 2), then the orientation of the projection will be the same for X and Y. But doing 3), the projection is
based on the data, <o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black">e.g. svd(filter) * data and svd(filter*covX*filter’)*data give different results; so that the orientation of svd(filter*covX*filter’) is a different orientation than
svd(filter*covY*filter). I worry that the difference in orientation between the two datasets might confound experimental conditions effect differences in X and Y. Are the “data sources” different, or is it just a chance occurrence due to the orientation differences.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black">One reason this came up is that we have two related sets of data, like X and transform(X), where the transform is a cwt operation. It turns out that<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black">Correlation (X and transformX in the channel*time) = 1<br>
svd(filter)*X and svd(filter)*transform(x) also result in an identity matrix across nvoxels; (correlation over time, for each nvoxel)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black">But svd(filter*covX*filter’)*X, and svd(filter*CovY*filter’)*Y, show weird patterns of correlations—some nvoxels are 1, some nvoxeks are -1, and then some are in the
middle range; or they are strong positive but not 1 (like .8 to 1). <o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black">The use of the cov in the svd definitely changes the results<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black">This might not make a difference in the pattern of responses, but the orientation of some of the analyses flips from 1 to -1, and the intermediate correlations mean that
the results from the svd(filter*COV*filter’) is changing the results.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black">John<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black">Hi John,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black">I'm not sure the following is a full answer to your questions, but<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black">it's definitely relevant to both of them. As you say, there are by<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black">default 3 dipole orientations along which activity is considered. We<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black">can combine these three into one (using SVD or similar) at (at least)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black">three possible levels:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black">(a) the level of the leadfield;<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black">(b) the level of the filters;<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black">(c) the level of the source-reconstructed data.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black">What you are suggesting in question 2 is approach b. Your phrasing<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black">("the leadfield step") suggests that your proposal would be approach<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black">a, but unless I'm misunderstanding you really are proposing approach<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black">b.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black">What by default is implemented in FieldTrip (cfg.projectmom = 'yes')<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black">is approach c. This I think answers your question 1: the data<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black">covariance is projected through the filters in order to determine the<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black">maximum orientation of the source-reconstructed data.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black">Also of relevance: you can use the non-downprojected (3xN) filters, as<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black">computed based on some data X, and apply them to some data Y, and only<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black">downproject after that. This might result in a different orientation<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black">being the "maximal" one, as the maximum (in approach c) depends not<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black">only on the filters (and hence the leadfield), but also on the data.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black">Hope that helps.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black">Best,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Courier New";color:black">Eelke<o:p></o:p></span></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas;color:black">***********************************************<br>
John E. Richards<br>
Carolina Distinguished Professor<br>
Department of Psychology<br>
University of South Carolina<br>
Columbia, SC 29208<br>
Dept Phone: 803 777 2079<br>
Fax: 803 777 9558<br>
Email: </span><a href="mailto:richards-john@sc.edu"><span style="font-size:10.0pt;font-family:Consolas;color:#0563C1">richards-john@sc.edu</span></a><u><span style="font-size:10.0pt;font-family:Consolas;color:blue"><br>
</span></u><span style="font-size:10.0pt;font-family:Consolas;color:black">https://jerlab.sc.edu<br>
*************************************************<br>
<br>
</span><o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
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