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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link="#0563C1" vlink="#954F72"><div class=WordSection1><p class=MsoNormal><span style='color:black'>Hi Iman,<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>When you do re-referencing, you impose a condition on the estimated map vectors. E.g. average reference enforces the sum over the channels of the map potential to equal zero (that the map be orthogonal to e, the vector of all 1’s). Average mastoid reference will guarantee that the average of the mastoid channels in all the learned maps will be zero. Basically you make all the learned maps orthogonal to a certain direction, and you lose a degree of freedom, or a dimension in the rank of the data.<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>If the head had perfect sensor coverage over the head “sphere”, and there was limited shunting of electric field due to bone and tissue, then a source inside the head would be expected to sum to zero by charge conservation—any instantaneous increase in charge in one area must be accompanied by decrease in the charge in another area.<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>However, e.g. in the case of a radial source on the cortical surface, the negative field detected by electrodes on the side of the head/neck opposite the radial source may not have sufficient coverage or may be shunted to the extent that the source should appears to have a net positive charge, with weaker negative field detected relative to positive field. So the “actual” net charge may be non-zero.<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>Average reference though enforces zero net charge, and thus will in effect add a negative constant to each channel, decreasing the positivity, increasing the negativity, resulting in a radial dipolar source that appear to be deeper in the head than it actually is.<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>In dipole fitting, a number of factors are taken into consideration, including residual variance of a dipolar model, and physiological plausibility given say a known MRI. I would suggest that dipole fitting of a learned ICA map be carried out by optimizing the fit and plausibility of the source over both (1) dipole location/orientation, and (2) unknown constant channel offset, particularly for radial sources.<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>I believe that radial sources are often localized to deeper than MRI cortical surface, which is consistent with this idea. However, given the imprecision in tissue conductance values (see Akalin-Acar and Makeig 2013), and the general controversy over the nature of EEG sources themselves (are they confined to cortical patches, or do they represent a larger scale charge redistribution involving sub-cortical and cortical regions?), it is difficult to be certain of anything.<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>The main point about ICA being reference-free is that it however you reference the data, it won’t limit the ability of ICA to find the source. You are just imposing the reference condition on the estimated map and losing a degree of freedom (location along a single dimension). If you presume that radial sources are confined to cortical patches, then the depth ambiguity can be resolved using prior MRI information.<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>Note: this should not be taken as an official position of any organizations or communities, just my own comments argued such as they are.<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>Best,<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'>Jason<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><div><div style='border:none;border-top:solid #B5C4DF 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal><b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'>From:</span></b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'> Iman M.Rezazadeh [mailto:irezazadeh@ucdavis.edu] <br><b>Sent:</b> Friday, March 21, 2014 12:24 AM<br><b>To:</b> japalmer@ucsd.edu; 'EEGLAB List'<br><b>Subject:</b> RE: [Eeglablist] why ICA is reference-free?<o:p></o:p></span></p></div></div><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><span style='color:#1F497D'>Thanks a lot Jason! <o:p></o:p></span></p><p class=MsoNormal><span style='color:#1F497D'>It was really informative. Could you please elaborate this “</span><span style='color:black'>So when you do dipole localization with a given map, there is really an arbitrary additive constant, but presumably only one value of this constant will be consistent with a physiological source.”?<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>Best<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'>Iman</span><span style='color:#1F497D'><o:p></o:p></span></p><p class=MsoNormal><b><span style='color:#1F497D'>-------------------------------------------------------------<o:p></o:p></span></b></p><p class=MsoNormal><b><span style='color:#1F497D'>Iman M.Rezazadeh, Ph.D<o:p></o:p></span></b></p><p class=MsoNormal><span style='color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:#1F497D'>Research Associate II <o:p></o:p></span></p><p class=MsoNormal><span style='color:#1F497D'>Semel Intitute, UCLA , Los Angeles<o:p></o:p></span></p><p class=MsoNormal><span style='color:#1F497D'>& Center for Mind and Brain, UC DAVIS, Davis<o:p></o:p></span></p><p class=MsoNormal><span style='color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><a name="_MailEndCompose"></a><span style='color:#1F497D'><o:p> </o:p></span></p><div><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal><b>From:</b> Jason Palmer [<a href="mailto:japalmer29@gmail.com">mailto:japalmer29@gmail.com</a>] <br><b>Sent:</b> Thursday, March 20, 2014 8:18 PM<br><b>To:</b> 'Iman M.Rezazadeh'; 'EEGLAB List'<br><b>Subject:</b> RE: [Eeglablist] why ICA is reference-free?<o:p></o:p></p></div></div><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><span style='color:black'>Hi Iman,<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>The reference used in average referencing, or single channel or avg fiducials reference, is a linear function of the data. So e.g. in avg reference,<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal style='text-indent:.5in'><span style='color:black'>r(t) = e^T * x(t) / n<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>where e is a vector of all ones, e = [1 1 1 … ]^T, and ^T means transpose, and n is number of channels.<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>Re-referencing the data is equivalent to doing:<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'> y(t) = x(t) – e*e^T*x(t) / n<o:p></o:p></span></p><p class=MsoNormal style='text-indent:.5in'><span style='color:black'> = (I – e*e^T/n) * x(t)<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>Where I is the identity matrix, which shows that the re-referenced data is just a matrix times the original data, and has rank reduced by 1. Similarly for avgs of subsets of channels, which use I – e*g^T with a general vector g, instead of I – e*e^T.<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>So we can look at the new data as generated by,<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'> </span><span lang=FR style='color:black'>y(t) = M’ * s(t)<o:p></o:p></span></p><p class=MsoNormal><span lang=FR style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span lang=FR style='color:black'>where,<o:p></o:p></span></p><p class=MsoNormal><span lang=FR style='color:black'><o:p> </o:p></span></p><p class=MsoNormal style='text-indent:.5in'><span lang=IT style='color:black'>M’ = (I – e*g^T)*M<o:p></o:p></span></p><p class=MsoNormal style='text-indent:.5in'><span lang=IT style='color:black'> = M – e*(g^T*M)<o:p></o:p></span></p><p class=MsoNormal><span lang=IT style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>This new mixing matrix is just the original matrix with a single constant potential subtracted from each mixing map (generally different number for each map, but same number for each channel of a map).<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>So what the reference does is essentially add a constant to each channel. Average reference will tend to produce maps such that the sum over the channels of the potential of each map is zero, consistent with charge conservation and dipolarity.<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>So when you do dipole localization with a given map, there is really an arbitrary additive constant, but presumably only one value of this constant will be consistent with a physiological source.<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>Hope that is helpful.<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>Best,<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'>Jason<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><div><div style='border:none;border-top:solid #B5C4DF 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal><b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'>From:</span></b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'> <a href="mailto:eeglablist-bounces@sccn.ucsd.edu">eeglablist-bounces@sccn.ucsd.edu</a> [<a href="mailto:eeglablist-bounces@sccn.ucsd.edu">mailto:eeglablist-bounces@sccn.ucsd.edu</a>] <b>On Behalf Of </b>Iman M.Rezazadeh<br><b>Sent:</b> Monday, March 17, 2014 4:31 PM<br><b>To:</b> 'EEGLAB List'<br><b>Subject:</b> [Eeglablist] why ICA is reference-free?<o:p></o:p></span></p></div></div><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Hi, <o:p></o:p></p><p class=MsoNormal>Could you please elaborate why ICA is reference-free? In other words, does different kinds of referencing methods (avg-ref or …) effect on ICA maps and source series ? <o:p></o:p></p><p class=MsoNormal>Suppose: x(t) is the signal then we have s(t)=M(^-1). x(t) ;where s(t) is source signals and M is the mixing matrix.<o:p></o:p></p><p class=MsoNormal>Now how come for y=x(t)-r(t) - where r(t) is another reference- result same/different maps and source series would be obtained and how could someone get the same dipole locations with different re-referencing methods?<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>It would be great if someone gives in depth <b>methodological and mathematical explanations</b> rather than just qualitative explanations.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Best<o:p></o:p></p><p class=MsoNormal>Iman<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><b>-------------------------------------------------------------<o:p></o:p></b></p><p class=MsoNormal><b>Iman M.Rezazadeh, Ph.D<o:p></o:p></b></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Research Fellow<o:p></o:p></p><p class=MsoNormal>Semel Intitute, UCLA , Los Angeles<o:p></o:p></p><p class=MsoNormal>& Center for Mind and Brain, UC DAVIS, Davis<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p></div></body></html>