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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D">Thanks Makoto. I think I understand that if you apply PCA and picked the first 30 components from it then your K-factor is increased , since you have 30 PCA signals
– instead of 100ch.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D">However:<o:p></o:p></span></p>
<p class="MsoListParagraph" style="text-indent:-.25in;mso-list:l0 level1 lfo1"><![if !supportLists]><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D"><span style="mso-list:Ignore">1)<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><span dir="LTR"></span><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D">Picking up the first 30 PCA components would not let you to reconstruct the data perfectly!<o:p></o:p></span></p>
<p class="MsoListParagraph" style="text-indent:-.25in;mso-list:l0 level1 lfo1"><![if !supportLists]><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D"><span style="mso-list:Ignore">2)<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><span dir="LTR"></span><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D">If you apply ICA to those 30 PCA signals ( not the original 100ch data) then you will have 30 ICA sources. But what is the relationship
btw each ICA source and original recording? In other words, how can you back-project each ICA source to the original recording montage ( ie , 100ch) ? After performing PCA and later ICA , the (un)mixing matrix dimension is 30 x 30 not 100 x 100. Thus, I am
still confused how the outcome IC maps after PCA+ICA would be meaningful !<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D">Iman
<o:p></o:p></span></p>
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<span dir="LTR" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><a name="_MailEndCompose"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D"><o:p> </o:p></span></a></p>
<p class="MsoNormal"><b><span style="font-size:11.0pt;font-family:"Calibri",sans-serif">From:</span></b><span style="font-size:11.0pt;font-family:"Calibri",sans-serif"> Makoto Miyakoshi [mailto:mmiyakoshi@ucsd.edu]
<br>
<b>Sent:</b> Thursday, April 21, 2016 10:04 AM<br>
<b>To:</b> Iman Mohammad-Rezazadeh <irezazadeh@UCDAVIS.EDU><br>
<b>Cc:</b> EEGLAB List <eeglablist@sccn.ucsd.edu>; Arnaud Delorme <arno@ucsd.edu>; Loo, Sandra <SLoo@mednet.ucla.edu>; Jeste, Shafali M.D. <SJeste@mednet.ucla.edu>; ADickinson@mednet.ucla.edu; Scott Makeig <smakeig@ucsd.edu><br>
<b>Subject:</b> Re: ICA after PCA<o:p></o:p></span></p>
<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">Dear Iman,<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">It does not increase K directly, but effectively it does.<o:p></o:p></p>
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<p class="MsoNormal">If you have 100ch and K==30 (fixed), you need (100^2) * 30 data points.<o:p></o:p></p>
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<p class="MsoNormal">But if you apply PCA on it and reduce it to 10 PCs, you need only (10^2) * 30 data points. In this case, your K is effectively multiplied by 100^2/10^2 ==100.<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">Note that the value K should increase exponentially as the number of channels increases. K==30 is for the case of 32ch. There is no good study on the question how many data points are necessary for stable ICA results, but Jason says 1 million
datapoints for 100ch is a rule of thumb (in this case, K==100).<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">Makoto<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">On Thu, Apr 21, 2016 at 12:22 AM, Iman Mohammad-Rezazadeh <<a href="mailto:irezazadeh@ucdavis.edu" target="_blank">irezazadeh@ucdavis.edu</a>> wrote:<o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D">Hi Makoto,
</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D">My question is : does doing PCA before ICA helps for increasing K or in other words the quality of
ICA output? Could you please describe it in a simple language </span><span style="font-size:11.0pt;font-family:Wingdings;color:#1F497D">J</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><a name="m_3005474271639261324__MailEndCompose"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D">Thanks</span></a><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D">Iman</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><b><span style="font-size:11.0pt;font-family:"Calibri",sans-serif">From:</span></b><span style="font-size:11.0pt;font-family:"Calibri",sans-serif"> Makoto Miyakoshi [mailto:<a href="mailto:mmiyakoshi@ucsd.edu" target="_blank">mmiyakoshi@ucsd.edu</a>]
<br>
<b>Sent:</b> Wednesday, April 20, 2016 7:01 PM<br>
<b>To:</b> Iman Mohammad-Rezazadeh <<a href="mailto:irezazadeh@UCDAVIS.EDU" target="_blank">irezazadeh@UCDAVIS.EDU</a>><br>
<b>Cc:</b> EEGLAB List <<a href="mailto:eeglablist@sccn.ucsd.edu" target="_blank">eeglablist@sccn.ucsd.edu</a>>; Arnaud Delorme <<a href="mailto:arno@ucsd.edu" target="_blank">arno@ucsd.edu</a>>; Loo, Sandra <<a href="mailto:SLoo@mednet.ucla.edu" target="_blank">SLoo@mednet.ucla.edu</a>>;
Jeste, Shafali M.D. <<a href="mailto:SJeste@mednet.ucla.edu" target="_blank">SJeste@mednet.ucla.edu</a>>;
<a href="mailto:ADickinson@mednet.ucla.edu" target="_blank">ADickinson@mednet.ucla.edu</a>; Scott Makeig <<a href="mailto:smakeig@ucsd.edu" target="_blank">smakeig@ucsd.edu</a>><br>
<b>Subject:</b> Re: ICA after PCA</span><o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">Dear Iman,<o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">> I have found few papers and discussions about doing PCA and then ICA for increasing the K-factor and dimensionality reduction.<o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">K-factor you mean is the term you see in the equation?<o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">minimumDataPointsToRunICA = ((number of channels)^2) * K<o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">> However, I cannot completely understand what is the meaning of the ICA outputs? <o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">ICA output rotates PCA-dimension-reduced data. You can reconstruct full-channel (but now rank-deficient) data using PCA output.<o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">Actually there is another rotation, sphering, as a preprocess for ICA. So you rotate data three times to find unmixing matrix using PCA rank-reduction option. That's why you feel
dizzy :-)<o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">Makoto<o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">On Wed, Apr 13, 2016 at 11:59 PM, Iman Mohammad-Rezazadeh <<a href="mailto:irezazadeh@ucdavis.edu" target="_blank">irezazadeh@ucdavis.edu</a>> wrote:<o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">Hi EEGLABers,<o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">I have found few papers and discussions about doing PCA and then ICA for increasing the K-factor and dimensionality reduction. The (un)mixing matrix would be m x m which m is the
number of PCA. Each row (column) is the weights for ICA sources.<o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">However, I cannot completely understand what is the meaning of the ICA outputs? How are the IC maps (topo maps) constructed since we need the location of PCA components (similar
to the channels locations) to plot the spatial filters/IC maps. <o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">In other words, how can we plot the IC maps given the fact that we don’t have the spatial information about PCA components?<o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">Best<o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">Iman
<o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">============================================<o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><b><span style="font-size:10.0pt;font-family:"Arial Rounded MT Bold",sans-serif;color:#7030A0">Iman M.Rezazadeh, Ph.D</span></b><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:10.0pt;font-family:"Arial",sans-serif">UCLA David Geffen School of Medicine</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:10.0pt;font-family:"Arial",sans-serif">Semel Institute for Neuroscience and Human Behavior</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:10.0pt;font-family:"Arial",sans-serif">760 Westwood Plaza, Ste 47-448</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:10.0pt;font-family:"Arial",sans-serif">Los Angeles, CA 90095</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><a href="http://www.linkedin.com/pub/iman-m-rezazadeh/10/859/840/" target="_blank"><span style="color:#0563C1">http://www.linkedin.com/pub/iman-m-rezazadeh/10/859/840/</span></a><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
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<o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">--
<o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">Makoto Miyakoshi<br>
Swartz Center for Computational Neuroscience<br>
Institute for Neural Computation, University of California San Diego<o:p></o:p></p>
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<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">-- <o:p></o:p></p>
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<p class="MsoNormal">Makoto Miyakoshi<br>
Swartz Center for Computational Neuroscience<br>
Institute for Neural Computation, University of California San Diego<o:p></o:p></p>
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