<div dir="ltr">Dear Joelle,<div><br></div><div>Thank you for asking pvaf measure which is my favoirte.</div><div>The pvaf is computed as follows (from envtopo.m help)</div><div><br></div><div><div>pvaf(comp) = 100-100*mean(var(data - back_proj))/mean(var(data));<br></div></div><div><br></div><div>Here, variance is computed across channels/ICactivations.<br></div><div><br></div><div>> What exactly does the „percent variance accounted for (pvaf)“ mean? For example if I got a pvaf of about 60, does this mean that this component explains 60% of the original data (or is it more complicated)?</div><div><br></div><div>As it is clear in the equation, pvaf 60 means that the selected ICs explains 60% of the temporal average of the EEG variance across channels.</div><div><br></div><div>> These pvaf’s sum up to about 80, does this mean that 20% of the original data cannot be explained by all the components?<br></div><div><br></div><div>By all the 'selected' components.</div><div><br></div><div>> These pvaf’s add to over 400 (whereas the ones from above sum up to only 80 which seems to be more reasonable to me), does this mean that the independent components overlap? </div><div><br></div><div>There is subadditivity in the variance calculation, namely </div><div><br></div><div>var(A+B+C) <= var(A) + var(B) + var(C)</div><div><br></div><div>this is because when you perform (A+B+C) cancellation happens. So you cannot add up each pvaf values to 100, but it will be always larger than 100. I know that this is confusing although totally valid...</div><div><br></div><div>Makoto</div><div><br></div><div><br></div><div class="gmail_extra"><br><div class="gmail_quote">On Fri, Dec 12, 2014 at 4:00 AM, Joëlle Albrecht <span dir="ltr"><<a href="mailto:joelle.albrecht@hotmail.com" target="_blank">joelle.albrecht@hotmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex">
<div><div dir="ltr"><p class="MsoNormal">Dear EEGLAB-ers<u></u><u></u></p><p class="MsoNormal"><br></p>
<p class="MsoNormal">I’m trying to find out, how much variance of the original
data the components (computed by ICA) explain, but I’m not sure how to do this.
(My goal is something like: Component 1 explains 60% of the variance in the
original data. etc.)<u></u><u></u></p>
<p class="MsoNormal"><u></u> <u></u></p>
<p class="MsoNormal" style="margin-bottom:0.0001pt">1) I used the following
function:<u></u><u></u></p>
<p class="MsoNormal" style="margin-bottom:0.0001pt"><u></u> <u></u></p>
<p class="MsoNormal" style="margin-bottom:0.0001pt"><span style="font-size:10pt;font-family:'Courier New'">[pc,eigvec,sv] = runpca(EEG.data);</span><span style="font-size:12pt;font-family:'Courier New'"><u></u><u></u></span></p>
<p class="MsoNormal" style="margin-bottom:0.0001pt"><span style="font-size:10pt;font-family:'Courier New'">[proj pvaf] = compvar(EEG.data,
pc, eigvec, components);</span><span style="font-size:12pt;font-family:'Courier New'"><u></u><u></u></span></p>
<p class="MsoNormal"><u></u> <u></u></p>
<p class="MsoNormal">What exactly does the „percent variance accounted for (pvaf)“
mean? For example if I got a pvaf of about 60, does this mean that this
component explains 60% of the original data (or is it more complicated)? These
pvaf’s sum up to about 80, does this mean that 20% of the original data cannot
be explained by all the components?<u></u><u></u></p>
<p class="MsoNormal"><u></u> <u></u></p>
<p class="MsoNormal">2) I used another function, too (after completing the ICA):<u></u><u></u></p>
<p class="MsoNormal" style="margin-bottom:0.0001pt"><span style="font-size:10pt;font-family:'Courier New'">[pvaf,pvafs,vars]=eeg_pvaf(EEG,component);</span><span style="font-size:12pt;font-family:'Courier New'"><u></u><u></u></span></p>
<p class="MsoNormal"><u></u> <u></u></p>
<p class="MsoNormal">Again: What exactly do the pvaf’s mean? Plus, these pvaf‘s
are very different from the pvaf’s I obtained with the function above. What is
the difference? These pvaf’s add to over 400 (whereas the ones from above sum
up to only 80 which seems to be more reasonable to me), does this mean that the
independent components overlap? The pvaf’s resulting from this function (but
not the ones from the one above) are not
monotonously decreasing – how are they sorted?<u></u><u></u></p>
<p class="MsoNormal"><u></u> <u></u></p>
<p class="MsoNormal">Thank you very much for the support! <span class=""><font color="#888888"><u></u><u></u></font></span></p><span class=""><font color="#888888"><p class="MsoNormal">Joëlle </p> </font></span></div></div>
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