<div dir="ltr">Dear Salim,<div><br></div><div><div style="color:rgb(0,0,0);font-family:arial,helvetica,sans-serif;font-size:13.142857551574707px">> 1- Are the predicted S1(60) and S2(60) independent as the actual ones which obtained using ICA.</div>
<div style="color:rgb(0,0,0);font-family:arial,helvetica,sans-serif;font-size:13.142857551574707px"><br></div><div style="color:rgb(0,0,0);font-family:arial,helvetica,sans-serif;font-size:13.142857551574707px">If the S1(60) and S2(60) are the predictions made by i.e. AR model from S1(1-59) and S2(1-59) respectively, then they are most likely independent.</div>
<div style="color:rgb(0,0,0);font-family:arial,helvetica,sans-serif;font-size:13.142857551574707px"><br></div><div style="color:rgb(0,0,0);font-family:arial,helvetica,sans-serif;font-size:13.142857551574707px">> 2- The past values that it used to predict S1(60) and S2(60) are independent. Does this independence affect the predict variables?<br>
</div></div><div class="gmail_extra"><br></div><div class="gmail_extra">Yes, why not?</div><div class="gmail_extra"><br></div><div class="gmail_extra">Makoto</div><div class="gmail_extra"><br><div class="gmail_quote">On Sun, Jul 27, 2014 at 8:22 AM, Salim Al-wasity <span dir="ltr"><<a href="mailto:salim_alwasity@yahoo.com" target="_blank">salim_alwasity@yahoo.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 style="color:rgb(0,0,0);font-family:arial,helvetica,sans-serif;font-size:10pt;background-color:rgb(255,255,255)">
<div>Dear Mr. Miyakoshi</div><div>Thanks for your reply. Let assumes that an ICA is applied to an observe matrix X (of 2 channels and 100 samples), therefore an S decomposed independent source signal is obtain.</div><div>
After that GC is used to find the connectivity between S1 and S2 (channel 1 and channel 2 of S), for instance to predict S1(60) and S2(60) based on the past values of S1 and S2 (for a predefined order), then:</div><div>1- Are the predicted S1(60) and S2(60) independent as the actual ones which obtained using ICA.</div>
<div>2- The past values that it used to predict S1(60) and S2(60) are independent. Does this independence affect the predict variables?</div><div><br></div><div style="color:rgb(0,0,0);font-size:13px;font-family:arial,helvetica,sans-serif;font-style:normal;background-color:transparent">
Sincerely</div><span class=""><font color="#888888"><div style="color:rgb(0,0,0);font-size:13px;font-family:arial,helvetica,sans-serif;font-style:normal;background-color:transparent">Salim</div></font></span><div><div class="h5">
<div><br><br></div><div style="display:block"> <div style="font-family:arial,helvetica,sans-serif;font-size:10pt"> <div style="font-family:'times new roman','new york',times,serif;font-size:12pt"> <div dir="ltr">
<font face="Arial"> On Friday, 25 July 2014, 20:41, Makoto Miyakoshi <<a href="mailto:mmiyakoshi@ucsd.edu" target="_blank">mmiyakoshi@ucsd.edu</a>> wrote:<br> </font> </div> <br><br> <div><div><div><div dir="ltr">
Dear Salim,<div><br clear="none"></div><div>ICA assures <i>instantaneous</i> independence, while GC calculates <i>temporal</i> causality. This means that ICA does not know what happens in the next moment, but GC does.</div>
<div><br clear="none"></div><div>By the way if you have more than 3 ICs for GC don't use GC but use RPDC or normalized dDTF.</div><div><br clear="none"></div><div>Makoto</div></div><div><br clear="none"><br clear="none">
<div>On Fri, Jul 25, 2014 at 4:41 AM, Salim Al-wasity <span dir="ltr"><<a rel="nofollow" shape="rect" href="mailto:salim_alwasity@yahoo.com" target="_blank">salim_alwasity@yahoo.com</a>></span> wrote:<br clear="none">
<blockquote 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><div style="color:rgb(0,0,0);font-family:arial,helvetica,sans-serif;font-size:10pt;background-color:rgb(255,255,255)">
<div><span style="font-size:10pt">Dears<u></u><u></u></span></div>
<div><span>Have a nice day. Kindly I have a question regarding ICA:</span><br clear="none">
<span>I have EEG data of (44 channels X 294000 samples)</span><br clear="none">
<br clear="none">
<span>1- I applied the ICA to separate the noise and
find the ICs which are belong to brain activities.</span><br clear="none"><span>2- I used the Granger Causality (GC) in SIFT to
find the connectivity between these ICs and discover which component influence
which. However I am not sure about the results that I have got.</span></div><div style="color:rgb(0,0,0);font-size:13px;font-family:arial,helvetica,sans-serif;font-style:normal;background-color:transparent"><br clear="none">
<span>My question is that If I used ICA to decompose the
EEG signal into their sources (hint: the decomposed ICs is much less than the
actual brain sources), theoretically these ICs would be independent, and the
use of GC would be useless since the latter algorithm search for the dependence
across ICs?</span><br clear="none">
<span>Or the ICA will minimize the mutual information, and the separated components will not be ~100% independent, therefore each component has more that one source,
and GC can find some influence across these components for the remaining not separated sources. </span><span style="font-size:10pt"><u></u><u></u></span></div><div><span style="font-size:10pt"> </span></div><div><span>Your cooperation is highly appreciated</span><span style="font-size:10pt"><u></u><u></u></span></div>
<div><span style="font-size:10pt"> </span></div><div><span>Yours</span><span><font color="#888888"><span style="font-size:10pt"><u></u><u></u></span></font></span></div><span><font color="#888888"></font></span><div>
<span>Salim Al-Wasity</span><span style="font-size:10pt"><u></u><u></u></span></div><div><span>PhD student</span><span style="font-size:10pt"><u></u><u></u></span></div><div><span>Rehabilitation Centre</span><span style="font-size:10pt"><u></u><u></u></span></div>
<div><span>Biomedical Engineering Department-School of Engineering</span><span style="font-size:10pt"><u></u><u></u></span></div><div><span>University of Glasgow</span><span style="font-size:10pt"><u></u><u></u></span></div>
<div><span>Glasgow-United Kingdom</span><span style="font-size:10pt"><u></u><u></u></span></div><div>
</div><div><span><a rel="nofollow" shape="rect">+44 742 371 4444</a></span><span style="font-size:10pt"><u></u><u></u></span></div></div></div></div><br clear="none">_______________________________________________<br clear="none">
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</blockquote></div><br clear="none"><br clear="all"><div><br clear="none"></div>
-- <br clear="none"><div dir="ltr">Makoto Miyakoshi<br clear="none">Swartz Center for Computational Neuroscience<br clear="none">Institute for Neural Computation, University of California San Diego<br clear="none"></div>
</div></div></div><br><br></div> </div> </div> </div> </div></div></div></div></blockquote></div><br><br clear="all"><div><br></div>-- <br><div dir="ltr">Makoto Miyakoshi<br>Swartz Center for Computational Neuroscience<br>
Institute for Neural Computation, University of California San Diego<br></div>
</div></div>