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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple><div class=WordSection1><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:black'>Hi Ewa,<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:black'>I don’t think there is actually a problem … Your 4x1000 data is most likely full rank (covariance matrix has 4 significant eigenvalues), so it needs 4 components (or dimensions in the basis set) to represent the data without error. With only 3 components, you get an approximation of the data, where one direction is not represented. This may or may not correspond to the smallest dimension of the data (the smallest eigenvalue/eigenvector) since ICA tries to find independent directions, not necessarily the largest variance (like PCA does).<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:black'>So you would expect the reconstructed 4 dimensional data using 3 components to be different from the original data.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:black'>Best,<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:black'>Jason<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:black'><o:p> </o:p></span></p><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"'> Ewa Beldzik [mailto:ewa.beldzik@gmail.com] <br><b>Sent:</b> Friday, May 11, 2012 3:18 PM<br><b>To:</b> mmiyakoshi@ucsd.edu<br><b>Cc:</b> eeglablist@sccn.ucsd.edu; Jason Palmer<br><b>Subject:</b> Re: [Eeglablist] Question regarding fastICA<o:p></o:p></span></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal style='margin-bottom:12.0pt'>Dear Makoto,<br><br>As far as I'm concern, fastICA community does not have forum nor mailing list, so I did write the same e-mail to Professor Hyvarinen and one of his colleagues but I haven't got any answer yet.<br><br>Thank you for replicating it though. At least I'm sure it is the algorithm and not my mistake.<br><br>Ewa<o:p></o:p></p><div><p class=MsoNormal>On 11 May 2012 22:33, Makoto Miyakoshi <<a href="mailto:mmiyakoshi@ucsd.edu" target="_blank">mmiyakoshi@ucsd.edu</a>> wrote:<o:p></o:p></p><p class=MsoNormal>Dear Ewa,<br><br>I replicated it. I don't know why this is so though... you'd better<br>ask fastica community. Jason, do you by any chance know what it is?<br><br>Makoto<br><br>2012/5/11 Ewa Beldzik <<a href="mailto:ewa.beldzik@gmail.com">ewa.beldzik@gmail.com</a>>:<o:p></o:p></p><div><div><p class=MsoNormal>> Dear Mokoto,<br>><br>> Thank you for the interest. I'm not sure if I can enclose the plots here so<br>> I'm gonna use min and max values as a reconstruction criteria.<br>> I have a data x (matrix size 4x1024; ranging <-3.882;2,466>)<br>><br>> When I apply following command line in matlab:<br>> [icasig,A,W]=fastica(x,'numOfIC',4)<br>> and when I reconstruct x with the formula:<br>> x4=A*icasig<br>> I get x4 (matrix size 4x1024; ranging <-3.882;2,466>) which presents the<br>> exact plot as x.<br>><br>> Now, when I apply following command line in matlab:<br>> [icasig2,A2,W2]=fastica(x,'numOfIC',3)<br>> and then I reconstruct x with:<br>> x3=A2*icasig2<br>> I get x3 (matrix size 4x1024; ranging <-4.453;2,469>) which presents far<br>> more noise plots then x.<br>><br>> I'm not sure whether I'm not doing something wrong. But if the algorithm<br>> works this way why is it so?<br>><br>> Best regards,<br>> Ewa<br>><br>><br>> On 10 May 2012 21:47, Makoto Miyakoshi <<a href="mailto:mmiyakoshi@ucsd.edu">mmiyakoshi@ucsd.edu</a>> wrote:<br>>><br>>> Dear Ewa,<br>>><br>>> What do you mean by 'imprecisely'? Or how did you now it is imprecise?<br>>> Please tell us more detail.<br>>><br>>> Makoto<br>>><br>>> 2012/5/10 Ewa Beldzik <<a href="mailto:ewa.beldzik@gmail.com">ewa.beldzik@gmail.com</a>>:<br>>> > Dear all,<br>>> ><br>>> > When applying fastICA algorithm in Matlab to a data consisting of 4<br>>> > signals,<br>>> > I have noticed that only when I choose 4 IC to be estimated, the formula<br>>> > A*icasig =X actually works. After choosing 2 or 3 IC the data (X) is<br>>> > reconstructed imprecisely.<br>>> > Could you explain why? I wish to understand the methods fully.<br>>> ><br>>> > Thank you in advance,<br>>> > Ewa<br>>> > PhD student from Cracow<br>>> ><br>>> > _______________________________________________<br>>> > Eeglablist page: <a href="http://sccn.ucsd.edu/eeglab/eeglabmail.html" target="_blank">http://sccn.ucsd.edu/eeglab/eeglabmail.html</a><br>>> > To unsubscribe, send an empty email to<br>>> > <a href="mailto:eeglablist-unsubscribe@sccn.ucsd.edu">eeglablist-unsubscribe@sccn.ucsd.edu</a><br>>> > For digest mode, send an email with the subject "set digest mime" to<br>>> > <a href="mailto:eeglablist-request@sccn.ucsd.edu">eeglablist-request@sccn.ucsd.edu</a><br>>><br>>><br>>><br>>> --<br>>> Makoto Miyakoshi<br>>> JSPS Postdoctral Fellow for Research Abroad<br>>> Swartz Center for Computational Neuroscience<br>>> Institute for Neural Computation, University of California San Diego<br>><br>><br><br><br><br>--<br>Makoto Miyakoshi<br>JSPS Postdoctral Fellow for Research Abroad<br>Swartz Center for Computational Neuroscience<br>Institute for Neural Computation, University of California San Diego<o:p></o:p></p></div></div></div><p class=MsoNormal><o:p> </o:p></p></div></body></html>