[Eeglablist] Question regarding fastICA

[Ewa Beldzik]

Hi Jason,

Thank you very much for the answer, just to clarify..
So when I choose 3 components to be estimated is actually search for 4 of
them and then delete the one with the smallest eigenvalues from the data?
How come everybody use the equation in their theory section if the formula
X=s*A is incorrect (considering that data reduction is substantial in
neuroimaging)?

Kind regards,
Ewa

On 12 May 2012 00:43, Jason Palmer <japalmer29 at gmail.com> wrote:

> Hi Ewa,****
>
> ** **
>
> 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).****
>
> ** **
>
> So you would expect the reconstructed 4 dimensional data using 3
> components to be different from the original data.****
>
> ** **
>
> Best,****
>
> Jason****
>
> ** **
>
> *From:* Ewa Beldzik [mailto:ewa.beldzik at gmail.com]
> *Sent:* Friday, May 11, 2012 3:18 PM
> *To:* mmiyakoshi at ucsd.edu
> *Cc:* eeglablist at sccn.ucsd.edu; Jason Palmer
> *Subject:* Re: [Eeglablist] Question regarding fastICA****
>
> ** **
>
> Dear Makoto,
>
> 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.
>
> Thank you for replicating it though. At least I'm sure it is the algorithm
> and not my mistake.
>
> Ewa****
>
> On 11 May 2012 22:33, Makoto Miyakoshi <mmiyakoshi at ucsd.edu> wrote:****
>
> Dear Ewa,
>
> I replicated it. I don't know why this is so though... you'd better
> ask fastica community. Jason, do you by any chance know what it is?
>
> Makoto
>
> 2012/5/11 Ewa Beldzik <ewa.beldzik at gmail.com>:****
>
> > Dear Mokoto,
> >
> > Thank you for the interest. I'm not sure if I can enclose the plots here
> so
> > I'm gonna use min and max values as a reconstruction criteria.
> > I have a data x (matrix size 4x1024; ranging <-3.882;2,466>)
> >
> > When I apply following command line in matlab:
> > [icasig,A,W]=fastica(x,'numOfIC',4)
> > and when I reconstruct x with the formula:
> > x4=A*icasig
> > I get x4 (matrix size 4x1024; ranging <-3.882;2,466>) which presents the
> > exact plot as x.
> >
> > Now, when I apply following command line in matlab:
> > [icasig2,A2,W2]=fastica(x,'numOfIC',3)
> > and then I reconstruct x with:
> > x3=A2*icasig2
> > I get x3 (matrix size 4x1024; ranging <-4.453;2,469>) which presents far
> > more noise plots then x.
> >
> > I'm not sure whether I'm not doing something wrong. But if the algorithm
> > works this way why is it so?
> >
> > Best regards,
> > Ewa
> >
> >
> > On 10 May 2012 21:47, Makoto Miyakoshi <mmiyakoshi at ucsd.edu> wrote:
> >>
> >> Dear Ewa,
> >>
> >> What do you mean by 'imprecisely'? Or how did you now it is imprecise?
> >> Please tell us more detail.
> >>
> >> Makoto
> >>
> >> 2012/5/10 Ewa Beldzik <ewa.beldzik at gmail.com>:
> >> > Dear all,
> >> >
> >> > When applying fastICA algorithm in Matlab to a data consisting of 4
> >> > signals,
> >> > I have noticed that only when I choose 4 IC to be estimated, the
> formula
> >> > A*icasig =X actually works. After choosing 2 or 3 IC the data (X) is
> >> > reconstructed imprecisely.
> >> > Could you explain why? I wish to understand the methods fully.
> >> >
> >> > Thank you in advance,
> >> > Ewa
> >> > PhD student from Cracow
> >> >
> >> > _______________________________________________
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> >>
> >>
> >>
> >> --
> >> Makoto Miyakoshi
> >> JSPS Postdoctral Fellow for Research Abroad
> >> Swartz Center for Computational Neuroscience
> >> Institute for Neural Computation, University of California San Diego
> >
> >
>
>
>
> --
> Makoto Miyakoshi
> JSPS Postdoctral Fellow for Research Abroad
> Swartz Center for Computational Neuroscience
> Institute for Neural Computation, University of California San Diego****
>
> ** **
>
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