[Eeglablist] Question regarding fastICA

[Jason Palmer]

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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