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<P>The ICA:DTU Toolbox holds a collection of Independent Component
Analysis (ICA) algorithms implemented for Matlab™. All code can be used
freely in research and other non-profit applications. If you publish
results obtained with the ICA:DTU Toolbox we kindly ask that our and other
relevant sources are properly cited. Description, cititation and
implementation notes for the individual algorithms, are provided with each
ICA algorithm.</P>
<P align=center>- <A
href="http://www.imm.dtu.dk/pubdb/personal/showbasket.php?cmd=full_view&id=70&title=ICA%20Publications&header=&footer=&css=http://mole.imm.dtu.dk/toolbox/stylesheet_pub.css&b=1&e=1&year=&fmt=html&order=year">See
relevant ICA publications by the ISP Group at IMM, DTU</A><BR>- <A
href="http://mole.imm.dtu.dk/toolbox/mail/maillist.php">For news and
updates subscribe to DTU:Toolbox mailing list</A></P>
<P>This toolbox has been developed for the <A
href="http://www-sop.inria.fr/epidaure/Collaborations/MAPAWAMO/mapawamo.html"
target=_blank>European Union MAPAWAMO project</A>.</P>
<P><B>Algorithms:</B></P>
<UL>
<LI><A
href="http://mole.imm.dtu.dk/toolbox/ica/index.html#icaML">icaML</A>: Is
an iterative fast and robust algorithm, also known as Infomax.
<LI><A
href="http://mole.imm.dtu.dk/toolbox/ica/index.html#icaMF">icaMF</A>: Is
an iterative algorithm, that offers a variety of possible source priors
and mixing matrix constraints, e.g. positivity. It can also handle over
and under-complete mixing.
<LI><A
href="http://mole.imm.dtu.dk/toolbox/ica/index.html#icaMS">icaMS</A>: Is
a "one shot" fast algorithm that requires time correlation between
samples. </LI></UL>
<P><B><BR>Common algorithm properties</B></P>
<UL>
<LI>No parameters need to be set by default.
<LI>Log likelihoods are calculated.
<LI>Estimating number of components using Bayes Information Criterion.
</LI></UL>
<P><BR><B>Demonstrators:</B><BR></P>
<UL>
<LI><A
href="http://mole.imm.dtu.dk/toolbox/ica/index.html#ICAdemofMRI">fMRI</A>:
on human and monkey subjects where PCA, icaML, icaMS, icaMF and icaMF
(positive sources) are used.
<LI><A
href="http://mole.imm.dtu.dk/toolbox/ica/index.html#ICAdemoText">Text</A>:
classification of medical abstracts (MED dataset) using icaML. </LI></UL>
<P> </P>
<P><IMG border=1 height=3 src="ICADTU Toolbox.files/bevel2.jpg"
width=640></P>
<H1>Algorithms</H1>
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<H2><A name=icaML></A>Maximum likelihood (Infomax) -
icaML</H2></TD></TR>
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<P>The algorithm is equivalent to Infomax by Bell and Sejnowski 1995
[1] using a maximum likelihood formulation. No noise is assumed and
the number of observations must equal the number of sources. The
BFGS method [2] is used for optimization. </P>
<P>The number of independent components are calculated using Bayes
Information Criterion [3] (BIC), with PCA for dimension
reduction.</P>
<P>Properties:</P>
<UL>
<LI>Linear and instantaneous mixing.
<LI>Square mixing matrix.
<LI>No noise. </LI></UL>
<P>Update history:</P>
<UL>
<LI>020103 Version 1.4 Included pre-processing with SVD to reduce
input dimension. Added optimisation parameter setting and removed
log likelihood problem with icaML output </LI></UL></TD></TR>
<TR>
<TD width=344>
<P>[<A
href="http://mole.imm.dtu.dk/toolbox/ica/ml/bibtex.bib.txt">Citations</A>][<SPAN
class=algorithm>Code <A
href="http://mole.imm.dtu.dk/toolbox/ica/ML/icaML.tar.gz">GZ</A> <A
href="http://mole.imm.dtu.dk/toolbox/ica/ml/icaML.zip">ZIP</A></SPAN>]</P></TD>
<TD width=262>
<P align=right>[Version 1.4 ]</P></TD></TR></TBODY></TABLE>
<P> </P>
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class=algorithm width=640>
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<TD rowSpan=3 width=2> </TD>
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<H2><A name=icaMF></A>Mean Field - icaMF</H2></TD></TR>
<TR>
<TD colSpan=2>
<P>This is a Bayesian ICA algorithm for the linear instantaneous
mixing model with additive Gaussian noise [1]. The inference problem
is solved by ML-II, i.e. the sources are found by integration over
the source posterior and the noise covariance and mixing matrix are
found by maximization of the marginal likelihood [1]. The sufficient
statistics are estimated by either variational mean field theory
with the linear response correction or by adaptive TAP mean field
theory [2,3]. The mean field equations are solved by a belief
propagation method [4] or sequential iteration. The computational
complexity is N M^3, where N is the number of time samples and M the
number of sources. </P>
<P>Properties:</P>
<UL>
<LI>Linear and instantaneous mixing.
<LI>Any type of mixing matrix (quadratic, over- and
under-complete).
<LI>Mixing matrix - free/positivity constraint estimation and
constant for test sets.
<LI>Noise covariance - isotropic/diagonal/full noise covariance
and constant for test sets.
<LI>Variety of source distributions: exponential for positive
sources, binary (both +1/-1 and 0/1), Gauss (for probabilistic PCA
and factor analysis), bi-Gauss (for negative kurtosis sources) and
Laplace and heavy tailed (for positive kurtosis sources). </LI></UL>
<P>Update history:</P>
<UL>
<LI>021002 Version 2.0
<LI>021011 Version 2.1 Bug in par.solver='beliefprop2' corrected,
new par.method='constant'.
<LI>021014 Version 2.1 Bug in prior.S='bigauss' corrected.
</LI></UL></TD></TR>
<TR>
<TD width=352>
<P>[<A
href="http://mole.imm.dtu.dk/toolbox/ica/mf/bibtex.bib.txt">Citations</A>][<SPAN
class=algorithm>Code <A
href="http://mole.imm.dtu.dk/toolbox/ica/mf/icaMF.tar.gz">GZ</A> <A
href="http://mole.imm.dtu.dk/toolbox/ica/mf/icaMF.zip">ZIP</A></SPAN>]</P></TD>
<TD width=256>
<P align=right>[Version 2.1 ]</P></TD></TR></TBODY></TABLE>
<P> </P>
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class=algorithm width=640>
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<TD rowSpan=3 width=1> </TD>
<TD colSpan=2>
<H2><A name=icaMS></A>Molgedey and Schouster - icaMS</H2></TD></TR>
<TR>
<TD colSpan=2>
<P>The Molgedey and Schuster decorrelation algorithm, having square
mixing matrix and no noise [1]. Truncation is used for the time
shifted matrix, and it is forced to be symmetric [2]. The delay Tau
is estimated [3].</P>
<P>The number of independent components are calculated using Bayes
Information Criterion [4] (BIC), with PCA for dimension
reduction.</P>
<P></P>
<P>Properties:</P>
<UL>
<LI>Linear and instantaneous mixing .
<LI>Square mixing matrix.
<LI>No noise.
<LI>Very fast / no iterations.
<LI>Time correlation needed in observed signals.
<LI>Time delay tau estimated. </LI></UL></TD></TR>
<TR>
<TD width=363>
<P>[<A
href="http://mole.imm.dtu.dk/toolbox/ica/ms/bibtex.bib.txt">Citations</A>][<SPAN
class=algorithm>Code <A
href="http://mole.imm.dtu.dk/toolbox/ica/MS/icaMS.tar.gz">GZ</A> <A
href="http://mole.imm.dtu.dk/toolbox/ica/ms/icaMS.zip">ZIP</A></SPAN>]</P></TD>
<TD width=246>
<P align=right>[Version 1.3 ]</P></TD></TR></TBODY></TABLE>
<P> </P>
<P><IMG border=1 height=3 src="ICADTU Toolbox.files/bevel2.jpg"
width=640></P>
<H1>Demonstrations</H1>
<TABLE bgColor=#ffffff border=0 cellPadding=5 cellSpacing=0
class=algorithm width=640>
<TBODY>
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<TD rowSpan=3 width=1><IMG align=top height=168
src="ICADTU Toolbox.files/ICAfMRIDemo.png" width=200></TD>
<TD colSpan=2 vAlign=top>
<H2><A name=ICAdemofMRI></A>fMRI</H2></TD></TR>
<TR>
<TD align=left colSpan=2 vAlign=top>
<P>ICA can be used in brain activation studies to reduce the number
of dimension and filter out independent and interesting activations.
This demonstration shows two studies. One provided by Hvidovre
Universitets Hospital, Denmark, that consists of fMRI scannings of
humans. Another provided by the EU sponsored <A
href="http://www-sop.inria.fr/epidaure/Collaborations/MAPAWAMO/mapawamo.html"
target=_blank>MAPAWAMO</A> project from fMRI scannings of monkeys.
In the demo comparison between icaMS, icaML, icaMF, icaMF (positive
sources) and PCA can be made. More detailes can found in
[2].</P></TD></TR>
<TR>
<TD vAlign=bottom width=367>
<P>[<A
href="http://mole.imm.dtu.dk/toolbox/ica/demos/bibtex.bib.txt">Citations</A>][<SPAN
class=algorithm>Demo 2.7MB <A
href="http://mole.imm.dtu.dk/toolbox/ica/demos/ICA_demo_fMRI.tar.gz">GZ</A>
<A
href="http://mole.imm.dtu.dk/toolbox/ica/demos/ICA_demo_fMRI.zip">ZIP</A></SPAN>]</P></TD>
<TD width=242>
<P align=right> </P></TD></TR></TBODY></TABLE>
<P> </P>
<TABLE bgColor=#ffffff border=0 cellPadding=5 cellSpacing=0
class=algorithm width=640>
<TBODY>
<TR>
<TD rowSpan=3 width=1><IMG align=top height=168
src="ICADTU Toolbox.files/ICATextDemo.png" width=200></TD>
<TD colSpan=2 vAlign=top>
<H2><A name=ICAdemoText></A>Text classification</H2></TD></TR>
<TR>
<TD align=left colSpan=2 vAlign=top>
<P>ICA is used to classify text in extension to the latent semantic
indexing framework. ICA show to align the context grouping structure
well in a human sense [1], thus can be used for unsupervised
classification. The demonstration shows this on medical abstracts
(<A href="http://mole.imm.dtu.dk/faq/MEDdata/index.html">MED
dataset</A>), that uses BIC to estimate the number of classes and
produces keywords for each class. The icaML algorithm is
used.</P></TD></TR>
<TR>
<TD vAlign=bottom width=367>
<P>[<A
href="http://mole.imm.dtu.dk/toolbox/ica/demos/bibtex.bib.txt">Citations</A>][<SPAN
class=algorithm>Demo 2.4MB <A
href="http://mole.imm.dtu.dk/toolbox/ica/demos/ICA_demo_text.tar.gz">GZ</A>
<A
href="http://mole.imm.dtu.dk/toolbox/ica/demos/ICA_demo_text.zip">ZIP</A></SPAN>]</P></TD>
<TD width=242>
<P align=right> </P></TD></TR></TBODY></TABLE>
<P align=center>[<A href="http://mole.imm.dtu.dk/toolbox/menu.html"> Back
to the toolbox menu </A>]</P>
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