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window. The numbers in the respective fields specify the current starting and
ending positions for the processing. Press the <tt><span style='font-size:10.0pt'>OK</span></tt>
button (In the window below, this appears in the highlighted area) to load
selected signals. Unselected channels (in our example, channels No. 2 and 4)
are ignored (removed from original data). You can <tt><span style='font-size:
10.0pt'>also SAVE</span></tt> the selected signals to a *.mat file. </p>
<p class=MsoNormal align=center style='margin-left:36.0pt;text-align:center;
line-height:18.0pt'><span style='color:blue'><img border=0 width=520
height=569 id="_x0000_i1031" src="icalab_files/image005.jpg"
alt="Select signals"></span></p>
<h6 style='margin-left:36.0pt;line-height:18.0pt'><span class=GramE><b>Fig. 4</b>
Window illustrating the selection of channels and time window.</span> In this
window channels s2 and s4 are deleted.</h6>
<h2>Mixing the signals</h2>
<p>You can mix the signals synthetically, in case they are not originally
mixed. Leave the option with <i>identity</i> (unit matrix) for real world
(superimposed or mixed) data. </p>
<p class=MsoNormal align=center style='text-align:center'><img border=0
width=518 height=543 id="_x0000_i1032" src="icalab_files/image006.jpg"></p>
<h6><span class=GramE><b>Fig. 5</b> Window illustrating how to choose the
mixing matrix <b>H</b>.</span> If your data are real-data (not benchmark or
test data) please ignore this option. Default mixing matrix is identity matrix
(<b>H</b> = <b>I</b>). </h6>
<p>The option to mix the source signals is applied only for testing and
comparing the performance of various algorithms. In <b>ICALAB</b>, 12
alternative ways to generate such mixing matrices are available: </p>
<p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent:
-36.0pt;line-height:18.0pt'><span style='font-size:10.0pt;font-family:Symbol'>·</span><span
style='font-size:7.0pt'> </span>Identity
(unit matrix) - for real world data signals, </p>
<p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent:
-36.0pt;line-height:18.0pt'><span style='font-size:10.0pt;font-family:Symbol'>·</span><span
style='font-size:7.0pt'> </span><span
class=GramE>Randomly</span> generated nonsingular matrix, </p>
<p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent:
-36.0pt;line-height:18.0pt'><span style='font-size:10.0pt;font-family:Symbol'>·</span><span
style='font-size:7.0pt'> </span><span
class=GramE>Randomly</span> generated nonsingular symmetric matrix, </p>
<p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent:
-36.0pt;line-height:18.0pt'><span style='font-size:10.0pt;font-family:Symbol'>·</span><span
style='font-size:7.0pt'> </span><span
class=GramE>Randomly</span> generated nonsingular ill-conditioned matrix with
the conditioning number larger than 10000, </p>
<p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent:
-36.0pt;line-height:18.0pt'><span style='font-size:10.0pt;font-family:Symbol'>·</span><span
style='font-size:7.0pt'> </span>Hilbert
matrix (which is very ill conditioned), </p>
<p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent:
-36.0pt;line-height:18.0pt'><span style='font-size:10.0pt;font-family:Symbol'>·</span><span
style='font-size:7.0pt'> </span>Toeplitz
matrix, </p>
<p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent:
-36.0pt;line-height:18.0pt'><span style='font-size:10.0pt;font-family:Symbol'>·</span><span
style='font-size:7.0pt'> </span>Hankel
matrix,</p>
<p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent:
-36.0pt;line-height:18.0pt'><span style='font-size:10.0pt;font-family:Symbol'>·</span><span
style='font-size:7.0pt'> </span>Orthogonal</p>
<p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent:
-36.0pt;line-height:18.0pt'><span style='font-size:10.0pt;font-family:Symbol'>·</span><span
style='font-size:7.0pt'> </span>Nonnegative
symmetric</p>
<p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent:
-36.0pt;line-height:18.0pt'><span style='font-size:10.0pt;font-family:Symbol'>·</span><span
style='font-size:7.0pt'> </span>Bipolar
symmetric</p>
<p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent:
-36.0pt;line-height:18.0pt'><span style='font-size:10.0pt;font-family:Symbol'>·</span><span
style='font-size:7.0pt'> </span>Skew-symmetric</p>
<p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent:
-36.0pt;line-height:18.0pt'><span style='font-size:10.0pt;font-family:Symbol'>·</span><span
style='font-size:7.0pt'> </span><span
class=GramE>Any</span> specific matrix edited manually by user.</p>
<p>The last option is limited to be a 15x15 mixing matrix. For this option,
click on the <tt><span style='font-size:10.0pt'>EDIT</span></tt> button and the
following window will show up. This enables you to edit every element of the
mixing matrix. After typing in the entries, you will see that both the
determinant and condition numbers of the mixing matrix <b>H</b> are updated
automatically. </p>
<p class=MsoNormal align=center style='text-align:center'><span
style='color:blue'><img border=0 width=440 height=282 id="_x0000_i1033"
src="icalab_files/image007.gif" alt="Mixing matrix editor"></span></p>
<h6><span class=GramE><b>Fig. 6</b> Window illustrating how to edit the mixing
matrix <b>H</b>.</span> The editable mixing matrix <b>H</b> can not be larger
than 15x15 in size.</h6>
<h2>Adding noise to the signals</h2>
<p>You can also add noise to the each sensor signal before performing <st1:City
w:st="on"><st1:place w:st="on">ICA</st1:place></st1:City> or BSS with the
following options: </p>
<p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent:
-36.0pt;line-height:18.0pt'><span style='font-size:10.0pt;font-family:Symbol'>·</span><span
style='font-size:7.0pt'> </span><b>No
noise</b> - the sensor signals are not changed.</p>
<p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent:
-36.0pt;line-height:18.0pt'><span style='font-size:10.0pt;font-family:Symbol'>·</span><span
style='font-size:7.0pt'> </span><b>Gaussian
noise</b> with SNR level from 20dB down to 15dB, 10dB, 5dB, and 0dB - the white
Gaussian noise is added to the signals with the selected SNR level.</p>
<p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent:
-36.0pt;line-height:18.0pt'><span style='font-size:10.0pt;font-family:Symbol'>·</span><span
style='font-size:7.0pt'> </span><b>Uniform
noise</b> with SNR level from 20dB down to 15dB, 10dB, 5dB, and 0dB - the
uniformly distributed noise is added to the signals with the selected SNR
level.</p>
<p>This option can be used e.g., to investigate the robustness of a specific
algorithm with respect to the additive noise. </p>
<p class=MsoNormal align=center style='text-align:center'><img border=0
width=518 height=543 id="_x0000_i1034" src="icalab_files/image008.jpg"></p>
<h6><b>Fig. 7</b> Window illustrating the procedure of adding noise
synthetically. Please ignore this option for real data. The noise can be added
to test robustness of algorithms for benchmarks.</h6>
<h2>Choosing the algorithm</h2>
<p>Once you have loaded data and chosen the (optional) mixing matrix, you can
select one of the available algorithms. There is a list of about 20 algorithms
which can be applied. Inexperienced users should try to use AMUSE, SOBI (SOS
algorithms), SANG, JADE, SIMBEC (HOS algorithms) first. You can find detailed
descriptions of algorithms either in the <a href="#book">Book</a> or through
the online help <a href="#algorithms">here</a>. </p>
<p>In this version of <b>ICALAB</b> we have implemented also several versions
of constrained <st1:City w:st="on">ICA</st1:City> (cICA) or <st1:City w:st="on"><st1:place
w:st="on">ICA</st1:place></st1:City> with Reference (ICA-R) algorithms. Such
algorithms require additional information about references signal or signals.
The objective is to estimate hidden components which are correlated or in some
sense have some “similarity” to a specific reference signal. The
group of these algorithms is called as <i>constrained <st1:City w:st="on"><st1:place
w:st="on">ICA</st1:place></st1:City></i> (cICA) or <i>ICA with Reference</i>
(ICA-R). Generally, we can use a hierarchical or multi-stage BSS approach
to ICA-R. In this approach at the first stage, we can apply a
simple standard <st1:City w:st="on"><st1:place w:st="on">ICA</st1:place></st1:City>
algorithm like SOBI but with automatic ordering of components to extract
the suitable references signals. In the second stage we can use some
selected components as references signals in ICA-R in order to
extract more precisely physiological meaningful components corresponding for
example to some periodic stimulus or events. We can repeat this procedure
several times using various components and/or various algorithms. I worth
to note that for some sensor data as reference signals can used directly
specific observed signals with strong responses or artifacts with some
waveforms which are potentially interesting but not sufficiently enhanced. In
such cases, for ICA-R algorithm the user must specify a data file in which reference
signal or signals are available as additional inputs.</p>
<p>You can also add your own algorithm(s) or algorithms available from other
sources to test and compare their performance and choose the optimal one for
your purpose. Please refer to the example m-files: <a href="#user_alg">user_alg<i>k</i>.m</a>
to see how <b>ICALAB</b> calls the user-defined algorithms or <code><span
style='font-size:10.0pt'>amuse.m</span></code> file. The user algorithm can
return only demixing (separating) matrix <b>W</b>. </p>
<p class=MsoNormal align=center style='text-align:center'><a name="alg_names"></a><img
border=0 width=518 height=543 id="_x0000_i1035" src="icalab_files/image009.jpg"></p>
<h6><span class=GramE><b>Fig. 8</b> Window illustrating how to select an
algorithm from the list of available algorithms for <st1:City w:st="on"><st1:place
w:st="on">ICA</st1:place></st1:City>, BSS, BSE.</span> They are three types of
algorithms: <st1:City w:st="on"><st1:place w:st="on">ICA</st1:place></st1:City>
algorithms exploiting mutual independence based on higher order statistics
(HOS) (e.g., Natural Gradient (NG) algorithms, JADE, FICA (Fixed Point
algorithms)), BSS algorithms based on second order statistics (SOS) and
exploiting spatio-temporal decorrelation (e.g., AMUSE, EVD2, SOBI, SONS). BSE
algorithms can extract arbitrary group of sources sequentially one by one.
Users can add their own algorithms or algorithms available on the Internet
using available <code>user_alg<i>k</i>.m</code> files.</h6>
<p class=MsoNormal align=center style='text-align:center'><img border=0
width=406 height=256 id="_x0000_i1036" src="icalab_files/image010.jpg"></p>
<h6><span class=GramE><b>Fig. 9</b> Window illustrating how to use Advanced
Options.</span> Experienced users can use the advanced options by clicking on
the <tt>ADV. OPTIONS</tt> button and set the parameters. As an example the
window of advanced parameters for SOBI algorithm is shown. </h6>
<h2>Setting the advanced parameters</h2>
<p>In the package, most of the algorithms are given default parameters which
often close to optimal. Thus, you can start testing the algorithms without the
need for adjusting or preselecting the parameters. The default parameters are
already tuned approximate optimum values for typical data. Otherwise, you can
tune the parameters for most of the algorithms by clicking on the advanced
option button <tt><span style='font-size:10.0pt'>ADV. OPTIONS</span></tt>. It
is recommended that you use this option and tune the parameters if you are
already familiar with the algorithm (see references (publications) for
derivation, properties, and description of the algorithms).</p>
<p>Some advanced parameters are designed globally and/or automatically for all
algorithms, or each algorithm in a specific group of algorithms. For example,
the advanced parameter ORDERING (i.e., ranking or sorting of estimated
components) allows automatic sorting the estimated components by many different
criteria (see Fig. 10).</p>
<p class=figure><img border=0 width=410 height=269 id="_x0000_i1037"
src="icalab_files/image011.jpg"></p>
<h6><a name="OLE_LINK9"></a><a name="OLE_LINK1"></a><a name="OLE_LINK2"></a><a
name="OLE_LINK8"></a><span style='mso-bookmark:OLE_LINK9'><b>Fig. <span
class=GramE>10</span></b></span><span class=GramE><b><span style='color:blue'>
</span></b>Illustration</span> of automatic ranking of components in the
Advanced parameter option by selecting several criteria:
complexity–linear predictability, value kurtosis, skewness, sparsity,
canonical correlation, <st1:place w:st="on"><st1:City w:st="on">Hurst</st1:City></st1:place>
exponent.</h6>
<p>ICA-R group of algorithms requires additional parameters in the form of
reference signal and detail reference signal. User needs to select the set of
reference signals and choose one specific component as the reference signal.
More information how to use cICA algorithms will be explained later in more
details.</p>
<p class=figure><img border=0 width=407 height=402 id="_x0000_i1038"
src="icalab_files/image012.jpg"></p>
<h6><b>Fig. 11<span class=GramE> Illustration</span> how to select
parameters for a cICA (ICA-R) algorithm.</b> .</h6>
<p>In many cases, the user extensively tests an algorithm or a set of
algorithms and chooses optimal set of his/<span class=GramE>her own</span>
parameters for specific data. This set of parameters can be conveniently saved
and used in the next sessions by selecting (pressing) the button <tt><span
style='font-size:10.0pt'>SET AS DEFAULT</span></tt>. In other words, after
adjusting the advanced parameters, the user could store and use them latter as
the user-default parameters by pressing the button <tt><span style='font-size:
10.0pt'>SET AS DEFAULT</span></tt>. They are saved and next loaded
automatically from data file “<i>defaultpars.mat</i>” as a specific
algorithm is called. To restore the default program value, we could press
button <tt><span style='font-size:10.0pt'>DEFAULT</span></tt> (set default
values for current algorithm) or just delete data file “<i>defaultpars.mat</i>”
(set default values for all algorithms).</p>
<p class=figure><img border=0 width=408 height=255 id="_x0000_i1039"
src="icalab_files/image013.jpg"> <img border=0 width=408 height=257
id="_x0000_i1040" src="icalab_files/image014.jpg"></p>
<h6><b>Fig. 12<span class=GramE> <span style='font-weight:normal'>Set</span></span></b>
and save the user preferable parameters by “Set as Default”.</h6>
<p>After selecting the algorithm and adjusting its free parameters, you can
click on the button <tt><span style='font-size:10.0pt'>RUN ALGORITHM</span></tt>.
The learning procedure will be started and the algorithm specific messages will
appear in the main MATLAB command window. During the computation, an additional
window will display the algorithm name will appear. You can stop the learning
process by clicking on the <tt><span style='font-size:10.0pt'>INTERRUPT</span></tt>
button. </p>
<p>In the version 3, the interrupting feature is enabled for almost all
algorithms and Monte- Carlo analysis. </p>
<p class=MsoNormal align=center style='text-align:center'><span
style='font-size:10.0pt;font-family:Tahoma'><img border=0 width=366 height=206
id="_x0000_i1041" src="icalab_files/image015.jpg"></span></p>
<h6><b>Fig. 13</b> Interrupt Window. Please click on the <tt>INTERRUPT</tt>
button to stop algorithm for example if the convergence is slow and you want to
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