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<head><title>Nonlinear noise reduction</title></head>
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<h3>Nonlinear noise reduction</h3>
<font color=blue><tt>project <font color=red>-m# -q# -r# -k#</font> [-i# -o </tt><em>outfile</em><tt> -l# -x# -c# -V# -h] </tt><em> file</em>
</font>
<blockquote>
<br> <font color=red><tt> -m </tt></font>embedding dimension
<br> <font color=red><tt> -q </tt></font>dimension of manifold
<br> <font color=red><tt> -r </tt></font>radius of neighbourhoods
<br> <font color=red><tt> -k </tt></font>minimal number of neighbours
<br> <font color=blue><tt> -i </tt></font>number of iterations (1)
<br> <font color=blue><tt> -l </tt></font>number of values to be read (all)
<br> <font color=blue><tt> -x </tt></font>number of values to be skipped (0)
<br> <font color=blue><tt> -c </tt></font><a href="../general.html#column" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/general.html#column">column to be read</a> (1 or <font color=blue><em>file</em></font>,#)
<br> <font color=blue><tt> -o </tt></font><a href="../general.html#outfile" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/general.html#outfile">output file name</a>, just <font color=blue><tt> -o </tt></font>means <font color=blue><em>file</em></font><font color=blue><tt>_c</tt></font>, <font color=blue><em>file</em></font><font color=blue><tt>_cc</tt></font> (etc.)
<br> <font color=blue><tt> -V </tt></font><a href="../general.html#verbosity" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/general.html#verbosity">verbosity level</a> (0 = only fatal errors)
<br> <font color=blue><tt> -h </tt></font>show this message
<p>
<a href="../general.html#verbosity" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/general.html#verbosity">verbosity level</a> (add what you want):
<p>
<font color=blue> 1</font> = input/output<br>
<font color=blue> 2</font> = state of neighbour search<br>
</blockquote>
Performs <a href="../chaospaper/node24.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/chaospaper/node24.html">nonlinear projective noise reduction</a>. Output file (the cleaned
sequence) is <font color=blue><em>file</em><tt>_c[ccc]</tt></font>
(one letter <font color=blue><tt>c</tt></font> per iteration). As a second
column, the difference between original and cleaned sequence is printed.
<p>
<font color=red><b>Note:</b></font> This routine is largely redundant with
<a href="../dresden/ghkss.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/dresden/ghkss.html">ghkss</a>.
<p>
This routine is based on
<blockquote>
P. Grassberger, R. Hegger, H. Kantz, C. Schaffrath, and T. Schreiber,
<br><em> On noise reduction methods for chaotic data</em>,
<br>Chaos <b>3</b>, 127 (1993);
<br>Reprinted in: E. Ott, T. Sauer, and J. A. Yorke, eds.,
<br><em> Coping With Chaos</em>, Wiley, New York (1994)
</blockquote>
<p>
<hr>
<h3>Usage example</h3>
Try also just running: <font color=blue><tt>gnuplot project.gnu</tt></font> in
the <font color=blue><tt>examples</tt></font> directory.
<p>
<pre>
> <font color=blue><tt>henon -l10000 > data</tt></font>
> <font color=blue><tt>addnoise -v0.02 data</tt></font>
> <font color=blue><tt>project -m7 -q2 -r0.05 -k20 -i3 data_noisy</tt></font>
gnuplot> <font color=blue><tt>plot '< cat data_noisy | delay'</tt></font>
gnuplot> <font color=blue><tt>plot '< cat data_noisy_ccc | delay'</tt></font>
</pre>
<p>
<IMG SRC="addnoise.gif" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/wuppertal/addnoise.gif" alt="noisy data">
<IMG SRC="project.gif" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/wuppertal/project.gif" alt="corrected data">
<p>
<a href="../contents.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/docs/contents.html">Table of Contents</a> * <a href="../../index.html" tppabs="http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.0/index.html" target="_top">TISEAN home</a>
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