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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2//EN"><!--Converted with LaTeX2HTML 97.1 (release) (July 13th, 1997) by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan* with significant contributions from: Jens Lippman, Marek Rouchal, Martin Wilck and others --><HTML><HEAD><TITLE>5.4.2 Hard Competitive Learning</TITLE><META NAME="description" CONTENT="5.4.2 Hard Competitive Learning"><META NAME="keywords" CONTENT="DemoGNG"><META NAME="resource-type" CONTENT="document"><META NAME="distribution" CONTENT="global"><META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=iso_8859_1"><LINK REL="STYLESHEET" HREF="DemoGNG.css"><LINK REL="next" HREF="node17.html"><LINK REL="previous" HREF="node15.html"><LINK REL="up" HREF="node14.html"><LINK REL="next" HREF="node17.html"></HEAD><BODY ><!--Navigation Panel--><A NAME="tex2html257" HREF="node17.html"><IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="http://www.neuroinformatik.ruhr-uni-bochum.de/icons/next_motif.gif"></A> <A NAME="tex2html254" HREF="node14.html"><IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="http://www.neuroinformatik.ruhr-uni-bochum.de/icons/up_motif.gif"></A> <A NAME="tex2html248" HREF="node15.html"><IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="http://www.neuroinformatik.ruhr-uni-bochum.de/icons/previous_motif.gif"></A> <A NAME="tex2html256" HREF="node1.html"><IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="http://www.neuroinformatik.ruhr-uni-bochum.de/icons/contents_motif.gif"></A> <BR><B> Next:</B> <A NAME="tex2html258" HREF="node17.html">5.4.3 Neural Gas</A><B> Up:</B> <A NAME="tex2html255" HREF="node14.html">5.4 Model Specific Options</A><B> Previous:</B> <A NAME="tex2html249" HREF="node15.html">5.4.1 LBG , LBG-U</A><BR><BR><!--End of Navigation Panel--><A NAME="tex2html1" HREF="http://www.neuroinformatik.ruhr-uni-bochum.de/ini/VDM/research/gsn/DemoGNG/HCL_5.html">Hard Competitive Learning</A><IMG WIDTH="49" HEIGHT="38" ALIGN="BOTTOM" BORDER="0" SRC="../smallDuke.gif"><H3><A NAME="SECTION00074200000000000000">5.4.2 </A></H3><DL><DT><STRONG>Variable</STRONG><DD>Switches from a constant to a variable learning rate.<DT><STRONG>epsilon</STRONG><DD>This value (<IMG WIDTH="9" HEIGHT="12" ALIGN="BOTTOM" BORDER="0" SRC="img9.gif" ALT="$\epsilon$">) determines the extent to which thewinner is adapted towards the input signal (constant learning rate).<DT><STRONG>epsilon_i</STRONG><DD>epsilon initial (<IMG WIDTH="14" HEIGHT="24" ALIGN="MIDDLE" BORDER="0" SRC="img10.gif" ALT="$\epsilon_i$">).<DT><STRONG>epsilon_f</STRONG><DD>epsilon final (<IMG WIDTH="17" HEIGHT="24" ALIGN="MIDDLE" BORDER="0" SRC="img11.gif" ALT="$\epsilon_f$">).<DT><STRONG>t_max</STRONG><DD>The simulation ends, if the number of input signals exceeds this value (<I>t</I><SUB><I>max</I></SUB>).</DL><P>The variable learning rate is determined according to<P ALIGN="CENTER"><IMG WIDTH="144" HEIGHT="27" SRC="img12.gif" ALT="\begin{displaymath}\qquad\epsilon(t) = \epsilon_i(\epsilon_f/\epsilon_i)^{t/t_{\rm max}}.\end{displaymath}"></P><BR><HR><ADDRESS><I>Hartmut S. Loos</I><BR><I>10/19/1998</I></ADDRESS></BODY></HTML>
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