📄 node7.html
字号:
<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML 2.2//EN"><!--Converted with LaTeX2HTML 96.1-h (September 30, 1996) by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds --><HTML><HEAD><TITLE>Embedding parameters</TITLE><META NAME="description" CONTENT="Embedding parameters"><META NAME="keywords" CONTENT="TiseanHTML"><META NAME="resource-type" CONTENT="document"><META NAME="distribution" CONTENT="global"><LINK REL=STYLESHEET HREF="TiseanHTML.css"></HEAD><BODY bgcolor=ffffff LANG="EN" > <A NAME="tex2html142" HREF="node8.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="icons/next_motif.gif"></A> <A NAME="tex2html140" HREF="node5.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="icons/up_motif.gif"></A> <A NAME="tex2html134" HREF="node6.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="icons/previous_motif.gif"></A> <BR><B> Next:</B> <A NAME="tex2html143" HREF="node8.html">Mutual information</A><B>Up:</B> <A NAME="tex2html141" HREF="node5.html">Phase space representation</A><B> Previous:</B> <A NAME="tex2html135" HREF="node6.html">Delay coordinates</A><BR> <P><H2><A NAME="SECTION00032000000000000000">Embedding parameters</A></H2><P>A reasonable choice of the delay gains importance through the fact that wealways have to deal with a finite amount of noisy data. Both noise andfiniteness will prevent us from having access to infinitesimal length scales,so that the structure we want to exploit should persists up to the largestpossible length scales. Depending on the type of structure we want to explorewe have to choose a suitable time delay. Most obviously, delay unity forhighly sampled flow data will yield delay vectors which are all concentratedaround the diagonal in the embedding space and thus all structureperpendicular to the diagonal is almost invisible. In [<A HREF="citation.html#Casdagli">24</A>] theterms <I>redundancy</I> and <I>irrelevance</I> were used to characterize theproblem: Small delays yield strongly correlated vector elements, large delayslead to vectors whose components are (almost) uncorrelated and the data arethus (seemingly) randomly distributed in the embedding space. Quite a numberof papers have been published on the proper choice of the delay and embeddingdimension. We have argued repeatedly [<A HREF="citation.html#gss">11</A>, <A HREF="citation.html#KantzSchreiber">2</A>, <A HREF="citation.html#habil">3</A>] that an``optimal'' embedding can - if at all - only be defined relative to aspecific purpose for which the embedding is used. Nevertheless, somequantitative tools are available to guide the choice.<P>The usual autocorrelation function (<ahref="../docs_f/autocor.html">autocor</a>, <a href="../docs_c/corr.html">corr</a>) and the time delayedmutual information (<a href="../docs_c/mutual.html">mutual</a>), as well as visual inspection of delayrepresentations with various lags provide important information about reasonable delay times whilethe false neighbors statistic (<a href="../docs_c/false_nearest.html">false_nearest</a>) can give guidance about the proper embeddingdimension. Again, ``optimal'' parameters cannot be thus established except inthe context of a specific application.<P><BR> <HR><UL><A NAME="CHILD_LINKS"> </A><LI> <A NAME="tex2html144" HREF="node8.html#SECTION00032100000000000000">Mutual information</A><LI> <A NAME="tex2html145" HREF="node9.html#SECTION00032200000000000000">False nearest neighbors</A></UL><HR><A NAME="tex2html142" HREF="node8.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="icons/next_motif.gif"></A> <A NAME="tex2html140" HREF="node5.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="icons/up_motif.gif"></A> <A NAME="tex2html134" HREF="node6.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="icons/previous_motif.gif"></A> <BR><B> Next:</B> <A NAME="tex2html143" HREF="node8.html">Mutual information</A><B>Up:</B> <A NAME="tex2html141" HREF="node5.html">Phase space representation</A><B> Previous:</B> <A NAME="tex2html135" HREF="node6.html">Delay coordinates</A><P><ADDRESS><I>Thomas Schreiber <BR>Wed Jan 6 15:38:27 CET 1999</I></ADDRESS></BODY></HTML>⌨️ 快捷键说明
复制代码
Ctrl + C
搜索代码
Ctrl + F
全屏模式
F11
切换主题
Ctrl + Shift + D
显示快捷键
?
增大字号
Ctrl + =
减小字号
Ctrl + -