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<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML 2.0//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>Multivariate data</TITLE><META NAME="description" CONTENT="Multivariate data"><META NAME="keywords" CONTENT="Surrogates"><META NAME="resource-type" CONTENT="document"><META NAME="distribution" CONTENT="global"><LINK REL=STYLESHEET HREF="Surrogates.css"></HEAD><BODY bgcolor=#ffffff LANG="EN" > <A NAME="tex2html317" HREF="node25.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="next_motif.gif"></A> <A NAME="tex2html315" HREF="node22.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="up_motif.gif"></A> <A NAME="tex2html309" HREF="node23.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="previous_motif.gif"></A> <BR><B> Next:</B> <A NAME="tex2html318" HREF="node25.html">Uneven sampling</A><B>Up:</B> <A NAME="tex2html316" HREF="node22.html">Various Examples</A><B> Previous:</B> <A NAME="tex2html310" HREF="node23.html">Including non-stationarity</A><BR> <P><H2><A NAME="SECTION00062000000000000000">Multivariate data</A></H2><A NAME="secmulti2"> </A> In Ref. [<A HREF="node36.html#anneal">26</A>], the flexibility of the approach was illustrated by asimultaneous recording of the breath rate and the instantaneous heart rate of ahuman subject during sleep. The interesting question was, how much of thestructure in the heart rate data can be explained by linear dependence on thebreath rate. In order to answer this question, surrogates were made that hadthe same autocorrelation structure but also the same cross-correlation withrespect to the fixed input signal, the breath rate. While the linearcross-correlation with the breath rate explained the coherent structure of theheart rate, other features, in particular its asymmetry under time reversal,remained unexplained. Possible explanations include artefacts due to thepeculiar way of deriving heart rate from inter-beat intervals, nonlinearcoupling to the breath activity, nonlinearity in the cardiac system, andothers.<P>Within the general framework, multivariate data can be treated very much the same way as scalar time series. In the above example, we chose to use one ofthe channels as a reference signal which was not randomised. The rationalebehind this was that we were not looking for nonlinear structure in the breathrate itself and thus we didn't want to destroy any such structure in thesurrogates. In other cases, we can decide either to keep or to destroycross-correlations between channels. The former can be achieved by applying thesame permutations to all channels. Due to the limited experience we have so farand the multitude of possible cases, multivariate problems have not beenincluded in the TISEAN implementation yet.<P><HR><A NAME="tex2html317" HREF="node25.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="next_motif.gif"></A> <A NAME="tex2html315" HREF="node22.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="up_motif.gif"></A> <A NAME="tex2html309" HREF="node23.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="previous_motif.gif"></A> <BR><B> Next:</B> <A NAME="tex2html318" HREF="node25.html">Uneven sampling</A><B>Up:</B> <A NAME="tex2html316" HREF="node22.html">Various Examples</A><B> Previous:</B> <A NAME="tex2html310" HREF="node23.html">Including non-stationarity</A><P><ADDRESS><I>Thomas Schreiber <BR>Mon Aug 30 17:31:48 CEST 1999</I></ADDRESS></BODY></HTML>⌨️ 快捷键说明
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