Article View: sci.nonlinear
Article #33Re: Practical problems with correlation dimension
From: Pavel Pokorny
Date: Wed, 21 Jan 2004 14:30
Date: Wed, 21 Jan 2004 14:30
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In sci.nonlinear Karl <karlknoblich@yahoo.de> wrote: > Hallo! > I want to calculate the correlation dimension of a time serie. > What I have done > I calculated the correlation integral C(r) (number of point having a > distance smaller than r) for different embedding dimensions. Taking > the slopes of the curve of log C(r) against log r for the different > embedding dimensions and plotting them against the embedding dimension > should result in a limes of the slopes: the correlation dimension. > My problem > Which slope shall I take? > In examples I saw in text books there is a nice limit of the slopes > with higher embedding dimensions. In my data I do not know which slope > I should take because the slope of the curve varies. If I take the > slope at a certain value of log r I can not get a limes. > My curves (log C(r) against log r) can be seen in > http://karlknoblich.4t.com/korrdim.jpg > What to do? Does anybody knows such data and how to handle it? > Hope somebody can help! > Karl There is no guarantee that the limit exists. There may be different slopes on different scales with different widths. There is a huge difference between real life data and solution of low dim mathematical models without noise (as seen in books). -- Pavel Pokorny Math Dept, Prague Institute of Chemical Technology http://www.vscht.cz/mat/Pavel.Pokorny
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From: Pavel Pokorny <Pavel.Pokorny@vscht.REMOVEME.cz>
Newsgroups: sci.nonlinear,sci.bio.technology,sci.math,bionet.neuroscience,sci.fractals
Subject: Re: Practical problems with correlation dimension
Date: Wed, 21 Jan 2004 14:30:11 +0000 (UTC)
Organization: Czech Technical University
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