Practical problems with correlation dimension

dmitri dimag at mindspring.com
Fri Jan 23 04:30:49 EST 2004


"Karl" <karlknoblich at yahoo.de> wrote in message
news:235b9607.0401210500.3ebedda5 at posting.google.com...
> 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


Value of C.D. depends on several factors: level of data stationarity,
the length of a stationary segment, external noise, sampling
rate, and embedding dimension.
For example, if we choose "stationary" region of time series, the length of
this
region must be about 10^(D+2) points. Therefore to
determine D=10 we need about 10^6 points of suficiently stationary
observable.

I guess you are trying apply the method of C.D. to EEG series,
if so, you'll be disappointed unless you can  find a subject with
sufficiently (see above)
long segment of quasi-stationary data.

Some time ago I got similar results for EEG series.

If you want, you can check the paper at:
http://mindspring.com/~nldap/publ/ind2000.pdf


Hope this help,

D.Gribkov





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