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Practical problems with correlation dimension

k p Collins kpaulc at [----------]earthlink.net
Wed Jan 21 08:38:40 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

What I will say has not yet been accepted by others,
so keep that in mind as you consider it.

You're missing some crucial data that cross-correlates
your 'time' series to the cerebellar topology.

The cerebellum is a topographically-mapped subsystem.

Any analysis must preserve, and incorporate, that mapping
if the correlations are to be meaningful.

And, then, to continue, one has to follow this mapping into
the rest of the brain.

It's a =big= problem, but the mapping is mapped :-] through
the efforts of Neuroscientists, and all one has to do is 'grind'
through it.

There a couple of other things that make your analysis Difficult.

One is that the data is virtually always, itself, a transformation.

The other is that the activation that occurs within the cerebellum
is extremely-dynamic, with a =lot= of different inputs converging
and 'sliding' with respect to each other. There is such 'sliding'
stuff with respect to every joint in the skelleton. [These enter
into the way that the nervous system maintains it's 'awareness'
of the body's orientation in 3-D space [climbing fibers from
the inferior olive].] And this is only one set of such 'sliding-field'
stuff that occurs within the cerebellum. There are hundreds
[perhaps thousands] more.

So your analysis is Hard.

ken [k. p. collins]

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