Hello,
I am studying time-series analysis of the human heart rate.
Does anyone have some source code already prepared for estimation of
time delay and correlation dimension of time series data?

In order to Estimate the embedding dimension I need essentially two
papers that I can not find them, please help me to get them:
F.Takens, Detecting strange attractors in turbulence (1980)
P.Grassberger, I.Procaccia (1983a,b)
I strongly need this help.
Eric Maik
ericmaik@yahoo.co.uk

From:	Dr Chaos
Subject:	Re: code for estimation of correlation dimension
Date:	Wed, 22 Dec 2004 11:16:23 -0800

Eric wrote:
> Hello,
> I am studying time-series analysis of the human heart rate.
> Does anyone have some source code already prepared for estimation of
> time delay and correlation dimension of time series data?
>
> In order to Estimate the embedding dimension I need essentially two
> papers that I can not find them, please help me to get them:
> F.Takens, Detecting strange attractors in turbulence (1980)
> P.Grassberger, I.Procaccia (1983a,b)
> I strongly need this help.
> Eric Maik
> ericmaik@yahoo.co.uk
>

Note, that estimating the correlation dimension does not give evidence
for the minimum embedding dimension.

Also, most analyses that I've seen of cardiac time series dynamics does
not show low-dimensional chaos, but complex multiscale fat-tailed noise
dynamics. Correlation dimension may not give that interesting a number,
and it would certainly not have any single geometric dimension which
unfolds the dataset onto a nice manifold.

From:	Tony Roberts
Subject:	Re: code for estimation of correlation dimension
Date:	Fri, 17 Dec 2004 09:30:18 +1000

Eric wrote:
> Hello,
> I am studying time-series analysis of the human heart rate.
> Does anyone have some source code already prepared for estimation of
> time delay and correlation dimension of time series data?
>
> Eric Maik
> ericmaik@yahoo.co.uk
>

See my software page http://www.sci.usq.edu.au/staff/robertsa/soft.html
for fdim.sh which contains some pretty good matlab code for estimating
generalised dimensions. To apply to time series data is trivial
transformation of the data into consectutive m-tuples.

Tony

From:	Lou Pecora
Subject:	Re: code for estimation of correlation dimension
Date:	Mon, 20 Dec 2004 10:26:11 -0500

In article <41c21af8@news.connect.usq.edu.au>,
Tony Roberts wrote:

> Eric wrote:
> > Hello,
> > I am studying time-series analysis of the human heart rate.
> > Does anyone have some source code already prepared for estimation of
> > time delay and correlation dimension of time series data?
> >
> > Eric Maik
> > ericmaik@yahoo.co.uk

I recommend you know what you're doing before blindly applying
algorithms to time series. Read relevant parts of Kantz and Schreiber's
Nonlinear Time Series Analysis or Abarbanel's Analysis of Observed
Chaotic Data. And read over Kennel and Abarbanel's paper on False
Nearest Strands for determining embedding dimension.

Taken's paper is a beautiful mathematical proof of why, generically,
time-delay reconstructions will faithfully (up to diffeomorphism)
reproduce the system's attractor, but it is an 'existence' proof. It
doesn't give information on how to do this in a practical or robust way
with real data (that's not a criticism, just an observation of Taken's
paper). You need to be aware of the pitfalls and caveats, hence, my
suggested readings above.

Having said that, I suspect that you are not going to get anything much
out of cardiac time series. Most biological data is too non-stationary
and/or too high dimensional to do attractor reconstruction. In
particular, I doubt the correlation dimension will be insightful or even
meaningful. It's notoriously prone to errors from noise or
non-stationarity.

IMHO.

-- Lou Pecora (my views are my own)

From:	Jürgen_Kahrs
Subject:	Re: code for estimation of correlation dimension
Date:	Mon, 20 Dec 2004 17:03:41 +0100

Lou Pecora wrote:

> Having said that, I suspect that you are not going to get anything much
> out of cardiac time series. Most biological data is too non-stationary
> and/or too high dimensional to do attractor reconstruction. In

What Lou Pecora says about biological time series
is definitely right.

Eric, before you go and analyze the data you should
also find out which kind of "pre-processing" has been
done on the data to "clean it up". Traditional measurement
devices often do some kind of analog or digital filtering
to emphasize those aspects of the signal that are interesting.
Nonrecursive filters are "smearing" the original signal,
making it hard to detect all dimensions. Recursive filters
can introduce additional dimensions that don't actually
exist in the signal but only in the device's filter.

> particular, I doubt the correlation dimension will be insightful or even
> meaningful. It's notoriously prone to errors from noise or
> non-stationarity.

I can confirm this from my own experience with analyzing data.
But I can also confirm that there are tons of publications
filled with "results" from analyzing this kind of data. For
example, there are textbooks (authored by established scientists)
which show how the correlation dimension of the EEG signal
is distributed over surface of the human head. If Eric does
his research mainly for advancing his position in a scientific
community, then he can safely ignore what I said here:
Algorithms for calculation of correlation dimension always
produce some output which is open to the most sophisticated
kind of interpretation.

From:	Roger Bagula
Subject:	Re: code for estimation of correlation dimension
Date:	Fri, 07 Jan 2005 00:32:58 GMT

Just what good did Lou Pecora's response or yours do anyway?
You both didn't respond to the question of well known cardiac research
in this area?
Give us all a break : if you don't know
then don't "guess".
You were both far from the point of the question.
I think they have set up in analog hardware, now. that gives the largest
Lyapunov
for a heart monitor. It seems to measure how bad the heart attack is.
You embaress us all when people come from other fields and ask simple
questions and get totally misleading answers.
Jürgen Kahrs wrote:

> Lou Pecora wrote:
>
>> Having said that, I suspect that you are not going to get anything
>> much out of cardiac time series. Most biological data is too
>> non-stationary and/or too high dimensional to do attractor
>> reconstruction. In
>
>
> What Lou Pecora says about biological time series
> is definitely right.
>
> Eric, before you go and analyze the data you should
> also find out which kind of "pre-processing" has been
> done on the data to "clean it up". Traditional measurement
> devices often do some kind of analog or digital filtering
> to emphasize those aspects of the signal that are interesting.
> Nonrecursive filters are "smearing" the original signal,
> making it hard to detect all dimensions. Recursive filters
> can introduce additional dimensions that don't actually
> exist in the signal but only in the device's filter.
>
>> particular, I doubt the correlation dimension will be insightful or
>> even meaningful. It's notoriously prone to errors from noise or
>> non-stationarity.
>
>
> I can confirm this from my own experience with analyzing data.
> But I can also confirm that there are tons of publications
> filled with "results" from analyzing this kind of data. For
> example, there are textbooks (authored by established scientists)
> which show how the correlation dimension of the EEG signal
> is distributed over surface of the human head. If Eric does
> his research mainly for advancing his position in a scientific
> community, then he can safely ignore what I said here:
> Algorithms for calculation of correlation dimension always
> produce some output which is open to the most sophisticated
> kind of interpretation.

--
Respectfully, Roger L. Bagula
tftn@earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
alternative email: rlbtftn@netscape.net
URL : http://home.earthlink.net/~tftn

From:	Lou Pecora
Subject:	Re: code for estimation of correlation dimension
Date:	Fri, 07 Jan 2005 12:20:28 -0800

In article <41DDD88C.5010502@earthlink.net>,
Roger Bagula wrote:

> Just what good did Lou Pecora's response or yours do anyway?
> You both didn't respond to the question of well known cardiac research
> in this area?

I hope it gave everyone my point of view. That mostly what goes on here
and elsewhere in good news groups. The poster can do what he wants
with my information. I can only recount what I know and suspect.
Nothing wrong with that.

Now stop being the net nag and just help out.

-- Lou Pecora (my views are my own)

From:	Jürgen_Kahrs
Subject:	Re: code for estimation of correlation dimension
Date:	Fri, 07 Jan 2005 13:33:12 +0100

Roger Bagula wrote:

> Just what good did Lou Pecora's response or yours do anyway?

Lou Pecora had serious doubts about attractor reconstruction
from biological data when the data is prone to noise or
non-stationarity.

> You both didn't respond to the question of well known cardiac research
> in this area?
> Give us all a break : if you don't know
> then don't "guess".

Eric (the original poster) asked this question:

"I am studying time-series analysis of the human heart rate."

There is no specific reference in it. So, a bit of guessing
on our side was necessary when trying to understand what Eric
means.

> You were both far from the point of the question.
> I think they have set up in analog hardware, now. that gives the largest
> Lyapunov
> for a heart monitor. It seems to measure how bad the heart attack is.

Phrases like "I think" and "It seems" are indications that
you are also guessing here. There is of course nothing wrong
in guessing when trying to understand and help other people.

> You embaress us all when people come from other fields and ask simple
> questions and get totally misleading answers.

If we really misunderstood Eric, then Eric is of course
free to ignore what we said. In a constructive discussion,
I would have liked Eric to answer and tell us what we
misunderstood.

From:	Lou Pecora
Subject:	Re: code for estimation of correlation dimension
Date:	Fri, 07 Jan 2005 12:23:47 -0800

In article <347ds8F48q1u6U1@individual.net>,
Jurgen Kahrs wrote:

> If we really misunderstood Eric, then Eric is of course
> free to ignore what we said. In a constructive discussion,
> I would have liked Eric to answer and tell us what we
> misunderstood.

Completely right. It's the dialog that helps focus the information flow.

No one is lying. When we guess we say so. I have some experience
working with biological time series. I think that counts and would be
of interest to Eric. If he needs something else or thinks I'm
misinterpreting what he says, then he's free to follow up with a reply.

-- Lou Pecora (my views are my own)

From:	Roger Bagula
Subject:	Re: code for estimation of correlation dimension
Date:	Thu, 06 Jan 2005 15:32:55 GMT

Dear Eric Maik,
A lot of work has actually been done on cardiaic arthmia
and the strange attaractors associated with it.
I think I posted here about it several months ago.
I must say that I was disappointed in the responses by
this group. A very short google of chaos and Cardiac Arrhythmias will
pull up a lot of stuff.
There is a whole medical speciality since the 80's in this area.
One famous Russian even claimed it as his own ( from a lecture
published in Math Monthly)
after a Canadian started publishing in that area.
I thionk that approximate entropy may be more
definitive for a time series type analysis
of heart rates during heart attacks.
Glass is the guy who's paperes you need to read:
http://www.cnd.mcgill.ca/bios/glass/cardiac(new).htm

Eric wrote:

>Hello,
>I am studying time-series analysis of the human heart rate.
>Does anyone have some source code already prepared for estimation of
>time delay and correlation dimension of time series data?
>
>In order to Estimate the embedding dimension I need essentially two
>papers that I can not find them, please help me to get them:
>F.Takens, Detecting strange attractors in turbulence (1980)
>P.Grassberger, I.Procaccia (1983a,b)
>I strongly need this help.
>Eric Maik
>ericmaik@yahoo.co.uk
>
>
>

--
Respectfully, Roger L. Bagula
tftn@earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
alternative email: rlbtftn@netscape.net
URL : http://home.earthlink.net/~tftn

From:	Jürgen_Kahrs
Subject:	Re: code for estimation of correlation dimension
Date:	Thu, 06 Jan 2005 17:29:53 +0100

Roger Bagula wrote:

> I must say that I was disappointed in the responses by
> this group.

I found the responses adequate and constructive.
The signal-to-noise-ratio in this thread was
remarkably high.

> A very short google of chaos and Cardiac Arrhythmias will
> pull up a lot of stuff.

What does this prove ?
A very short Google about extraterrastrial visitors
from outer space will also produce a lot of stuff.
There is a whole philosophical speciality since
the 50's in this area.

From:	Roger Bagula
Subject:	Re: code for estimation of correlation dimension
Date:	Fri, 07 Jan 2005 00:25:43 GMT

You're very funny.
About as funny as the Russian who claimed to have invented
chaos analysis of Cardiac Arrhythmias after Glass started publishing
about it.
Try paying attention to the posts.
These guys didn't know and didn't respond as if they did.
And they all read my post about it.
I know them ... they just didn't take time to think about it.
I'm really ashamed they did so badly after I had posted several
links about this very subject.
An Undergrad in my chaos theory egroup
who wants software for Lyapunov calculations ( not Kaplan-Yorke dimension).
And we all know how badly they responsed in that area here.
I at least showed where people could download programs that mostly worked.
Have you ever done those calculations on time series?

Jürgen Kahrs wrote:

> Roger Bagula wrote:
>
>> I must say that I was disappointed in the responses by
>> this group.
>
>
> I found the responses adequate and constructive.
> The signal-to-noise-ratio in this thread was
> remarkably high.
>
>> A very short google of chaos and Cardiac Arrhythmias will pull up a
>> lot of stuff.
>
>
> What does this prove ?
> A very short Google about extraterrastrial visitors
> from outer space will also produce a lot of stuff.
> There is a whole philosophical speciality since
> the 50's in this area.

--
Respectfully, Roger L. Bagula
tftn@earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
alternative email: rlbtftn@netscape.net
URL : http://home.earthlink.net/~tftn

From:	Jürgen_Kahrs
Subject:	Re: code for estimation of correlation dimension
Date:	Fri, 07 Jan 2005 13:50:21 +0100

Roger Bagula wrote:

> And we all know how badly they responsed in that area here.

You should not interpret too much evil-willingness
into what I wrote. I wish Eric had answered and
clarified the situation.

> I at least showed where people could download programs that mostly worked.

Lou also did recommend software (TISEAN by Kantz & Schreiber).
Seeing Lou recommend the same papers that I appreciate told
me that I was not completely off-topic.

> Have you ever done those calculations on time series?

Yes, some years ago I wrote some software myself
and tested it on data. When you start working with
experimental data, you notice many pitfalls. For
example, non-stationary data makes it impossible
to get anything but garbage from most algorithms (GIGO).
Another problem is the resolution of an A/D converter:
you need at least 12 bits to get meaningful results
in Lyapunov and correlation dimension. These 12 bits
have to be noise-free and the signal has to really
cover the full range of the 12 bits.