Kevin,
The documentation is quite clear.
What "embedding" does is that it takes a scalar time series, x[t], and
"embeds" it in a higher-dimensional space of dimension, "dimension". The
entries in the matrix you see are the indices of the time-series.
So, for example, if dimension = 2, you embed your time-series on a 2-Dim
space: (x, y), where the points are: (x[2], x[1]), (x[3], x[2]), ...,
(x[N], x[N-1]).
> embed(x, dimension=2)
[,1] [,2]
[1,] 2 1
[2,] 3 2
[3,] 4 3
[4,] 5 4
[5,] 6 5
[6,] 7 6
[7,] 8 7
[8,] 9 8
[9,] 10 9
>
This is allso known as Ruelle-Takens embedding in non-linear dynamical
systems, where this device is helpful in detecting the existence of a
low-dimensional attractor of the time-series.
Ravi.
----------------------------------------------------------------------------
-------
Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health
Division of Geriatric Medicine and Gerontology
Johns Hopkins University
Ph: (410) 502-2619
Fax: (410) 614-9625
Email: rvarad...@jhmi.edu
Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html
----------------------------------------------------------------------------
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-----Original Message-----
From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On
Behalf Of rkevinbur...@charter.net
Sent: Friday, April 03, 2009 11:05 AM
To: r-help@r-project.org
Subject: [R] embed?
I have a question on the function 'embed'. I ran the example
x <- 1:10
embed(x, dimension=3)
This gives the output:
[,1] [,2] [,3]
[1,] 3 2 1
[2,] 4 3 2
[3,] 5 4 3
[4,] 6 5 4
[5,] 7 6 5
[6,] 8 7 6
[7,] 9 8 7
[8,] 10 9 8
I don't quite understand the output and why it is useful. First, there are
only 8 rows down from 10 and the first element starts with 3. Of course I
can think of explanations as to what is occuring but I cannot see how this
is useful. I am sure it has application as i see this command used in much
of the source but I just cannot see it now.
The documentation states:
Each row of the resulting matrix consists of sequences x[t], x[t-1], ...,
x[t-dimension+1], where t is the original index of x. If x is a matrix,
i.e., x contains more than one variable, then x[t] consists of the tth
observation on each variable.
This explanation doesn't seem to account for the dimension argument.
Thank you for your comments.
Kevin
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