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
embed?
4 messages · rkevinburton at charter.net, Gabor Grothendieck, Ravi Varadhan +1 more
Its lets you perform rolling summaries using apply:
apply(embed(1:10, 3), 1, mean)
[1] 2 3 4 5 6 7 8 9 Note that 2 is the mean of 1:3, 3 is the mean of 2:4, ..., 9 is the mean of 8:10.
On Fri, Apr 3, 2009 at 11:04 AM, <rkevinburton at charter.net> wrote:
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
______________________________________________ R-help at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
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: rvaradhan at jhmi.edu Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html ---------------------------------------------------------------------------- -------- -----Original Message----- From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On Behalf Of rkevinburton at charter.net Sent: Friday, April 03, 2009 11:05 AM To: r-help at 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 ______________________________________________ R-help at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
rkevinburton at charter.net wrote:
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.
following this 'explanation', the first row consists of values x[t],
x[t-1], ... x[t-3+1], that is, x[t], x[t-1], x[t-2]. how does t, the
original index of x, relate to positions in the matrix? does it
correspond to the row number, or the column number? it can't be the
former, because then the first row would include x[1], x[0], x[-1] --
nonsense. it can't be the latter, because the first row would include
x[1], x[1], x[1] (nonsense), and so all other rows (nonsense).
for a vector, say x, the output, say matrix, contains values calculated
as follows:
m[i,j] = x[i + dimension - j], with i = 1, ...,
length(x)-dimension+1 and j = 1, ..., dimension
so that you have a rolling window over the vector, with row indices
corresponding to the start of the window, and column indices
corresponding to the position within the window.
arguably, the authors could have done their homework better.
vQ