R help - Sep 2004 - decompose a correlation matrix

Is there a simple way to decompose the upper triangle
of a correlation matrix to a linear list;

For example:

  X Y Z
X 1 2 3
Y 2 1 4
Z 3 4 1

so you get a list like:

xy 2
XZ 3
YZ 4

I suspect you can do it with a matrix transformation, but
that beyond me at present.

Many thanks

Mark
_________________________
Department of Molecular and Human Genetics,
Baylor College of Medicine,

On Thu, 23 Sep 2004 13:08:53 -0500, "Mark Strivens"
<strivens at bcm.tmc.edu> wrote :
>Is there a simple way to decompose the upper triangle
>of a correlation matrix to a linear list;
>
>For example:
>
>  X Y Z
>X 1 2 3
>Y 2 1 4
>Z 3 4 1
>
>so you get a list like:
>
>xy 2
>XZ 3
>YZ 4
>
>I suspect you can do it with a matrix transformation, but
>that beyond me at present.
x[ row(x) < col(x) ]

will give the entries you want.

Duncan Murdoch

This may not have things in the order you want but you can see if it gets
close to what you want:
> x <- matrix(1:16,ncol=4)
> x
     [,1] [,2] [,3] [,4]
[1,]    1    5    9   13
[2,]    2    6   10   14
[3,]    3    7   11   15
[4,]    4    8   12   16
> y <- x[row(x) < col(x)]
> y
[1]  5  9 10 13 14 15
> 
bob



-----Original Message-----
From: Mark Strivens [mailto:strivens at bcm.tmc.edu] 
Sent: Thursday, September 23, 2004 2:09 PM
To: r-help at stat.math.ethz.ch
Subject: [R] decompose a correlation matrix


Is there a simple way to decompose the upper triangle
of a correlation matrix to a linear list;

For example:

  X Y Z
X 1 2 3
Y 2 1 4
Z 3 4 1

so you get a list like:

xy 2
XZ 3
YZ 4

I suspect you can do it with a matrix transformation, but
that beyond me at present.

Many thanks

Mark
_________________________
Department of Molecular and Human Genetics,
Baylor College of Medicine,

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Thanks for the answers the appear to be just
right. 

i.e. 

corrmat[upper.tri(corrmat)]

or

x[col(x)>row(x)] 

The slight problem is I lose all the column &
row labels from the correlation matrix, so I 
am not sure of the order of the values (i.e.
which combination of markers the value 
represents).

Is there anyway to drag the labels along with
the value extraction?
_________________________
Department of Molecular and Human Genetics,
Baylor College of Medicine,

> From: Duncan Murdoch
> 
> On Thu, 23 Sep 2004 13:08:53 -0500, "Mark Strivens"
> <strivens at bcm.tmc.edu> wrote :
> 
> >Is there a simple way to decompose the upper triangle
> >of a correlation matrix to a linear list;
> >
> >For example:
> >
> >  X Y Z
> >X 1 2 3
> >Y 2 1 4
> >Z 3 4 1
> >
> >so you get a list like:
> >
> >xy 2
> >XZ 3
> >YZ 4
> >
> >I suspect you can do it with a matrix transformation, but
> >that beyond me at present.
> 
> x[ row(x) < col(x) ]
> 
> will give the entries you want.
> 
> Duncan Murdoch
Perhaps slightly more transparent:

x[upper.tri(x)]

or

x[lower.tri(x)]

Best,
Andy

> From: Mark Strivens
> 
> Thanks for the answers the appear to be just
> right. 
> 
> i.e. 
> 
> corrmat[upper.tri(corrmat)]
> 
> or
> 
> x[col(x)>row(x)] 
> 
> The slight problem is I lose all the column &
> row labels from the correlation matrix, so I 
> am not sure of the order of the values (i.e.
> which combination of markers the value 
> represents).
> 
> Is there anyway to drag the labels along with
> the value extraction?
> _________________________
> Department of Molecular and Human Genetics,
> Baylor College of Medicine,
idx <- upper.tri(x)
cbind(row=row(x)[idx], col=col(x)[idx], value=x[idx])

Best,
Andy

On 23-Sep-04 Mark Strivens wrote:
> Is there a simple way to decompose the upper triangle
> of a correlation matrix to a linear list;
> 
> For example:
> 
>   X Y Z
> X 1 2 3
> Y 2 1 4
> Z 3 4 1
> 
> so you get a list like:
> 
> xy 2
> XZ 3
> YZ 4
> 
> I suspect you can do it with a matrix transformation, but
> that beyond me at present.
Let C be your correlation matrix. Then:

  C[lower.tri(C)]

or equivalently

  C[upper.tri(C)]

E.g. (in your notation):

  > C
       [,1] [,2] [,3] [,4]
  [1,]    1    2    3    4
  [2,]    2    1    5    6
  [3,]    3    5    1    7
  [4,]    4    6    7    1

  > (C[lower.tri(C)])
  [1] 2 3 4 5 6 7

See ?lower.tri

Best wishes,
Ted.


--------------------------------------------------------------------
E-Mail: (Ted Harding) <Ted.Harding at nessie.mcc.ac.uk>
Fax-to-email: +44 (0)870 094 0861   [NB: New number!]
Date: 23-Sep-04                                       Time: 20:37:36
------------------------------ XFMail ------------------------------

Thanks guys for the help, here's the final (grizzly?)
solution:

#generate a correlation matrix
cm<-cor(someDataFrame, y = NULL ...)

# get the list of labels (included in the dataframe)
labels<-labels(cm)[[1]]

# retrieve the uppper portion of the correlation matrix (as logical values)
idx <- upper.tri(cm)

# combine the logical values with the marker list
mcm<-cbind(marker=paste((markers[col(t(cm))[idx]],'&',markers[row(t(cm))[idx
]]),
	row=row(t(cm))[idx], col=col(t(cm))[idx], value=cm[idx])

gives the format:

label2 & label1	1	2	0.97712
label3 & label1	1	3	0.84587
label4 & label1	1	4	0.92184
label5 & label1	1	5	0.54698


There seemed to be some issues with the row()and col()
commands not thinking the output of cor() was a matrix
so I used t() to force it into a table...

_________________________
Department of Molecular and Human Genetics,
Baylor College of Medicine,
1 Baylor Plaza,
Houston,
TX 77030.

713-798-1947 (work)
832-876-7956 (cell)