# [R] Obtaining covariance matrices for kmeans output clusters

Luke Hutchison lukeh at email.byu.edu
Wed Oct 23 22:41:06 CEST 2002

```I am having trouble getting a covariance matrix for each cluster which
is output by kmeans().  My input looks like:

> imagedat
Red Green Blue
0_0       5     7    8
1_0       5     5   18
2_0       7     8   49
3_0      22     8   76
4_0      54    10   67
5_0      50     9   28
6_0      18    10   15
7_0       9     7    6
8_0       2     5    7
...

I cluster using

> cl <- kmeans(imagedat, nclust, maxsteps)
> cl
\$cluster
[1]  1  1  9  8  2  9  1  1  1  1  1  1  1  1  1  8  8  8  8  4
[25]  9  9  8  8  8  2  2  9  1  1  9  9  7 10 10 10 10 10 10 10 10
...
\$centers
Red      Green      Blue
1    9.940421   7.744428  11.11652
2   85.198120  18.363348  68.10173
3  109.247072  80.873439  87.42371
...

I then try applying "var" to each Red, Green, Blue triplet (i.e. row) in
the cluster output using

> covar <- tapply(imagedat, factor(cl\$clust), var)
arguments must have same length

but obviously imagedat is being looked at as a stacked array, three
times the length of cl\$clust, so I get the above error.

So my questions are:
(1) How can I get ten 3x3 covariance matrices from the clustering
results "cl\$clust", i.e. one for each cluster, with the covariance of
Red, Blue and Green from "imagedat" for each cluster?
(2) How then can I apply operations to all of the matrices at once, i.e.
take the inverse of all of them, or multiply them all by a constant,
without having to write a for-loop?  How can I apply operations to them
each in turn, say in a for-loop?

Thanks very much for any pointers, I'm new to R and its
data-manipulation and storage mechanisms are puzzling to me.

Luke Hutchison.

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```