Dear IDLers,
I am doing clustering using CLUST_WTS and CLUSTER I have a doc-related
problem. The doc for CLUST_WTS says:
"The CLUST_WTS function computes the weights (the cluster centers) of an
n-column, m-row array, where n is the number of variables and m is the
number of observations or samples. CLUST_WTS uses k-means clustering.
With this technique, CLUST_WTS starts with k random clusters and then
iteratively moves items between clusters, minimizing variability within
each cluster and maximizing variability between clusters"
From what I know from my textbook (Wilks, "Statistical Methods in the
Atmospheric Sciences") k-mean clustering does work iteratively and
computes the centroids, and the centroids are computed as the mean of
the clustered population. Now, this "mean" value can be defined
according to any arbitrary distance measure, which in the case of
CLUST_WTS, is not clearly defined. So I assume it to be the euclidian
distance, and therefore I would assume that the cluster centers computed
by CLUST_WTS are also the mean values of my cluster populations, but
this is not *exactly* the case, no matter how many iterations I use.
They are close enough, sure, but not equal.
What am I missing?
Thanks,
Fab
For those interested, here is a programm (using cg). It is enough to run
it a few times to see what I mean:
pro test_cluster
; Construct 3 separate clusters in a 3D space:
n = 50
c1 = RANDOMN(seed, 2, n)
c1[0, *] -= 3
c2 = RANDOMN(seed, 2, n)
c2[0, *] += 3
array = [[c1], [c2]]
; Compute cluster weights, using three clusters:
weights = CLUST_WTS(array, N_CLUSTERS = 2, N_ITERATIONS=100)
; Compute the classification of each sample:
result = CLUSTER(array, weights, N_CLUSTERS = 2)
pc1 = where(result eq 0)
pc2 = where(result eq 1)
cgWindow
cgPlot, array[0,*], array[1,*], /ADDCMD, /NODATA
cgPlotS, c1[0,*], c1[1,*], /ADDCMD, COLOR='red', PSYM=1
cgPlotS, c2[0,*], c2[1,*], /ADDCMD, COLOR='blue', PSYM=1
cgPlots, weights[0, 0], weights[1, 0], PSYM=16, COLOR='black',
/ADDCMD, SYMSIZE=2
cgPlots, weights[0, 1], weights[1, 1], PSYM=16, COLOR='black',
/ADDCMD, SYMSIZE=2
cgPlots, mean(array[0,pc1]), mean(array[1,pc1]), PSYM=17,
COLOR='black', /ADDCMD, SYMSIZE=2
cgPlots, mean(array[0,pc2]), mean(array[1,pc2]), PSYM=17,
COLOR='black', /ADDCMD, SYMSIZE=2
end
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