[R] Weighted Clustering

[Christian Hennig]

Hi,

sorry, I do not have any references, it was only an intuitive idea (but
there might be references somewhere out in space).
The idea is that you can indeed weight the points. For this you have to
multiply the contribution of each point to the target function by the
weight, and you have to compute every case number for a cluster as the
sum of the weights (i.e., the means become weighted means). Some thought
about the target function should tell you where you need a sum of weights
instead of a case number.
ML estimation for normal mixture models does exactly this, by weighting
the points according to the a posteriori probability of membership in a
class. But these weights could also be multiplied by a fixed weight for a
point. (If the weights would be fractions with the same
denominator, this should lead to about the same clustering as if you 
would have
so many replications of each point as the numerator says; that's the
motivation.)

Best,
Christian 
 

On Thu, 23 Oct 2003, vishal goyal wrote:

> Hi,
> 
> I have read some of the papers on weighted clustering but those weigths
> are with respect to variables (say we are clustering height measured in
> cms and weights in tons etc) rather than each point itself and hence they
> just multiply the distances with the weights. In my case, it is something
> like a facility location. Each point has a weight (probability of its
> requirement) (all the variables have equal weightage) and i want to
> cluster and also move the mean to the point of highest weightage. I know
> in deterministic case, this is exactly the facility location problem but i
> was hoping to have some simpler-algorithm in probabilitsic case.
> 
> Or, did i mis-understand the theory and there is something other than just
> multpying the variables with the weights. I would appreciate any reference
> or pointer.
> 
> Regards
> Vishal
***********************************************************************
Christian Hennig
Fachbereich Mathematik-SPST/ZMS, Universitaet Hamburg
hennig at math.uni-hamburg.de, http://www.math.uni-hamburg.de/home/hennig/
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