AW: [R] estimating number of clusters ("Null or more")

Dear Christian,

  first of all thank you for your answer. I am going to parse through 
  the pages you told me. Meanwhile I'd like to note that probably it 
  is a good idea to put 2-3 lines of R-code demonstrating such a 
  simple needs somnewhere in docs of `cluster' package. E.g.

  x<-rnorm(500)
  ... # output means we have rather 1 claster

  x<-c(rnorm(500), rnorm(500)+5)
  ... # output means we have rather 2 or more claster

  It would be nice not only for me.

EMclust of library mclust decides about an optimal number of mixture
components using the BIC.

It is not clear for me whether one could use BIC without a
statement about the familiy of distribution. Indeed BIC is based 
on likelihood, and what the likelihood should be if the only 
adequate statement about the destribution is the ECDF itself?..

As far as I know, there is no direct answer to the problem of testing
homogeneity vs. clustering in R. There are lots of 
theoretical difficultiesand there is no "standard routine" to 
do this, neither in R, nor elsewhere.

I am not looking for the Holy Grail, or I hope so :-)

In particular, I beleive some entropy-based criteria should 
fully satisfy me here. BIC might be also good if it might be 
applied to a ECDF.

I would suggest to invent a null model for your  
data modelled as
homogeneous and to estimate the distribution of a 
suitable clustering
statistics (such as the silhouette avg.width in pam, 
BIC, average
distance of the points to kth nearest neighbor or ratio 
between 25% largest
and smallest distances in the dataset) by Monte
Carlo/parametric bootstrap. Perhaps I say this too quickly; 

a bit compressed, but something is clear anyway :-)

it's non-trivial and at least you have to design the 
simulation so that rejection/acceptance is not a 
consequence of different scaling of data and null model. 

not clear here :-)

thanks again
Valery A.Khamenya