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Re: Question - Cluster Analysis

  • To: mathgroup at smc.vnet.net
  • Subject: [mg89842] Re: Question - Cluster Analysis
  • From: magma <maderri2 at gmail.com>
  • Date: Sun, 22 Jun 2008 03:24:29 -0400 (EDT)
  • References: <g3ihn2$fb6$1@smc.vnet.net>

On Jun 21, 11:30 am, Steve Mahoney <patrick.bernh... at gmx.net> wrote:
> Hello,
>
> I have a question regarding hierarchical cluster analysis. One measure to determine the number of clusters is the so called elbow criteria, which is just a list of the single distances between the clusters.
>
> These values are inside the results from the Agglomerate function, but I am not able to extract them to a list.
>
> data = {{1, 2, 2}, {1, 3, 3}, {2, 4, 2}, {5, 4, 3}, {5, 4, 4}, {7, 6, 7}};
>
> Agglomerate[data]
>
> Cluster[Cluster[
>   Cluster[Cluster[{1, 2, 2}, {1, 3, 3}, 2, 1, 1], {2, 4, 2}, 3, 2, 1], Cluster[{5, 4, 3}, {5, 4, 4}, 1, 1, 1], 10, 3, 2], {7, 6, 7}, 17, 5, 1]
>
> --> now I have to extract the values manually
>
> elbowcriterium = ListLinePlot[{17, 10, 3, 2, 1}]
>
> --> suggesting three clusters
>
> Thanks a lot for a suggestion, how to handle this, which would be really helpful for me!

Hello,
this was a good excuse for me to learn some cluster analysis in the
past 2 hours !
Ok, now I know what you are talking about, so this is your function

ElbowCriterium[
  cl_Cluster] := {cl[[3]], ElbowCriterium[cl[[1]]],
   ElbowCriterium[cl[[2]]]} // Flatten

ElbowCriterium[x_] := {}

On your data:

data = {{1, 2, 2}, {1, 3, 3}, {2, 4, 2}, {5, 4, 3}, {5, 4, 4}, {7, 6,
    7}};

Agglomerate[data] // ElbowCriterium

the answer is....

{17, 10, 3, 2, 1}



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