Re: Finding Clusters

• To: mathgroup at smc.vnet.net
• Subject: [mg104558] Re: [mg104515] Finding Clusters
• From: mante <claude.mante at univmed.fr>
• Date: Wed, 4 Nov 2009 01:32:18 -0500 (EST)
• References: <200911030751.CAA01018@smc.vnet.net>

```fd a écrit :
> All.
>
> I have a list which represents some natural event. These events are
> listed pair-wise, which corresponds to event happening within certain
> time interval from each other, as below
>
> event={{1,2},{1,3},{3,4},{5,6},{7,8},{8,10}}
>
> I wish to find a thread of events, i.e. if event A is related to B and
> B to C, I wish to group {A,B,C} together. For the example above I
> would have
>
> {{1,2,3,4},{5,6},{7,8,10}}
>
> This would correspond to do a Graph Plot and identifying the parts
> which are disconnected It should be simple but I'm really finding it
> troublesome.
>
>
The 1st point is to build a convenient distance :
Dist01[list1_, list2_] := If[Length@Union[list1, list2] < 4, 0, 1];
then compute the distance matrix:
Adj = Outer[Dist01, event, event, 1];
and you get the graph:
GraphPlot[1 - Adj, VertexLabeling -> True]

You can also use another strategy :
Cls = FindClusters[event, DistanceFunction -> Dist01];
Map[Composition[Union, Flatten], Cls]

--
*********************************

Claude Manté, IR CNRS

UMR CNRS 6117 LMGEM
http://www.com.univ-mrs.fr/LMGEM/

Centre d'Océanologie de Marseille
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```

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