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Does anyone know of an algorithm that can perform the following tasks:

  1. Unsupervised clustering without specifying the number of clusters apriori. For example if all the buildings in wide geographical are plotted as as points on a 2d plane such an algorithm should be able to identify the number of settlements such as cities, towns and villages, regardless of the size of the settlements.

  2. Thinning the cluster of points to a representative points. In the wide geographical area example this thinning operation would select a number of "representative" dwellings (of minimum size 1, for the smallest settlements) for each settlement.

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    $\begingroup$ there are tons of algorithms for unsupervised clustering. You can find dozens of books with name "clustering". Your question seem standard, so it is not hard to choose/tailor the algorithms for your purpose. $\endgroup$
    – Yixin Cao
    Nov 26, 2012 at 22:47
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    $\begingroup$ In particular, HAC is something you should look into $\endgroup$
    – Suresh Venkat
    Nov 27, 2012 at 4:09

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You could use the DENCLUE algorithm, you don't need the number of clusters apriori and the attractor points could act as representative points for a cluster.

Also, the algorithm handles arbitrarily shaped clusters and is quite robust to noise.

Of course, there are other algorithms that could be used, but I believe DENCLUE is a good choice.

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