### Clustering Sets

I hear talks, referee papers, and space out trying to abstract larger problems during my days --- in many papers, good, bad and some pretty awful, there seems to be an attempt to solve the following: Given S_1, ..., S_k, each a set of say d dimensional points, find a suitable clustering of the sets. Yes, I realize the world does not need yet another clustering variant and yet another ''distance function''. Still, if someone has some nifty results/pointers, let me know.

## 3 Comments:

Perhaps the simplest reduction to standard clustering would be to just cluster representatives of sets (e.g. 1-centers).

One general approach is to consider distance functions for

point-sets, e.g., Hausdorff distance or Earth-Mover-Distance. Then one can use the usual distance-based methods (k-median, k-center) that we all know and cherish.Cheers,

I like both the approaches above, both really reductions, and it is not clear one needs anything more in real life. Typically the talks/papers I know seem to mainly stuggle with defining a distance function, and they get progressively complex, sigh.

-- metoo

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