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I have data (some behavioral features, measured on some scales) on people. I want to cluster people based on these features. This is an unsupervised scenario, as I have no prior knowledge on the clusters, nor any training data. I might have some good guesses about the number of clusters. All measures are continuous.

The caveat is this: I prefer "clean" clusters and would be happy to "throw away" noisy cases and mark them as "unclassified". Noisy cases may be outliers, or cases that are close enough to 2 or more clusters so that putting them in either cluster will make that cluster less homogeneous, and will put the clusters to one another. However, cases that are unclassified (that is, thrown away) must be far enough from each other (otherwise they could form a new cluster by themselves).

I wonder if there is any work that deal with this, or do you have any insights about how to do this and how to decide which cases should become "unclassified".

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You should look at K-mean clustering. It seems very related to what you plan on doing.

To exclude the outliers, use the following links

http://cs.joensuu.fi/~villeh/35400978.pdf

https://stackoverflow.com/questions/13989419/removing-outliers-from-a-k-mean-cluster

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