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I am not sure what statistical test to use for comparing clustering on related data.

I have two sets of measurements on each person. I cluster each person by each measurement. I then measure how much the two coincide. I want to know how I would test for how significance the agreement of the clustering is.

For example I have 10 people and for each person I have two sets of attributes say vector A and Vector B both 10 of length 10.

I cluster the 10 people into 2 clusters using vector A and get something like

1 2 1 1 2 1 1 1 2 2

That is person one is assigned to cluster one, person two to cluster two person three to cluster one etc

I cluster the 10 examples into 2 clusters using vector B and get something like

1 2 1 1 2 1 1 1 1 1

These two clustering agree to 80% but how significant is this? What is the formula for calculating this? Is there a variant for more than 2 clusters? would it make sense if there were a different number of clusters for each measurement or if some samples only had one set of measurements?

Thank you for any thoughts :)

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    $\begingroup$ I am not sure to understand precisely what you are after or what “significant” means in this context but you might be interested in measures of “inter-rater agreement”. $\endgroup$ – Gala Jul 10 '13 at 9:37
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Look up the literature on external evaluation of clusterings.

There are at least 30 measures to compute a similarity of two clusterings. Maybe one of these measures will give you significance values.

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