TITLE: Clustering distance
QUESTION [5 upvotes]: Is there a good notion of distance between partitions of a (fixed, finite) set? The context is this: suppose I have a clustering algorithm, which clusters points using some method or other. Now, I perturb the positions of the points, the clustering changes, and I want some quantitative estimate of how much it has changed. 
When there are two clusters $K_1, K_2$ which morph into $L_1, L_2,$ then it seems reasonable to look at the minimum of the sizes of $K_1 \Delta L_1$ and $K_1 \Delta L_2,$ but for more clusters it seems less clear.

REPLY [4 votes]: The variation of information seems to be the sort of thing you're looking for.