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.



Clustering distance
The [variation of information](https://en.wikipedia.org/wiki/Variation_of_information) seems to be the sort of thing you're looking for.


