I have a data set, which form 3 known groups. I performed k-means clustering algorithm on the data set, setting the number of clusters to be 3 as well. I end up with 3 groups by k-means.
Wishing to see how well k-means algorithm has worked, I am trying to benchmark these k-means groups against the known groups. The problem is, I do not know the correspondence. Maybe, group 1 by k-means corresponds to the real group 3 or 2.
My idea is quite brutal: test all $3!=6$ possible correspondences. See which correspondence gives me the "best results". The "best result" may be defined as the lowest false/postive (I am not sure about this point either)?
Is there a standard/better way of finding the correspondence which in turn allows me to do the evaluation of the clustering quality?