k-means clustering

If there is not an operational definition for the number of clusters, yes, you have to figure this out yourself. You can use an algorithm to figure it out, but how do you know the algorithm is trading off the # clusters vs. compactness the way you want? You have to have some idea of what you want, of course, but usually in my consulting engagements where k was unknown we would do the following. First, we compute the mean values of all the input variables to get the gist of where the clusters are centered. You can compute the mean values of every variable in the clusters, but it could be that all the variables except one have the same mean for every cluster--it's just one variable that is really responsible for driving the formation of the clusters.