Can we compare clusters with C-Index average?

Question

I use K-Means algorithm to create clusters. As you know K-means algorithm needs cluster count as parameter. I try cluster counts as starting two from eight and calculate all C-Index of clusters in every looping then get the avegare of these C-Indexes. Then compare C-Index avegares and choose the minimum C-Index average as best quality cluster count. Is that true way for detecting cluster count?

Answer 1

There is no one correct way to detect cluster count. See following google search, this is still an active research area. Wikipedia articles says that:

The correct choice of k is often ambiguous, with interpretations depending on the shape and scale of the distribution of points in a data set and the desired clustering resolution of the user.

Only you can determine if using c-index in this way is a good way to determine cluster numbers in your domain. See another question of using c-index in clustering.