# How can we compute the difference between two silhouette scores for the same dataset?

Given a dataset X on which I applied k-means and I computed the Silhouette Index score. I consider this score as the truth. I applied again k-means on X and I computed the Silhouette Index score. My question is how to compute the error (%) inducted by the second silhouette score compared to the first silhouette score. I thought to this formulate:

 |score1 - score2|/2.


I divided by 2 because the silhouette score is between -1 and 1.

• Same dataset? X and X? Were you using different K-means settings (different number of clusters?) – ttnphns Mar 8 at 18:30
• @ttnphns Yes the same dataset X and I apply different K-means settings – nabiltos Mar 8 at 18:34
• You may quantify their difference any way you like. Usually one just plots the values of such criterion for different cluster solutions. Visual comparison is enough. So far I can't understand from your question why you might be wishing more than that. – ttnphns Mar 8 at 18:51
• Well, I think you may go any reasonable formula for you. You should however use, with k-means, not classic Silhouette index but more suited for it "deviation" aka "simplified" version of Silhouette. You may want to read "Clustering criteria" document on my web-page. – ttnphns Mar 8 at 19:09
• The doc. to read is in the "Clustering criterions" archive here spsstools.net/en/macros/KO-spssmacros – ttnphns Mar 8 at 19:52