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Oct 30, 2019 at 20:56 comment added Has QUIT--Anony-Mousse As far as I can tell - your question doesn't discuss what exactly you use as "centroid distance", there is some ambiguity involved - the answer will still be the same: because the total sum of distances decomposes into intra and inter cluster distances, and dividing into k parts reduces by approximately k. A deviation from this trend can only be expected if you have a very good solution for k but not for k-1. Then there will be one k that is special, the others will still follow this trend.
Oct 30, 2019 at 8:46 comment added Jonathan To avoid misunderstandings and presumptions, I've edited the question.
Oct 28, 2019 at 6:58 history answered Has QUIT--Anony-Mousse CC BY-SA 4.0