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To validate the results of a clustering solution, I am using the ARI to quantify the agreement with a reference classification method.

Something which I do not quite understand is the concept of a "correct" or "true" clustering nature of a dataset, and as such if comparison with "Distribution" is appropriate for evaluating the clustering solutions.

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What is your aim of clustering? It all depends on what you want to know. If your aim is to reproduce the given classification, the ARI will tell you how well you do that. However I wonder why then would you want to cluster these data if you know the true clusters already? What you do here gives some sensible validation information for your clustering if, although you want to learn something new and therefore your aim is not simply to reproduce the given classification, you can argue that from your aim of clustering it can be expected to be positively related to that classification. Although this doesn't necessarily mean that the clustering with 0.2898 is necessarily better than the one with 0.2387. Both are somewhat but not very strongly related to the given classification, the one with $K=4$ a bit better, but there may be other criteria you may also want to look at.

However, if your aim of clustering is unrelated to the given classification, these values don't tell you anything useful.

Clustering relies crucially on what kind of clusters the user wants to find, what clusters are supposed to mean in terms of subject matter and background information etc. One shouldn't think about clustering as a fully automatic formal procedure.

You may want to read this, particularly Sec. 2 regarding the idea of "true" clusters: https://arxiv.org/abs/1503.02059

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  • $\begingroup$ Can't say much about this, because "I am told" basically means that somebody else has decided this and I have no idea on what basis. $\endgroup$ May 29 '20 at 23:00
  • $\begingroup$ The ARI says that the $K=4$ solution is more similar to the given classification. To what extent that means that it's better is another matter, see my answer. It may play some role... $\endgroup$ May 30 '20 at 10:52

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