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There are related questions but the answers don't seem to explain how to practically judge these measurements for non stats users. I have a dataset which I clustered with K=4 using hierarchical clustering (complete and average methods) and kmeans, and have calculated VI, Rand, and Dunn indexes. I know this is very simplistic but from what I understand: for these measures higher is better (clusters are farther apart). But these metrics give me contrasting answers.

Methods HC-comp HC-avg K-means
IV   1.6137 1.5365 1.5225
Rand 0.2703 0.2667 0.3914
Dunn 0.08468 0.07358 0.08006

Judging from these numbers: HC-comp is better according to IV and Dunn, but according to Rand K-means seem a better choice. Should I user other cluster statistics like average silhouette width, separation, diameter,etc?

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The first question to ask is: are they any good at all.

It does not matter if measure A puts approach X before Y if they all agree that none of the results is particularly good - they are meant to rank good results, not bad results.

Also. Measures such as VI, Silhouette etc. are heuristics. Silhouette would define a clustering algorithm on its own - there just isn't any fast way to search for a good solution. So when you are choosing based on Silhouette, you are in fact just picking that result that is closer to the unknown optimum Silhouette solution. I.e. you are then using for example x k-means runs as a fast approximation to the Silhouette clustering problem. But then: how good is Silhouette clustering?

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  • $\begingroup$ I appreciate the insight but it's not helping me reaching a solution to my problem. Could you suggest something more specific? $\endgroup$ – Herman Toothrot Oct 24 '18 at 7:40
  • $\begingroup$ The practical suggestion is: look at the actual clustering, not an index score. $\endgroup$ – Anony-Mousse Oct 24 '18 at 20:36

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