I'm aware a silhouette score ranges from -1 to 1. But what can be considered a significant increase? 0.1 to 0.2 (because 100%) or 0.5 to 0.6?
Obviously higher is better, but is there some measure of significance when it comes to silhouette scores?
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1$\begingroup$ Could you provide a reference to "silhouette scores", it's not a term I've seen before. $\endgroup$– Matthew DruryCommented Jul 13, 2016 at 15:05
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1$\begingroup$ It's you who decides. Typically, mean silhouette over 0.6 is considered a "good" clustering solution. $\endgroup$– ttnphnsCommented Jul 13, 2016 at 15:47
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$\begingroup$ @MatthewDrury en.wikipedia.org/wiki/Silhouette_(clustering) $\endgroup$– M.S.Commented Jul 13, 2016 at 23:05
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Since the scores are bounded by 1, I would consider going from 0.1 to 0.2 a 1-(0.8/0.9) about 11% improvement only, whereas 0.5 to 0.6 is 20% improvement on this scale (20% reduction in "error" from the optimum).
However, I would avoid the use of "significant" unless you can relate this to statistical testing!
Beware that Silhouette etc. should not be used to compare different methods because they have a bias. Silhouette is a heuristic tool to see whether you have chosen parameters reasonably, and can thus be okay to use when having to choose e.g. k in k-means. But an argument like "k-means is better than HAC because we had a significantly higher silhouette score on all our data sets" will likely be nonsense, because of bias towards one clustering algorithm or another.
answered Aug 7, 2016 at 8:04
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$\begingroup$ The first paragraph is weird to me. Can you explain? And where did you see "error" notion in silhouette index? $\endgroup$– ttnphnsCommented Aug 7, 2016 at 8:24
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$\begingroup$ Silhouette doesn't have a notion of error, but you can compute the "gain" twoards the optimum silhouette of 1. That makes more sense than considering 0.1 to 0.2 a 100% increase. $\endgroup$ Commented Aug 7, 2016 at 8:30
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$\begingroup$ Can you provide insight into your second statement ? Since the Silouhette only uses the partitions and the dissimilarity function I don't see where the bias can come from ? E.g. two runs of kmeans should be comparable, no ? kmeans vs kmedoids should work too ? $\endgroup$– oDDsKooLCommented Jan 3, 2017 at 8:07
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$\begingroup$ Compare silhouette with Euclidean distance and Manhattan distance, and you get different results. Furthermore, it clearlyprefers centroid-based and convex clusterings over e.g. DBSCAN by design. $\endgroup$ Commented Jan 4, 2017 at 13:14