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I want to compare two clustering algorithms. I took data that the first algorithm gathered in one cluster. The second algorithm gave 3 clusters for the same points. In order to compare the results, I tried to compute the two different silhouette for these algorithms, but I realized that in the first case, since there was only one cluster, there is no other cluster to compute the dissimilarities to. How can silhouette be defined in the case of one cluster? If it is not possible to define it, what would be a good way to compare the results of my two clustering methods?

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  • $\begingroup$ What do you want to find out from this comparison? That will tell you how you can compare them. $\endgroup$ – Peter Flom Feb 27 '14 at 10:36
  • $\begingroup$ @PeterFlom I want to find out which clustering method gives the best results, that is assigns on average each instance in the right sample and differentiates the clusters from each other. $\endgroup$ – bigTree Feb 27 '14 at 10:41
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    $\begingroup$ Well, then you have to define "best". But if one of the options is one cluster, then that assigns everything to one cluster so it doesn't differentiate anything. $\endgroup$ – Peter Flom Feb 27 '14 at 10:43
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    $\begingroup$ Silhouette needs at least 2 clusters. Try to use Gap statistic to decide whether you should prefer one cluster (= no clusters) or several clusters in the same data set. $\endgroup$ – ttnphns Feb 27 '14 at 15:58
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I'm not sure why you are doing things this way. It seems to me that the first algorithm found initially 2 clusters (from where you chose one to be clustered by the 2nd algorithm). Why don't you cluster the whole data set with both algorithms and compare the clusterings?

Its very difficult to compare one cluster vs 3 clusters on the same data set. To have one clusters makes little sense, and one should reasonably expect the output of the K-Means criterion to be much smaller when you have 3 clusters (so you can't use this for comparison).

Now what's the silhouette of the 2nd algorithm generating 3 clusters? is it in average closer >=0.5? if not the meaning of this clustering is debatable.

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  • $\begingroup$ Thank you for your interesting answer. In fact, I am trying to improve the first algorithm because, when interpreting the data, we realized it was possible to refine it. Since the whole dataset is 'big' and it takes days to run the algorithms on it, I took one cluster generated by the first algorithm and applied the second to it. It generated 3 clusters out of it. $\endgroup$ – bigTree Feb 27 '14 at 12:57

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