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I am conducting a cluster analysis involving 60 subjects and 5 continuous variables.

After appropriate scaling, I performed hierarchical clustering with Euclidean distance and complete linkage, and then k-means clustering with elbow point ispection and silhoutte width analysis relying on Euclidean distance.

Unfortunately, the results of these three different approaches to choose the appropriate number of clusters differ substantially. In particular, hierarchical clustering isolates 3 subjects early on, and thus at least 3 or 4 clusters appear appropriate. Elbow point inspection suggests that no single evident elbow is present. Conversely, silhoutte width is maximal with 2 clusters.

What should I do next? Is hierarchical preferable? I would trust more silhoutte width, at least in this case. Am I correct?

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  • $\begingroup$ @joe-74 I have a question about the distance measure. Is it the same for the three types of clustering you have used? if answer is yes, then it could be an initialization issue (mostly due to different initial random seeds used to select the initial centers). you should choose the clustering that produced the minimal Sum of Squared Eerror score.. $\endgroup$
    – mnm
    Mar 27, 2019 at 12:54
  • $\begingroup$ @ashish wrong. k=N, every object is a separate cluster, has "optimal" SSE=0. Choosing minimal SSE is not suitable for identifying the best clustering. $\endgroup$ Mar 28, 2019 at 2:15

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All of these measures are only heuristics. So they all can be wrong.

Also, what if none of the clusterings is good?

Looking just for the "best" score falls short of reality. For example Silhouette. If your maximum Silhouette is 0.1, it just means that all your clusterings failed to find good results! Because a Silhouette below 0.7 is not considered to be good. Unfortunately, you did not include any of these values or plots in your question.

Instead of looking at such scores, please look at the actual data. Are the clusters interpretable? Do they help solving your problems?

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  • $\begingroup$ Is there a bibliographic reference that says that below 0.7 is not good? $\endgroup$
    – Josir
    Nov 15, 2021 at 21:53
  • $\begingroup$ Iris, for example, has a 0.6 silhoutte. $\endgroup$
    – Josir
    Nov 15, 2021 at 22:06

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