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I am trying to do clustering on a distance matrix which contains numeric data. But I am not sure how to decide upon the number of clusters or value k for clara function in R. But after running it with some random number of clusters, I ran silhouette function on it and summary gives me like this:

Cluster sizes and average silhouette widths:

           7            3            4            5            7            4 
 0.222273330 -0.001592881  0.117937463  0.121326365  0.137911639  0.161932689 
Individual silhouette widths:
    Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
-0.10410  0.08961  0.12500  0.14140  0.19840  0.30580 

This is the result for value of k=6. If I change it to say 5 or 4, I obtain silhouette for each cluster and also mean value. How do I decide upon the number of clusters? Do I need to plot like mean silhouette vs k? How do we do something like this in a large dataset with around million observations?

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You can do one of these two things :

  1. Use fviz_nbclust() function like this

     fviz_nbclust(data, clara, method = "silhouette",k.max = yourMaxValue)+theme_classic()
    
  2. You could construct a graph by accessing silhouette width info in clara object.

     # If clara.res is the object resulting from using clara.
     clara.res$silinfo
    

Hope this helps.

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