In this recipe, we demonstrate how to find the optimum number of clusters by iteratively getting within the sum of squares and the average silhouette value. For the within sum of squares, lower values represent clusters with better quality. By plotting the within sum of squares in regard to different numbers of k, we find that the elbow of the plot is at k=4.

On the other hand, we also compute the average silhouette width based on the different numbers of clusters using cluster.stats. Also, we can use a line plot to plot the average silhouette width with regard to the different numbers of clusters. The preceding figure (step 4) shows the maximum average silhouette width appears at k=4. Lastly, we use which.max to obtain the value of k to determine the location of the maximum average silhouette width.