This is the elbow plot result I obtained from R. It looks quite unusual compared to the ones I have seen, so your insights will be appreciated. Referring to the attached image, it can be seen that there is a "flattening" that happened from 4 to 5 clusters; however, higher change in WSS can still be observe from 5 to 6 clusters. My questions is, is 4 clusters optimum already? Or 6 would be the optimum?
With clustering, there is no precise right or wrong. And criteria like the elbow method are only there to help the intuition a little. E.g., look at this dataset:
There is no "correct" way of clustering those 27 points. Are those three clusters or nine? Or maybe each point is its own cluster, or this is just one single large cluster? Without extra criteria, there is no way to decide, but those extra criteria would be subjective, depending on the current scenario. And the elbow plots are only there to give you more inside into your data, but, they cannot "decide" what the "right" number of clusters is.
Another way to express this is to do hierarchical clustering, i.e. to not choose a single clustering but to give many. But, of course, the hierarchies, too, can differ and depend on chosen criteria.
