The problem with inertia as only statistic to assess if clusters are good enough

Data Science, AI and ML
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#1
  1. Inertia is a monotonically decreasing function. Hence it drops with increase in cluster, however it doesn’t explain how many clusters are there naturally. Though it’s quite useful to determine optimum number of clusters, it can’t explain how many clusters are there.
  2. One of the cluster might have variance naturally. For example, let’s say there are either cats or dogs in animals. The variation amidst dogs itself in terms of size and complexion will be high.

So what’s the solution?
Look out for Hopman statistic and Sillhoutte’s coefficient maybe?