Inertia-Based Indices to Determine the Number of Clusters in K-Means: An Experimental Evaluation

This paper gives an experimentally supported review and comparison of several indices based on the conventional K-means inertia criterion for determining the number of clusters,
$K$
, in datasets, using the popular Silhouette width index as a benchmark. Our experiments involve a novel version of the Elbow index, defined using values of
$K$
two or three steps apart. We also discuss alternative ways of computing the inertia and summarizing its values. Even though there are no overall winners in our experiments, some of our results are very conclusive and can be used as a guide for indices determining the number of clusters in K-means.