Elbow method (clustering)

The elbow method is a heuristic in determining the number of clusters in a data set. We plot the K-mean score (% of variance explained) against the number of clusters and picking the “elbow of the curve” as the number to use.

Pick the $k\in \{2,3,\dots ,n-1\}$ that maximises ${\text{cost}}_{k-1}/{\text{cost}}_k$ where ${\text{cost}}_j$ is the cost of clustering with $j$ clusters. $k=1,n$ are ruled out as they result in trivial clusters.