Fig. 2

A A plot of the within sum-of-squares as a function of the number of clusters k (denoted wss(k)). The so-called elbow method can be used to determine the number of clusters, if a point on this graph exists that looks like an elbow (i.e. dramatic change in slope). B A plot of the slope of the line s(k) between the points wss(k) and \(wss(k+1)\). C A plot of the relative change f(k) in the slope s(k) (i.e., \(f(k) = \frac{s(k-1)- s(k)}{s(k-1)}\)). Note: the relative change of slope is highest for \(k=2\), then for \(k=4\) and next for \(k=7\) (point shown in red). D A plot of the results of our cluster analysis in the 2-dimensional space spanned by the two principal components of a PCA, which together explain 94.9% of the observed variation