Editing Cluster analysis (section)

==== [[Davies–Bouldin index]] ====
The [[Davies–Bouldin index]] can be calculated by the following formula:
<math>
DB = \frac {1} {n} \sum_{i=1}^{n} \max_{j\neq i}\left(\frac{\sigma_i + \sigma_j} {d(c_i,c_j)}\right)
</math>
where ''n'' is the number of clusters, <math>c_i</math> is the [[centroid]] of cluster <math>i</math>, <math>\sigma_i</math> is the average distance of all elements in cluster <math>i</math> to centroid <math>c_i</math>, and <math>d(c_i,c_j)</math> is the distance between centroids <math>c_i</math> and <math>c_j</math>. Since algorithms that produce clusters with low intra-cluster distances (high intra-cluster similarity) and high inter-cluster distances (low inter-cluster similarity) will have a low Davies–Bouldin index, the clustering algorithm that produces a collection of clusters with the smallest [[Davies–Bouldin index]] is considered the best algorithm based on this criterion.