Davies-Bouldin Index

The Davies-Bouldin Index is defined as:

$DB=\frac{1}{K}{\sum }_{i=1}^K{\max }_{j\ne i}\left(\frac{{\sigma }_i+{\sigma }_j}{\delta \left({\mathbf{\mu }}_i,{\mathbf{\mu }}_j\right)}\right)$

Where:

• $K$ is the number of clusters;
• ${\mathbf{\mu }}_k$ is the centroid of the cluster $C_k$;
• ${\sigma }_k$ is the average distance of all elements of cluster $C_k$ from its centroid ${\mathbf{\mu }}_k$.
• $\delta ({\mathbf{\mu }}_i,{\mathbf{\mu }}_j)$ is the distance between the centroids of $C_i$ and $C_j$.

The idea here is to find, for each cluster, the other cluster which elements are, in average, the furthest from it.

The smaller the index, the better.

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clustering