Davies-Bouldin Index

The Davies-Bouldin index rates a clustering by how compact clusters are relative to how far apart they are. Lower is better.

For each cluster $i$: $s_i$ is the mean distance of its points to its centroid. For each pair, $R_{ij} = \frac{s_i + s_j}{\|c_i - c_j\|}$. The index is the mean over clusters of $\max_{j \ne i} R_{ij}$.

Implement davies_bouldin(X, labels) (Euclidean distances, at least 2 clusters).