The Davies–Bouldin index (DBI), introduced by David L. Davies and Donald W. Bouldin in 1979, is a metric for evaluating clustering algorithms.
[1] This is an internal evaluation scheme, where the validation of how well the clustering has been done is made using quantities and features inherent to the dataset.
This has a drawback that a good value reported by this method does not imply the best information retrieval.
Here k indexes the features of the data, and this is essentially the Euclidean distance between the centers of clusters i and j when p equals 2.
A solution that satisfies these properties is: This is used to define Di: If N is the number of clusters: DB is called the Davies–Bouldin index.
[2] This extension is based on the category clustering approach according to the framework of fuzzy logic.
Therefore, this soft version of the Davies–Bouldin index is able to take into account, in addition to standard validation measures such as compactness and separation of clusters, the degree to which elements belong to classes.
The scikit-learn Python open source library provides an implementation of this metric in the sklearn.metrics module.
[4] A Java implementation is found in ELKI, and can be compared to many other clustering quality indexes.