The Davies-Bouldin index measures the average similarity between each cluster and the cluster most similar to it, where similarity is the ratio of within-cluster scatter to between-cluster separation. It is defined as \(DB = \frac{1}{k} \sum_{i=1}^{k} \max_{j \neq i} \frac{s_i + s_j}{d_{ij}}\) where \(s_i\) is the average distance of observations in cluster \(i\) to its centroid and \(d_{ij}\) is the Euclidean distance between centroids \(i\) and \(j\). Lower values indicate better clustering.
Dictionary
This mlr3::Measure can be instantiated via the dictionary mlr3::mlr_measures or with the
associated sugar function mlr3::msr():
Meta Information
Task type: “clust”
Range: \([0, \infty)\)
Minimize: TRUE
Average: macro
Required Prediction: “partition”
Required Packages: mlr3, mlr3cluster
References
Davies, L D, Bouldin, W D (1979). “A cluster separation measure.” IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-1(2), 224–227. doi:10.1109/TPAMI.1979.4766909 .
See also
Dictionary of Measures: mlr3::mlr_measures
as.data.table(mlr_measures) for a complete table of all (also dynamically created) mlr3::Measure implementations.
Other cluster measures:
mlr_measures_clust.avg_between,
mlr_measures_clust.avg_within,
mlr_measures_clust.ch,
mlr_measures_clust.dunn,
mlr_measures_clust.dunn2,
mlr_measures_clust.entropy,
mlr_measures_clust.pearsongamma,
mlr_measures_clust.silhouette,
mlr_measures_clust.wb_ratio,
mlr_measures_clust.wss