The ratio of the within-cluster sum of squares to the total sum of squares, \(WSS/TSS = \sum_{k=1}^{K} \sum_{i \in C_k} \| x_i - \mu_k \|^2 / \sum_{i=1}^{n} \| x_i - \mu \|^2\) where \(\mu_k\) is the centroid of cluster \(k\) and \(\mu\) is the centroid of all observations. The ratio lies in \([0, 1]\), with lower values indicating more compact clusters. Unlike the raw within sum of squares, it is comparable across datasets and feature scalings. It decreases monotonically with the number of clusters, which makes it the standard quantity for elbow plots.
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: \([0, 1]\)
Minimize: TRUE
Average: macro
Required Prediction: “partition”
Required Packages: mlr3, mlr3cluster
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.davies_bouldin,
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