mlr_measures_clust.sse_ratio: Within/Total Sum of Squares Ratio

In mlr3cluster: Cluster Extension for 'mlr3'

Within/Total Sum of Squares Ratio

Description

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():

mlr_measures$get("clust.sse_ratio")
msr("clust.sse_ratio")

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

mlr3cluster documentation built on Aug. 22, 2026, 1:07 a.m.