Feature Attributions for ClusTering



FACT - (Feature Attributions for Clustering)

To get value from a clustering algorithm, it is important to understand the assignment procedure of an algorithm that assigns instances to clusters. FACT is an algorithm agnostic framework that provides feature attribution while preserving the integrity of the data.


  • SMART (Scoring Metric After Permutation) permutes feature sets to measure the sensitivity of algorithms to changes in cluster assignments.
  • IDEA (Isolated Effect on Assignment) visualises local and global changes in cluster assignments over one- and two-dimensional feature spaces.


You can install the development version of FACT like so:

# Development version


We want to divide American states by their standardized crime rates in 3 clusters.

#> Lade nötiges Paket: mlr3
attributes_scale = attributes(scale(USArrests))
Murder Assault UrbanPop Rape
Alabama 1.24 0.78 -0.52 0.00
Alaska 0.51 1.11 -1.21 2.48
Arizona 0.07 1.48 1.00 1.04
Arkansas 0.23 0.23 -1.07 -0.18
California 0.28 1.26 1.76 2.07
Colorado 0.03 0.40 0.86 1.86

USArrests Data Set

Therefore, we use a c-means algorithm from mlr3cluster.

tsk_usa = TaskClust$new(id = "usarest", backend = data.frame(scale(USArrests)))
c_lrn = lrn("clust.cmeans", centers = 3, predict_type = "prob")

Then, we create a ClustPredictor that wraps all the information needed for our methods.

predictor = ClustPredictor$new(c_lrn, data = tsk_usa$data(), y = c_lrn$model$membership)

How does Assault effect the partitions created by c-means clustering?

The sIDEA plot shows:

  • x-Axis: The domain in the feature space of Assault were realizations of observations can be found (visualised by the geom_rug).
  • y-Axis: The associated soft labels score of cluster k, f(k).
  • solid line: The estimated marginal, global effect of a cluster k throughout feature space.
  • transparent area: 50% of the mass of individual effects. This area plots the variance in effects throughout feature space.
idea_assault = IDEA$new(predictor, "Assault", grid.size = 50)

Short Interpretation:

  • States in cluster 1 (red) are marginally associated with the lowest Assault rate.
  • States in cluster 3 (blue) are marginally associated with a relatively low Assault rate.
  • States in cluster 2 (green) are marginally associated with a relatively high Assault rate.


If you use FACT in a scientific publication, please cite it as:

Scholbeck, C. A., Funk, H., & Casalicchio, G. (2022). Algorithm-Agnostic Interpretations for Clustering. arXiv preprint arXiv:2209.10578.


  title={Algorithm-Agnostic Interpretations for Clustering},
  author={Scholbeck, Christian A and Funk, Henri and Casalicchio, Giuseppe},
  journal={arXiv preprint arXiv:2209.10578},