FACT - (Feature Attributions for Clustering)

To get value from a clustering algorithm, it is important to understand the mapping 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.

Features

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

Installation

You can install the development version of FACT like so:

# Development version
remotes::install_github("henrifnk/FACT")

Quickstart

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

library(FACT)
library(mlr3cluster)
#> 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$new(id = "usarest", backend = data.frame(scale(USArrests)))
c_lrn = lrn("clust.cmeans", centers = 3, predict_type = "prob")
c_lrn$train(tsk_usa)

Then, we create a ClustPredictor that wraps 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 (visualized 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 over the feature space.
transparent area: 50% of the mass of the individual effects. This area represents the variance of the effects across feature space.

idea_assault = IDEA$new(predictor, "Assault", grid.size = 50)
idea_assault$plot_globals(0.5)

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.

Citation

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.

BibTeX:

@article{FACT_22,
  title={Algorithm-Agnostic Interpretations for Clustering},
  author={Scholbeck, Christian A and Funk, Henri and Casalicchio, Giuseppe},
  journal={arXiv preprint arXiv:2209.10578},
  year={2022}
}