On Clustering and Interpreting with Rules by Means of Mathematical Optimization

Emilio Carrizosa, Kseniia Kurishchenko*, Alfredo Marín, Dolores Romero Morales

*Corresponding author for this work

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In this paper, we make Cluster Analysis more interpretable with a new approach that simultaneously allocates individuals to clusters and gives rule-based explanations to each cluster. The traditional homogeneity metric in clustering, namely the sum of the dissimilarities between individuals in the same cluster, is enriched by considering also, for each cluster and its associated explanation, two explainability criteria, namely, the accuracy of the explanation, i.e., how many individuals within the cluster satisfy its explanation, and the distinctiveness of the explanation, i.e., how many individuals outside the cluster satisfy its explanation. Finding the clusters and the explanations optimizing a joint measure of homogeneity, accuracy, and distinctiveness is formulated as a multi-objective Mixed Integer Linear Optimization problem, from which non-dominated solutions are generated. Our approach is tested on real-world datasets.
Original languageEnglish
Article number106180
JournalComputers & Operations Research
Number of pages19
Publication statusPublished - Jun 2023


  • Machine learning
  • Interpretability
  • Cluster analysis
  • Rules
  • Mixed-Integer Programming

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