# Attraction-Repulsion clustering with applications to fairness

## TL;DR

This paper introduces a novel clustering method that enhances diversity and fairness by applying attraction-repulsion perturbations to dissimilarities, improving demographic parity in various datasets.

## Contribution

It proposes a new pre-processing approach using attraction-repulsion dissimilarities to promote diversity in clustering, compatible with multiple methods and data types.

## Key findings

- Improves diversity with respect to protected attributes.
- Compatible with various clustering algorithms and non-Euclidean data.
- Demonstrated effectiveness on synthetic and real datasets.

## Abstract

We consider the problem of diversity enhancing clustering, i.e, developing clustering methods which produce clusters that favour diversity with respect to a set of protected attributes such as race, sex, age, etc. In the context of fair clustering, diversity plays a major role when fairness is understood as demographic parity. To promote diversity, we introduce perturbations to the distance in the unprotected attributes that account for protected attributes in a way that resembles attraction-repulsion of charged particles in Physics. These perturbations are defined through dissimilarities with a tractable interpretation. Cluster analysis based on attraction-repulsion dissimilarities penalizes homogeneity of the clusters with respect to the protected attributes and leads to an improvement in diversity. An advantage of our approach, which falls into a pre-processing set-up, is its compatibility with a wide variety of clustering methods and whit non-Euclidean data. We illustrate the use of our procedures with both synthetic and real data and provide discussion about the relation between diversity, fairness, and cluster structure. Our procedures are implemented in an R package freely available at https://github.com/HristoInouzhe/AttractionRepulsionClustering.