Fair Model-based Clustering

TL;DR

This paper introduces Fair Model-based Clustering (FMC), a scalable and flexible algorithm that achieves fair clustering by modeling data with a finite mixture model, suitable for large and non-metric datasets.

Contribution

FMC is a novel fair clustering method based on finite mixture models, with parameters independent of sample size, enabling scalable and applicable to non-metric data.

Findings

FMC scales efficiently to large datasets.

FMC achieves approximately fair clustering with mini-batch learning.

Theoretical and empirical results demonstrate FMC's superiority.

Abstract

The goal of fair clustering is to find clusters such that the proportion of sensitive attributes (e.g., gender, race, etc.) in each cluster is similar to that of the entire dataset. Various fair clustering algorithms have been proposed that modify standard K-means clustering to satisfy a given fairness constraint. A critical limitation of several existing fair clustering algorithms is that the number of parameters to be learned is proportional to the sample size because the cluster assignment of each datum should be optimized simultaneously with the cluster center, and thus scaling up the algorithms is difficult. In this paper, we propose a new fair clustering algorithm based on a finite mixture model, called Fair Model-based Clustering (FMC). A main advantage of FMC is that the number of learnable parameters is independent of the sample size and thus can be scaled up easily. In particular, mini-batch learning is possible to obtain clusters that are approximately fair. Moreover, FMC can be applied to non-metric data (e.g., categorical data) as long as the likelihood is well-defined. Theoretical and empirical justifications for the superiority of the proposed algorithm are provided.