Deep Fair Clustering via Maximizing and Minimizing Mutual Information: Theory, Algorithm and Metric

TL;DR

This paper introduces a deep fair clustering method called FCMI based on mutual information theory, which aims to produce compact, balanced, fair, and informative clusters, supported by a new unified evaluation metric.

Contribution

The paper develops a mutual information theory for deep fair clustering, proposes the FCMI algorithm, and introduces a novel metric for evaluating both clustering quality and fairness.

Findings

FCMI achieves superior fairness and clustering quality on six benchmarks.

The new metric effectively measures both fairness and clustering performance.

Experimental results outperform 11 state-of-the-art methods.

Abstract

Fair clustering aims to divide data into distinct clusters while preventing sensitive attributes (\textit{e.g.}, gender, race, RNA sequencing technique) from dominating the clustering. Although a number of works have been conducted and achieved huge success recently, most of them are heuristical, and there lacks a unified theory for algorithm design. In this work, we fill this blank by developing a mutual information theory for deep fair clustering and accordingly designing a novel algorithm, dubbed FCMI. In brief, through maximizing and minimizing mutual information, FCMI is designed to achieve four characteristics highly expected by deep fair clustering, \textit{i.e.}, compact, balanced, and fair clusters, as well as informative features. Besides the contributions to theory and algorithm, another contribution of this work is proposing a novel fair clustering metric built upon information theory as well. Unlike existing evaluation metrics, our metric measures the clustering quality and fairness as a whole instead of separate manner. To verify the effectiveness of the proposed FCMI, we conduct experiments on six benchmarks including a single-cell RNA-seq atlas compared with 11 state-of-the-art methods in terms of five metrics. The code could be accessed from \url{ https://pengxi.me}.