[Paper Review] Deep Fair Discriminative Clustering

Hongjing Zhang, Ian Davidson|arXiv (Cornell University)|May 28, 2021

Face and Expression Recognition35 references4 citations

TL;DR

This paper proposes Deep Fair Discriminative Clustering, a novel framework that integrates group-level fairness into deep clustering via an integer linear programming (ILP) formulation with totally unimodular constraints, enabling efficient, exact fair cluster assignment. The method combines this fair assignment with a discriminative deep clustering backbone and contrastive learning, achieving near-optimal fairness with competitive clustering performance on real-world datasets, including multi-state protected status variables and flexible fairness constraints.

ABSTRACT

Deep clustering has the potential to learn a strong representation and hence better clustering performance compared to traditional clustering methods such as $k$-means and spectral clustering. However, this strong representation learning ability may make the clustering unfair by discovering surrogates for protected information which we empirically show in our experiments. In this work, we study a general notion of group-level fairness for both binary and multi-state protected status variables (PSVs). We begin by formulating the group-level fairness problem as an integer linear programming formulation whose totally unimodular constraint matrix means it can be efficiently solved via linear programming. We then show how to inject this solver into a discriminative deep clustering backbone and hence propose a refinement learning algorithm to combine the clustering goal with the fairness objective to learn fair clusters adaptively. Experimental results on real-world datasets demonstrate that our model consistently outperforms state-of-the-art fair clustering algorithms. Our framework shows promising results for novel clustering tasks including flexible fairness constraints, multi-state PSVs and predictive clustering.

Motivation & Objective

• To address the challenge of unfair clustering in deep learning, where representation learning may amplify biases tied to protected status variables (PSVs).
• To develop a scalable, end-to-end deep clustering framework that enforces group-level fairness for both binary and multi-state PSVs.
• To enable flexible fairness constraints that reflect real-world regulatory variations across regions.
• To combine deep representation learning with discrete optimization to generate compact, fair, and meaningful clusters.

Proposed method

• Formulate group-level fairness as an integer linear programming (ILP) problem with a totally unimodular constraint matrix, ensuring exact integer solutions via linear programming.
• Integrate the ILP solver into a discriminative deep clustering backbone to refine cluster assignments while preserving clustering quality.
• Use a refinement learning algorithm that jointly optimizes clustering objectives, fairness constraints, and self-supervised contrastive learning.
• Train the entire model end-to-end, allowing backpropagation through the fair assignment layer.
• Support multi-state PSVs by generalizing the fairness measure to be equivalent to the balance measure under the disparate impact doctrine.
• Enable flexible fairness constraints by relaxing the optimal fairness condition within a tolerance interval, allowing practical deployment across regions with different fairness standards.

Experimental results

Research questions

• RQ1 Can deep clustering be made fair at the group level without relying on pre-processing or instance-level constraints?
• RQ2 How can group-level fairness for multi-state protected status variables be formally defined and optimized in an end-to-end deep learning framework?
• RQ3 Can an ILP formulation with total unimodularity be effectively integrated into a deep clustering pipeline to ensure exact fair cluster assignments?
• RQ4 How does the model perform under flexible fairness constraints that vary across regions or applications?
• RQ5 To what extent does enforcing fairness improve clustering performance, and how can the trade-off between fairness and accuracy be managed?

Key findings

• The proposed model achieves near-optimal fairness (balance = 0.200 on MNIST-USPS test set) while maintaining competitive clustering performance (NMI = 0.865, Acc = 0.930).
• On the Reverse-MNIST dataset, the model achieves a balance of 0.890 on the test set, approaching the optimal 1.000, with high clustering accuracy (Acc = 0.562).
• On the HAR dataset, the model achieves a balance of 0.167 on the test set, demonstrating effectiveness even in high-dimensional, real-world data with complex patterns.
• Relaxing fairness constraints (increasing ε) leads to lower balance, as expected, but also reduces clustering accuracy, indicating a trade-off between fairness and performance.
• Feature space visualization shows that fairness constraints successfully reassign biased instances (e.g., red and blue in t-SNE) into more balanced clusters without sacrificing clustering compactness.
• Empirical convergence analysis confirms that both training loss and balance metrics stabilize after 50 epochs, indicating stable and smooth optimization.