Incorporating Fairness Constraints into Archetypal Analysis

TL;DR

This paper introduces Fair Archetypal Analysis (FairAA) and its nonlinear extension FairKernelAA, which incorporate fairness constraints into archetypal analysis to reduce sensitive attribute influence while maintaining interpretability and utility.

Contribution

The paper proposes novel fairness-aware modifications to archetypal analysis, including a regularized formulation and a nonlinear kernel extension, enhancing fairness in data representations.

Findings

FairAA reduces group separability in synthetic datasets.

FairKernelAA effectively handles complex, nonlinear data distributions.

Both methods maintain interpretability and explain variance reasonably well.

Abstract

Archetypal Analysis (AA) is an unsupervised learning method that represents data as convex combinations of extreme patterns called archetypes. While AA provides interpretable and low-dimensional representations, it can inadvertently encode sensitive attributes, leading to fairness concerns. In this work, we propose Fair Archetypal Analysis (FairAA), a modified formulation that explicitly reduces the influence of sensitive group information in the learned projections. We also introduce FairKernelAA, a nonlinear extension that addresses fairness in more complex data distributions. Our approach incorporates a fairness regularization term while preserving the structure and interpretability of the archetypes. We evaluate FairAA and FairKernelAA on synthetic datasets, including linear, nonlinear, and multi-group scenarios, demonstrating their ability to reduce group separability -- as measured by mean maximum discrepancy and linear separability -- without substantially compromising explained variance. We further validate our methods on the real-world ANSUR I dataset, confirming their robustness and practical utility. The results show that FairAA achieves a favorable trade-off between utility and fairness, making it a promising tool for responsible representation learning in sensitive applications.