Can geodemographic clustering be fair? Incorporating social fairness in crisp and fuzzy approaches through a unified framework

Geodemographic analysis clusters geographic areas into socio-demographically homogeneous groups. Existing clustering methods prioritize overall effectiveness, measured by total costs, potentially misrepresenting specific subgroups. Despite a growing literature on fair clustering, it largely focuses on crisp clustering, failing to address the inherent fuzziness of the real world. This study introduces socially-fair geodemographic clustering (SFGC), which modifies classical clustering by minimizing the maximum average cost across subgroups instead of the total cost. SFGC also introduces a gradient descent algorithm to optimize this new cost function and can be directly applied to both crisp and fuzzy clustering. Evaluation on two benchmark datasets reveals significant cost disparities in existing clustering methods, specifically k-means and fuzzy c-means, with Black-dominant neighborhoods in Chicago having up to 50% higher costs than White-dominant neighborhoods. SFGC reduces this gap to up to 4%, producing clusters that better reflect the heterogeneity of Black-dominant neighborhoods. In addition, SFGC reduces by nearly 8% the misclassified Black-dominant neighborhoods, demonstrating that the inclusion of fairness can drastically change clustering outcomes and reveal latent spatial patterns in neighborhood disparities. The proposed framework could help policymakers better understand the nuances of neighborhood characteristics, ensuring social justice in planning and policymaking.