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

Geodemographic analysis involves clustering geographic areas into socio-demographically homogeneous groups. However, most existing methods prioritize overall effectiveness, measured by minimizing total costs, potentially misrepresenting specific subgroups within the data. Despite a growing literature on fair clustering, it focuses almost exclusively on crisp clustering, failing to address the inherent fuzziness of the real world. This study addresses these gaps by introducing a socially-fair geodemographic clustering (SFGC) framework, which modifies the classical fuzzy-c means (FCM) by incorporating a new cost function that, instead of minimizing total costs, minimizes the maximum average cost across all subgroups. SFGC also introduces a gradient descent-based algorithm to optimize this new cost function. In addition, SFGC can be directly adapted to crisp clustering, facilitating practical implementation and comparison of clustering algorithms.