Fairness constraint of Fuzzy C-means Clustering improves clustering fairness

Xia Xu (Southwest University of Science and Technology)*; hui zhang (Southwest University of Science and Technology); Chunming Yang (Southwest University of Science and Technology); xujian zhao (Southwest University of Science and Technology); Bo Li (Southwest University of Science and Technology)

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Abstract

Fuzzy C-Means (FCM) clustering is a classic clustering algorithm, which is widely used in the real world. Despite the distinct advantages of FCM algorithm, whether the usage of fairness constraint in the FCM could improve clustering fairness remains fully elusive. By introducing a novel fair loss term into the objective function, a Fair Fuzzy C-Means (FFCM) algorithm was proposed in this current study. We proved that the membership value was constrained by distance and fairness in the meantime during the optimization process in the proposed objective function. By studying the Fuzzy C-Means Clustering with fairness constraint problem and proposing a fair fuzzy C-means method, this study provided mechanism understanding in achieving the fairness constraint in Fuzzy C-Means clustering and bridged up the gap of fair fuzzy clustering.