Individual Fairness for Fuzzy C-Means Clustering

In the field of clustering algorithms, the Fuzzy CMeans algorithm stands out for its ability to deal with uncertainty by assigning membership degrees to data points. However, research on the fairness of Fuzzy C-Means algorithms has mainly focused on group fairness, with limited attention to individual fairness. To fill this gap, this paper proposes an Individual fair Fuzzy C-Means algorithm. By establishing a relaxed Lipschitz condition as the theoretical foundation and incorporating the random walk Laplacian matrix constructed from the similarity matrix into the clustering process, the Individual Fair Fuzzy CMeans algorithm optimizes the individual fairness of clustering. Experimental results show that individual fairness is significantly improved while maintaining clustering quality comparable to traditional Fuzzy C-Means algorithms.