Maity, BinitaDas, ShrutimoyDasgupta, Anirban2025-08-282025-08-282024-12-01http://arxiv.org/abs/2412.10923https://d8.irins.org/handle/IITG2025/19869Individual fairness guarantees are often desirable properties to have, but they become hard to formalize when the dataset contains outliers. Here, we investigate the problem of developing an individually fair k-means clustering algorithm for datasets that contain outliers. That is, given n points and k centers, we want that for each point which is not an outlier, there must be a center within the nk nearest neighbours of the given point. While a few of the recent works have looked into individually fair clustering, this is the first work that explores this problem in the presence of outliers for k-means clustering. For this purpose, we define and solve a linear program (LP) that helps us identify the outliers. We exclude these outliers from the dataset and apply a rounding algorithm that computes the k centers, such that the fairness constraint of the remaining points is satisfied. We also provide theoretical guarantees that our method leads to a guaranteed approximation of the fair radius as well as the clustering cost. We also demonstrate our techniques empirically on real-world datasetsen-USe-Printe-Print123456789/435