Fairness, Semi-Supervised Learning, and More: A General Framework for Clustering with Stochastic Pairwise Constraints

Metric clustering is fundamental in areas ranging from Combinatorial Optimization and Data Mining, to Machine Learning Operations Research. However, a variety of situations we may have additional requirements or knowledge, distinct the underlying metric, regarding which pairs points should be clustered together. To capture analyze such scenarios, introduce novel family stochastic pairwise constraints, incorporate into several essential objectives (radius/median/means). Moreover, demonstrate that these constraints can succinctly model an intriguing collection applications, including among others Individual Fairness Must-link semi-supervised learning. Our main result consists general framework yields approximation algorithms with provable guarantees for important objectives, while at same time producing solutions respect constraints. Furthermore, certain devise improved results case are also best possible theoretical perspective. Finally, present experimental evidence validates effectiveness our algorithms.