Variational Fair Clustering


  • Imtiaz Masud Ziko ÉTS Montreal, Canada
  • Jing Yuan Xidian University, China
  • Eric Granger ÉTS Montreal, Canada
  • Ismail Ben Ayed ÉTS Montreal, Canada


Clustering, Ethics -- Bias, Fairness, Transparency & Privacy, Societal Impact of AI, Optimization


We propose a general variational framework of fair clustering, which integrates an original Kullback-Leibler (KL) fairness term with a large class of clustering objectives, including prototype or graph based. Fundamentally different from the existing combinatorial and spectral solutions, our variational multi-term approach enables to control the trade-off levels between the fairness and clustering objectives. We derive a general tight upper bound based on a concave-convex decomposition of our fairness term, its Lipschitz-gradient property and the Pinsker’s inequality. Our tight upper bound can be jointly optimized with various clustering objectives, while yielding a scalable solution, with convergence guarantee. Interestingly, at each iteration, it performs an independent update for each assignment variable. Therefore, it can be easily distributed for large-scale datasets. This scalability is important as it enables to explore different trade-off levels between the fairness and clustering objectives. Unlike spectral relaxation, our formulation does not require computing its eigenvalue decomposition. We report comprehensive evaluations and comparisons with state-of-the-art methods over various fair clustering benchmarks, which show that our variational formulation can yield highly competitive solutions in terms of fairness and clustering objectives.




How to Cite

Ziko, I. M., Yuan, J., Granger, E., & Ben Ayed, I. (2021). Variational Fair Clustering. Proceedings of the AAAI Conference on Artificial Intelligence, 35(12), 11202-11209. Retrieved from



AAAI Technical Track on Machine Learning V