27 research outputs found
Variational Fair Clustering
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.Comment: Accepted to be published in AAAI 2021. The Code is available at:
https://github.com/imtiazziko/Variational-Fair-Clusterin