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Fair Kernel K-Means: from Single Kernel to Multiple Kernel
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Proposes Fair Kernel K-Means (FKKM) and Fair Multiple Kernel K-Means (FMKKM), which add a fairness regularization term to kernel k-means by modifying the kernel (K + αI − λGGᵀ) and directly solve for discrete cluster assignments.
Problem
Kernel k-means and multiple kernel k-means ignore group fairness, so clusters may over- or under-represent protected groups, causing discrimination.
Approach
A fairness regularization term Tr(YᵀGGᵀY(YᵀY)⁻¹), shown to be maximized-fairness when minimized, has the same form as the kernel k-means loss, so fairness is injected by replacing the kernel with a fair kernel K + αI − λGGᵀ, with λ set via a fairness-stability search guided by a generalization bound.
Key results
- On the single kernel setting, FKKM achieves the best ACC on D&S (0.648 vs 0.558 for SC) and on Jaffe (1.0), and reaches MNCE 0.991 on D&S, far above KKM's 0.531.
- FMKKM achieves the best fairness on all six datasets in the multiple kernel setting, e.g., Bal 0.471 vs 0 for all baselines on D&S and MNCE 0.985 vs at most 0.649.
- FMKKM attains the best ACC on HAR (0.791 vs 0.732 for EMKC) and Jaffe (0.995 vs 0.985 for FAMKKM), though it is not best on all datasets (e.g., D&S ACC 0.616 vs 0.646 for LFLKA).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add the fairness regularization term (ablation) | FMKKM · D&S | MNCE: 0.585 -> 0.985 | Helped |
| add the fairness regularization term (ablation) | FMKKM · HAR | MNCE: 0.888 -> 0.990 | Helped |
| add the fairness regularization term (ablation) | FMKKM · MNIST-USPS | MNCE: 0.986 -> 0.993 | Helped |
| add the fairness regularization term (ablation) | FMKKM · Jaffe | MNCE: 0.895 -> 0.989 | Helped |
| add the fairness regularization term (ablation) | FMKKM · Credit Card | MNCE: 0.964 -> 0.989 | Helped |
| add the fairness regularization term (ablation) | FMKKM · K1b | MNCE: 0.986 -> 1 | Helped |
| add the fairness regularization term (ablation) | FMKKM · D&S | ACC: 0.645 -> 0.616 | Hurt |
| add the fairness regularization term (ablation) | FMKKM · HAR | ACC: 0.697 -> 0.791 | Helped |
| add the fairness regularization term (ablation) | FMKKM · MNIST-USPS | ACC: 0.412 -> 0.495 | Helped |
| add the fairness regularization term (ablation) | FMKKM · Jaffe | ACC: 0.939 -> 0.995 | Helped |
| add the fairness regularization term (ablation) | FMKKM · Credit Card | ACC: 0.378 -> 0.375 | Hurt |
| add the fairness regularization term (ablation) | FMKKM · K1b | ACC: 0.826 -> 0.828 | Helped |
Surprising findings
- Fairness-regularized FMKKM is sometimes lower in ACC/NMI than some baselines on several datasets, showing a fairness-performance trade-off.
Limitations
- Protected groups must be pre-specified by humans; automatic group discovery is not addressed.
- Lambda is tuned by a heuristic search on MNCE rather than a fully principled selection, and clustering accuracy can decrease as lambda grows.
Experimental setup
Datasets: D&S HAR Jaffe MNIST-USPS Credit Card K1b
Benchmarks: D&S HAR Jaffe MNIST-USPS Credit Card K1b
Metrics: ACC NMI Bal MNCE
Baselines: K-means KKM SC FairSC VFC FFC ONKC MKCSS DPMKKM LFLKA EMKC OSLR
Builds on: kernel k-means multiple kernel k-means fairness definition of Bera et al. (2019) DPMKKM
Closest papers by meaning
- Multiple Kernel k-Means Clustering with Matrix-Induced Regularization (AAAI 2016 · similarity 0.87)
- Fusion Multiple Kernel K-means (AAAI 2022 · similarity 0.87)
- Kernel-based Equalized Odds: A Quantification of Accuracy-Fairness Trade-off in Fair Representation Learning (NeurIPS 2025 · similarity 0.87)
- FFB: A Fair Fairness Benchmark for In-Processing Group Fairness Methods (ICLR 2024 · similarity 0.83)
- fairret: a Framework for Differentiable Fairness Regularization Terms (ICLR 2024 · similarity 0.83)
- Scalable Multiple Kernel Clustering: Learning Clustering Structure from Expectation (ICML 2024 · similarity 0.83)
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