Fair Kernel K-Means: from Single Kernel to Multiple Kernel

Kernel k-means has been widely studied in machine learning. However, existing kernel k-means methods often ignore the \textit{fairness} issue, which may cause discrimination. To address this issue, in this paper, we propose a novel Fair Kernel K-Means (FKKM) framework. In this framework, we first propose a new fairness regularization term that can lead to a fair partition of data. The carefully designed fairness regularization term has a similar form to the kernel k-means which can be seamlessly integrated into the kernel k-means framework. Then, we extend this method to the multiple kernel setting, leading to a Fair Multiple Kernel K-Means (FMKKM) method. We also provide some theoretical analysis of the generalization error bound, and based on this bound we give a strategy to set the hyper-parameter, which makes the proposed methods easy to use. At last, we conduct extensive experiments on both the single kernel and multiple kernel settings to compare the proposed methods with state-of-the-art methods to demonstrate their effectiveness.