Clustering ensemble has been widely studied in data mining and machine learning. However, the existing clustering ensemble methods do not pay attention to fairness, which is important in real-world applications, especially in applications involving humans. To address this issue, this paper proposes a novel fair clustering ensemble method, which takes multiple base clustering results as inputs and learns a fair consensus clustering result. When designing the algorithm, we observe that one of the widely used definitions of fairness may cause a cluster imbalance problem. To tackle this problem, we give a new definition of fairness that can simultaneously characterize fairness and cluster capacity equality. Based on this new definition, we design an extremely simple yet effective regularized term to achieve fairness and cluster capacity equality. We plug this regularized term into our clustering ensemble framework, finally leading to our new fair clustering ensemble method. The extensive experiments show that, compared with the state-of-the-art clustering ensemble methods, our method can not only achieve a comparable or even better clustering performance, but also obtain a much fairer and better capacity equality result, which well demonstrates the effectiveness and superiority of our method.

Multi-view clustering is an important task in multimedia and machine learning. In multi-view clustering, multi-view spectral clustering is one kind of the most popular and effective methods. However, existing multi-view spectral clustering ignores the fairness in the clustering result, which may cause discrimination. To tackle this problem, in this paper, we propose an innovative Fair Multi-view Spectral Clustering (FMSC) method. Firstly, we provide a new perspective of fairness from the graph theory viewpoint, which constructs a relation between fairness and the average degree in graph theory. Secondly, based on this relation, we design a novel fairness-aware regularized term, which has the same form as the ratio cut in spectral clustering. Thirdly, we seamlessly plug this fairness-aware regularized term into the multi-view spectral clustering, leading to our one-stage FMSC, which can directly obtain the final clustering result without any post-processing. We also conduct extensive experiments compared with state-of-the-art fair clustering and multi-view clustering methods, which shows that our method can achieve better fairness.

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.