Cost Guarantee for Individual Fairness on Spectral Clustering.

The graph mining algorithm has been widely used in various fields in recent years, among which the spectral clustering algorithm is based on spectral graph theory, which has the ability to cluster on an arbitrarily shaped sample space and converge to the global optimal solution compared with the traditional clustering algorithm. As algorithmic fairness has become a research hot-spot recently, more and more fairness constraints have been introduced into spectral clustering. Most studies focus on group fairness, with only a small number providing individual-level fairness constraints. Existing fair spectral clustering algorithms focus only on whether the clustering results are fair or the decreased rate of fairness loss. To this end, we propose an Individual Fair Spectral Clustering with Cost constraints (IFSCC), which ensures the clustering effect while also improving a certain degree of individual fairness. The experimental results show that IFSCC has the lowest COST value while having a comparable clustering effect compared to other individual fair spectral clustering algorithms. To the best of our knowledge, this paper is the first study to make a trade-off between the clustering effect and fairness performance.