Fairness-Aware Clique-Preserving Spectral Clustering of Temporal Graphs

With the widespread development of algorithmic fairness, there has been a surge of research interest that aims to generalize the fairness notions from the attributed data to the relational data (graphs). The vast majority of existing work considers the fairness measure in terms of the low-order connectivity patterns (e.g., edges), while overlooking the higher-order patterns (e.g., k-cliques) and the dynamic nature of real-world graphs. For example, preserving triangles from graph cuts during clustering is the key to detecting compact communities; however, if the clustering algorithm only pays attention to triangle-based compactness, then the returned communities lose the fairness guarantee for each group in the graph. Furthermore, in practice, when the graph (e.g., social networks) topology constantly changes over time, one natural question is how can we ensure the compactness and demographic parity at each timestamp efficiently. To address these problems, we start from the static setting and propose a spectral method that preserves clique connections and incorporates demographic fairness constraints in returned clusters at the same time. To make this static method fit for the dynamic setting, we propose two core techniques, Laplacian Update via Edge Filtering and Searching and Eigen-Pairs Update with Singularity Avoided. Finally, all proposed components are combined into an end-to-end clustering framework named F-SEGA, and we conduct extensive experiments to demonstrate the effectiveness, efficiency, and robustness of F-SEGA.