Multi-Order Clustering on Dynamic Networks: On Error Accumulation and Its Elimination

Local clustering aims to find a high-quality cluster near a given vertex. Recently, higher-order units are introduced to local clustering, and the underlying information has been verified to be essential. However, original edges are underestimated in these techniques, leading to the degeneration of network information. Moreover, most of the higher-order models are designed for static networks, whereas real-world networks are generally large and evolve rapidly. Repeatedly conducting a static algorithm at each snapshot is usually computationally impractical, and recent approaches instead track a cluster by updating the cluster sequentially. However, errors would accumulate over lengthy evolutions, and the complete cluster needs to be recalculated periodically to maintain the accuracy, which naturally affects the efficiency. To bridge the two gaps, we design a multi-order hypergraph, and present a hybrid model for dynamic clustering. In particular, we propose an incremental method to track a personalized PageRank vector in the evolving hypergraph, which converges to the exact solution at each snapshot when significantly reducing the complexity. We further develop a dynamic sweep to identify a cut in each vector, whereby a cluster can be incrementally updated with no accumulated errors. We provide rigorous theoretical basis and conduct comprehensive experiments, which demonstrate the effectiveness.