Penalized Flow Hypergraph Local Clustering

In recent years, hypergraph analysis have attracted increasing attention due to their ability to model complex data correlation, with hypergraph clustering being one of the most important tasks. However, when the scale of hypergraph is large enough, clustering is difficult based on global consistency. Existing flow-based hypergraph local clustering methods have good theoretical cut improvements and runtime guarantees. However, these methods exhibit poor performance when the initial reference node set is small and are prone to causing the output set to shrink into a small subset, resulting in local minima. To address this issue, we propose the Penalized Flow Hypergraph Local Clustering(PFHLC) and provide new conductance guarantees and runtime analyses for our method. First, we use the random walk method to grow the initial seed set, and introduce the random walk information of nodes as penalized flow into the flow-based framework to optimize the output. Second, we propose a generalized objective function containing random walk information, which takes full advantage of the semi-supervised information of the target cluster to protect important nodes. This feature can avoid the local minima of previous flow-based methods. Importantly, our method is strongly-local and can run efficiently on large-scale hypergraphs. We contribute a real-world dataset and the experiments on real-world large-scale datasets show that PFHLC achieves the state-of-the-art significantly.