Local Hyper-Flow Diffusion
This work addresses the challenge of capturing local structure in large, complex hypergraphs, which is incremental as it builds on existing hypergraph clustering and seed set expansion problems.
The authors tackled the problem of local hypergraph clustering by proposing a new diffusion method that achieves edge-size-independent Cheeger-type guarantees, demonstrating significant improvements over state-of-the-art methods on synthetic and real-world data.
Recently, hypergraphs have attracted a lot of attention due to their ability to capture complex relations among entities. The insurgence of hypergraphs has resulted in data of increasing size and complexity that exhibit interesting small-scale and local structure, e.g., small-scale communities and localized node-ranking around a given set of seed nodes. Popular and principled ways to capture the local structure are the local hypergraph clustering problem and related seed set expansion problem. In this work, we propose the first local diffusion method that achieves edge-size-independent Cheeger-type guarantee for the problem of local hypergraph clustering while applying to a rich class of higher-order relations that covers many previously studied special cases. Our method is based on a primal-dual optimization formulation where the primal problem has a natural network flow interpretation, and the dual problem has a cut-based interpretation using the $\ell_2$-norm penalty on associated cut-costs. We demonstrate the new technique is significantly better than state-of-the-art methods on both synthetic and real-world data.