A plethora of real-world problems require utilization of hypergraphs and diffusion algorithms.Examples include recommendation systems, node ranking in food networks and community detection in social networks to mention a few. Due to the increased size and complexity of real hypergraphs, local and accurate diffusion algorithms that work with the most complex hypergraphs are in need. We propose the first local diffusion method that works on higher-order relations with only a submodularity assumption . 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 for general submodular cut-costs. We prove that the proposed formulation achieves quadratic approximation error for the problem of local hypergraph clustering. We demonstrate that the new technique is significantly better than state-of-the-art methods over a range of real datasets for the local hypergraph clustering and node ranking problems .
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 .
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A plethora of real-world problems require utilization of hypergraphs and diffusion algorithms.Examples include recommendation systems, node ranking in food networks and community detection in social networks to mention a few. Due to the increased size and complexity of real hypergraphs, local and accurate diffusion algorithms that work with the most complex hypergraphs are in need. We
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
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prove that the proposed formulation achieves quadratic approximation error for the problem of local hypergraph clustering. We demonstrate that
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