Previous hypergraph expansions are solely carried out on either vertex level or hyperedge level, thereby missing the symmetric nature of data co-occurrence, and resulting in information loss. To address the problem, this paper treats vertices and hyperedges equally and proposes a new hypergraph formulation named the line expansion (LE) for hypergraphs learning. The new expansion bijectively induces a homogeneous structure from the hypergraph by treating vertex-hyperedge pairs as "line nodes". By reducing the hypergraph to a simple graph, the proposed line expansion makes existing graph learning algorithms compatible with the higher-order structure and has been proven as a unifying framework for various hypergraph expansions. For simple graphs, we demonstrate that learning algorithms defined onLE s tie with their performance on the original graphs, implying that no loss of information occurs in the expansion . For hypergraphs, we show that learning over the new representation leads to algorithms that beat all prior state-of-the-art hypergraph learning baselines .
Previous hypergraph expansions are solely carried out on either vertex level or hyperedge level, thereby missing the symmetric nature of data co-occurrence, and resulting in information loss. To address the problem, this paper treats vertices and hyperedges equally and proposes a new hypergraph formulation named the line expansion (LE) for hypergraphs learning. The new expansion bijectively induces a homogeneous structure from the hypergraph by treating vertex-hyperedge pairs as "line nodes". By reducing the hypergraph to a simple graph, the proposed line expansion makes existing graph learning algorithms compatible with the higher-order structure and has been proven as a unifying framework for various hypergraph expansions. We evaluate the proposed line expansion on five hypergraph datasets, the results show that our method beats SOTA baselines by a significant margin .
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For simple graphs, we demonstrate that learning algorithms defined on
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LE
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s tie with their performance on the original graphs, implying that no loss of information occurs in the expansion . For hypergraphs, we show that learning over the new representation leads to algorithms that beat all prior state-of-the-art hypergraph learning baselines
We evaluate the proposed line expansion on five hypergraph datasets, the results show that our method beats SOTA baselines by a significant margin