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 emph{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 emph{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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