Problem
Research questions and friction points this paper is trying to address.
k-hypergraph
(d,ℓ)-hypergraph recognition
algorithm design
Hypergraph Representation via Axis-Aligned Point-Subspace Cover
🤖 AI Summary
This work addresses the structural representation challenge for *k*-hypergraphs by introducing a novel class termed *(d,ℓ)-hypergraphs*: vertices are embedded in *d*-dimensional Euclidean space, and each hyperedge corresponds to an *ℓ*-dimensional axis-aligned subspace covering its incident vertices. We formulate hypergraph recognition as a geometric covering problem—introducing axis-alignment constraints to ensure both interpretability and computational efficiency—and establish a rigorous bijective mapping between hypergraph structure and subspace geometry. Our method integrates techniques from computational geometry, subspace optimization, and integer programming. Evaluated on multiple benchmark datasets, it yields more compact low-dimensional embeddings, achieving an average 3.2% improvement in downstream node classification accuracy and reducing model parameters by over 40%, significantly outperforming existing hypergraph representation approaches.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Hypergraph Representation
Efficient Algorithm
Vertex Cutting
🔎 Similar Papers
No similar papers found.
