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September 10, 2025Open Access

Survey of Hypergraph-and Superhypergraph-Based Models: Deep Learning, Resource Allocation, Feature Selection, HyperGraph-Based Persistent Cohomology, Recommendation, and Mining

Key Points

Research identifies gaps in superhypergraph applications compared to hypergraphs in deep learning and mining.
Superhypergraphs facilitate connections among multiple vertices, enhancing modeling capabilities beyond hypergraphs.
Key findings highlight the need for further exploration into persistent cohomology within superhypergraph frameworks.
Applications in recommendation systems and feature selection are still underexplored, indicating areas for future research.

Abstract

Graph theory studies the mathematical structures of vertices and edges to model relationships and connectivity 1, 2. Hypergraphs extend this framework by allowing hyperedges to connect arbitrarily many vertices at once 3, and superhypergraphs further generalize hypergraphs via iterated powerset constructions to capture hierarchical linkages among edges 4,5. Many studies have been conducted on concepts such as deep learning, resource allocation, feature selection, hypergraph-based persistent cohomology, graph-based recommendation, and graph mining in the contexts of graphs and hypergraphs, but research in the context of superhypergraphs has been relatively limited. To address this gap, this paper investigates the counterparts of deep learning, resource allocation, feature selection, hypergraph-based persistent cohomology, graph-based recommendation, and graph mining in the framework of superhypergraphs.

Survey of Hypergraph-and Superhypergraph-Based Models: Deep Learning, Resource Allocation, Feature Selection, HyperGraph-Based Persistent Cohomology, Recommendation, and Mining

Key Points

Abstract

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