Maximal hypercliques search based on concept-cognitive learning

Abstract

Maximal hyperclique search, focused on finding the largest hypernode subsets in a hypergraph such that every combination of r nodes in these subsets forms a hyperedge, is a fundamental problem in hypergraph mining. However, compared to traditional graphs, the combinatorial explosion of hyperedges significantly increases the complexity of enumeration, especially as the r-value and the number of hypernodes grow, rapidly expanding the search space. Moreover, overlapping hyperedges in dense hypergraphs lead to substantial redundant checks, further exacerbating search inefficiency, making traditional methods inadequate for large-scale hypergraphs. To tackle these challenges, this paper proposes a novel approach MHSC that handles the maximal hyperclique search task in r-uniform hypergraph based on concept-cognitive learning. Concept-cognitive learning refers to the process of understanding and structuring knowledge through the formation of concepts and their interrelationships. Technically, the hypernode-neighbor structure of the hypergraph is first expressed as a formal context, and the required concepts are generated using the concept lattice algorithm. Based on the shared relationships between hypernodes represented by the hyperedges, a series of theorems are proposed to prune hypernodes that cannot form maximal hypercliques within the sets of 1-intent and 2-intent concepts, thereby narrowing the search space and reducing redundant computations. Furthermore, an optimization method termed MHSC+ is introduced. Extensive experiments conducted on both test datasets and real-world datasets demonstrate the effectiveness, efficiency, and applicability of the proposed algorithm.