Optimizations in Enumerating Maximal Balanced Bicliques: Pruning and Vertex Sorting

Abstract

A bipartite graph is an abstract discrete structure widely used to model relationships between two groups in areas such as Web mining, bioinformatics, social network analysis, and e-commerce. The problem of maximal biclique mining has received significant attention in the field of graph mining. A maximal biclique is defined as a complete bipartite subgraph and plays an important role in numerous applications, representing a community characterized by complete interaction between groups. A maximal balanced biclique, however, refers to a specific kind of maximal biclique where the two sets of vertices are equal in size. Enumerating maximal balanced bicliques presents significant computational difficulties and is often time consuming. In this paper, we present an optimized algorithm for mining maximal balanced bicliques in bipartite graphs utilizing formal concept analysis. We exploit the correspondence between semi-equiconcepts and maximal balanced bicliques to effectively tackle the mining challenge. In the preprocessing step, attribute sorting was applied, and a heuristic pruning strategy was introduced to systematically eliminate irrelevant formal concepts by leveraging their specific properties. We performed extensive experiments including comparisons with existing approaches. Results from six real-world and six synthetic random bipartite graphs demonstrate the effectiveness and efficiency of our algorithm. On average, the proposed algorithm produced 37 times fewer closures compared to previous algorithms. This computational optimization further reduced execution time by a factor of 7 on average. Additionally, our experiments provide valuable insight into the number of computed closures and their significant effect on execution time.