Mining Dense Structures by Enumerating Weighted and Multi-level Pseudo-Bicliques

Pseudo-bicliques model various problems encountered in bio-informatics, data mining and networks. They relax the rigid connectivity requirement of bicliques to cater missing and noisy data. In this paper, we consider the weighted density based model of pseudo-biclique. This model defines pseudo-biclique as a bipartite subgraph such that the ratio of the number of its edges to the number of edges in biclique of same size is no less than a given threshold value. The weighted model of pseudo-bicliques better fits the real-world situations and give much more flexibility to researchers. We propose an algorithm based on reverse search to generate all weighted pseudo-bicliques in a given graph. This is computationally non-trivial task as simple straightforward branch-and-bound and back-tracking schemes involve an NP complete problem. Furthermore, we proposed the use of multi-level pseudo-bicliques to discover knowledge at multiple levels and extend our algorithm to enumerate all multi-level pseudo-bicliques. We introduce various enhancements to our algorithm based on the structure of pseudo-bicliques and underlying bipartite graph. We evaluated the performance of our algorithms on random graphs and real-world problems. The results are quite promising and show that average linear time is incurred to generate each pseudo-biclique.