Identify bilayer modules via pseudo-3D clustering: applications to miRNA-gene bilayer networks.

Module identification is a frequently used approach for mining local structures with more significance in global networks. Recently, a wide variety of bilayer networks are emerging to characterize the more complex biological processes. In the light of special topological properties of bilayer networks and the accompanying challenges, there is yet no effective method aiming at bilayer module identification to probe the modular organizations from the more inspiring bilayer networks. To this end, we proposed the pseudo-3D clustering algorithm, which starts from extracting initial non-hierarchically organized modules and then iteratively deciphers the hierarchical organization of modules according to a bottom-up strategy. Specifically, a modularity function for bilayer modules was proposed to facilitate the algorithm reporting the optimal partition that gives the most accurate characterization of the bilayer network. Simulation studies demonstrated its robustness and outperformance against alternative competing methods. Specific applications to both the soybean and human miRNA-gene bilayer networks demonstrated that the pseudo-3D clustering algorithm successfully identified the overlapping, hierarchically organized and highly cohesive bilayer modules. The analyses on topology, functional and human disease enrichment and the bilayer subnetwork involved in soybean fat biosynthesis provided both the theoretical and biological evidence supporting the effectiveness and robustness of pseudo-3D clustering algorithm.