Blockmodel module identification in protein interaction networks through Markov random walk

To identify biologically meaningful modules in large-scale biological networks, general blockmodel network clustering algorithms have recently attracted much attention to search for groups of molecules that have similar interaction patterns in networks. However, existing blockmodel module identification algorithms suffer from the problems of prohibitive computational complexity and being trapped at local optima due to its inherent combinatorial complexity. In this paper, we propose a novel blockmodel module identification formulation based on Markov random walk to address those problems by finding high quality approximate solutions. A new convex optimization problem is formulated to find the low conductance (LC) sets as potential modules based on the two-hop transition matrix of Markov random walk on networks. We further propose a spectral approximate algorithm to find high quality modules in large-scale networks. The experimental results on two real-world PPI (protein-protein interaction) networks demonstrate that our method outperforms the state-of-the-art blockmodel module identification algorithms in terms of the accuracy measured by the F-measure based on curated annotations such as GO (Gene Ontology) and KOG (EuKaryotic Orthologous Groups) categories.