Mining Biological Interaction Networks Using Weighted Quasi-Bicliques

Biological network studies can provide fundamental insights into various biological tasks including the functional characterization of genes and their products, the characterization of DNA-protein interactions, and the identification of regulatory mechanisms. However, biological networks are confounded with unreliable interactions and are incomplete, and thus, their computational exploitation is fraught with algorithmic challenges. Here we introduce quasi-biclique problems to analyze biological networks when represented by bipartite graphs. In difference to previous quasi-biclique problems, we include biological interaction levels by using edge-weighted quasi-bicliques. While we prove that our problems are NP-hard, we also provide exact IP solutions that can compute moderately sized networks. We verify the effectiveness of our IP solutions using both simulation and empirical data. The simulation shows high quasi-biclique recall rates, and the empirical data corroborate the abilities of our weighted quasi-bicliques in extracting features and recovering missing interactions from the network.