Multilevel approach for combinatorial optimization in bipartite network

Multilevel approaches aim at reducing the cost of a target algorithm over a given network by applying it to a coarsened (or reduced) version of the original network. They have been successfully employed in a variety of problems, most notably community detection. However, current solutions are not directly applicable to bipartite networks and the literature lacks studies that illustrate their application for solving multilevel optimization problems in such networks. This article addresses this gap and introduces a multilevel optimization approach for bipartite networks and the implementation of a general multilevel framework including novel algorithms for coarsening and uncorsening, applicable to a variety of problems. We analyze how the proposed multilevel strategy affects the topological features of bipartite networks and show that a controlled coarsening strategy can preserve properties such as degree and clustering coefficient centralities. The applicability of the general framework is illustrated in two optimization problems, one for solving the Barber's modularity for community detection and the second for dimensionality reduction in text classification. We show that the solutions thus obtained are statistically equivalent, regarding accuracy, to those of conventional approaches, whilst requiring considerably lower execution times.