Multilevel method in bipartite networks - Alan Demetrius Baria Valejo (2019)
Bipartite networks comprise a particular class of network models in which the vertex set is split into two disjoint and independent subsets, with edges connecting only vertices placed in different subsets. They provide a powerful representation of the relationships in many realworld systems and have been widely employed to model data-intensive problems. In a related scenario, multilevel methods have been previously applied to handle computationally expensive optimization problems defined in networks. The strategy aims at reducing the cost of executing an expensive algorithm or task by exploiting a hierarchy of coarsened versions of the original network. There is a growing interest in multilevel methods in networked systems, motivated mostly by their capability of handling large-scale networks and applicability to a variety of problems, most notably community detection and network drawing. Despite their potential, existing approaches are not directly applicable to bipartite networks and, to the best of our knowledge, the multilevel strategy had not been considered in this context so far, opening a vast space for scientific exploration. This gap motivated this research project, which introduces a study on multilevel methods applicable to bipartite networks. In order to overcome the aforementioned limitations, this thesis presents two novel multilevel frameworks for handling bipartite structures, named OPM and MOb. OPM analyzes the bipartite network based on its one-mode projections, allowing the reuse of classical and already established solutions from the literature. MOb (and its Mdr, CSV and CSL variations) operate directly on the bipartite representation to execute the multilevel method, providing a cost-effective implementation. Empirical results obtained on a set of synthetic and real-world networks on diverse applications indicate a considerable speed up with no significant loss in the quality of the solutions obtained in the coarsened networks as compared to those obtained in the original network (i.e., conventional approaches). The potential applicability and reliability of the proposed methods have been illustrated in multiple scenarios, namely optimization, community detection, dimensionality reduction and visualization. Furthermore, the results provide empirical evidence that the proposed methods can foster novel applications of the multilevel method in bipartite networks, e.g. link prediction and trajectory mining and, therefore, that this thesis brings a relevant contribution to the field.