Multi-objective Optimization for Multi-level Networks
Social network analysis is a rich field with many practical applications like community formation and hub detection. Traditionally, we assume that edges in the network have homogeneous semantics, for instance, indicating friend relationships. However, we increasingly deal with networks for which we can define multiple heterogeneous types of connections between users; we refer to these distinct groups of edges as layers. Naïvely, we could perform standard network analyses on each layer independently, but this approach may fail to identify interesting signals that are apparent only when viewing all of the layers at once. Instead, we propose to analyze a multi-layered network as a single entity, potentially yielding a richer set of results that better reflect the underlying data. We apply the framework of multi-objective optimization and specifically the concept of Pareto optimality, which has been used in many contexts in engineering and science to deliver solutions that offer tradeoffs between various objective functions. We show that this approach can be well-suited to multi-layer network analysis, as we will encounter situations in which we wish to optimize contrasting quantities. As a case study, we utilize the Pareto framework to show how to bisect the network into equal parts in a way that attempts to minimize the cut-size on each layer. This type of procedure might be useful in determining differences in structure between layers, and in cases where there is an underlying true bisection over multiple layers, this procedure could give a more accurate cut.
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