Attribute-Driven Backbone Discovery

Backbones refer to critical tree structures that span a set of nodes of interests in networks. This paper introduces a novel class of attributed backbones and detection algorithms in richly attributed networks. Unlike conventional models, attributed backbones capture dynamics in edge cost model: it specifies affinitive attributes for each edge, and the cost of each edge is dynamically determined by the selection of its associated affinitive attributes and the closeness of their values at its end nodes. The backbone discovery is to compute an attributed backbone that covers interested nodes with smallest connection cost dynamically determined by selected affinitive attributes. While this problem is hard to approximate, we develop feasible algorithms within practical reach for large attributed networks. (1) We show that this problem is fixed-parameter approximable parameterized by the number of affinitive attributes, by providing a Lagrangean-preserving 2-approximation. (2) When the attribute number is large and specifying closeness function is difficult, we provide a fast heuristic, which learns an edge-generative model, and applies the model to infer best backbones, without the need of specifying closeness functions. Using real-world networks, we verify the effectiveness and efficiency of our algorithms and show their applications in collaboration recommendation.