Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

In many networks, including networks of protein-protein interactions, interdisciplinary collaboration networks, and semantic networks, connections are established between nodes with complementary rather than similar properties. What is complementarity? The Oxford Dictionary asserts that "two people or things that are complementary are different but together form a useful or attractive combination of skills, qualities or physical features." Sadly, our understanding of complementarity in networks does not go far beyond definition. While complementarity is abundant in networks, we lack mathematical intuition and quantitative methods to study complementarity mechanisms in these systems. Instead, we routinely retreat to using available off-the-shelf methods developed in the first place for similarity-driven networks.   In my talk, I will discuss my group's recent achievements in the analysis of complementarity mechanisms in networks. I will first explain why existing similarity-based inference and learning methods are not readily applicable to systems where complementarity between interacting nodes plays a significant role. I will then deduce, starting with the definition by the Oxford Dictionary, a general complementarity framework for networks capable of describing any matching relations and containing both similarity and antitheses relations as special cases. Using the general framework, I will formulate a minimal null model to learn complementarity embeddings of real networks via maximum-likelihood estimation. I will demonstrate how complementarity embeddings can be used to infer both complementary and similar nodes in a network, enabling network inference tasks, such as link  prediction and community detection. I will conclude my talk with an outlook on the interplay of similarity and complementarity in the formation of networks, arguing for for a careful re-evaluation of existing similarity-inspired methods.

 

Hosted by the Department of Computer Science.