Lovasz ϑ, SVMs and applications

Lovász introduced the theta function in his seminal paper [23] giving his celebrated solution to the problem of computing the Shannon capacity of the pentagon. Since then, the Lovász theta function has come to play a central role in information theory, graph theory and combinatorial optimization [11, 10], indeed Goemans [10] was led to remark: “it seems all paths lead to ϑ!”. The definition of the theta function also gives an elegant geometrical representation of the graph via an embedding in a spherical cap on the unit sphere which has many applications in graph theory and machine learning, some of them perhaps not yet fully appreciated. It is one of the goals of this paper to highlight how the Lovász embedding is a powerful and unifying tool in diverse graph theory and data mining applications.