D-Mercator: Network embedding into ultra low dimensional hyperbolic spaces
Date:
In this work we address that problem by introducing a method to map real complex networks into multidimensional hyperbolic spaces. The framework assumes that the structure of complex networks is well described by the $\mathbb{S}^D / \mathbb{H}^{D+1}$ model, i.e., the extension of well-known $\mathbb{S}^1/\mathbb{H}^2$ model into higher dimensions that has been proven to meaningfully explain properties of the real complex networks. Our method consists of two main parts. First, we leverage machine learning approach to infer the initial positions of the nodes on the $D$-sphere. Then by applying maximization likelihood technique we find the best matching between the observed network topology and the geometric model. Overall, our results suggest that mixing machine learning and ML techniques in a model-dependent framework can boost the meaningful mapping of complex networks.
Slides are available here.