Link prediction with hyperbolic geometry

Local-ring network automata and the impact of hyperbolic geometry in complex network link-prediction

Methods for topological link-prediction are generally referred as global or local. The former exploits the entire network topology, the latter adopts only the immediate neighbourhood of the link to predict. Global methods are ‘believed’ to be the best performing. Is this common belief well-founded? Stochastic-Block-Model (SBM) is a global method believed as one of the best link-predictors and w...

Hyperbolic Geometry

An Extension of Poincare Model of Hyperbolic Geometry with Gyrovector Space Approach

‎The aim of this paper is to show the importance of analytic hyperbolic geometry introduced in [9]‎. ‎In [1]‎, ‎Ungar and Chen showed that the algebra of the group $SL(2,mathbb C)$ naturally leads to the notion of gyrogroups ‎and gyrovector spaces for dealing with the Lorentz group and its ‎underlying hyperbolic geometry‎. ‎They defined the Chen addition and then Chen model of hyperbolic geomet...

Hyperbolic Geometry: Isometry Groups of Hyperbolic Space

The goal of this paper is twofold. First, it consists of an introduction to the basic features of hyperbolic geometry, and the geometry of an important class of functions of the hyperbolic plane, isometries. Second, it identifies a group structure in the set of isometries, specifically those that preserve orientation, and deals with the topological properties of their discrete subgroups. In the...

Emergent Hyperbolic Network Geometry

A large variety of interacting complex systems are characterized by interactions occurring between more than two nodes. These systems are described by simplicial complexes. Simplicial complexes are formed by simplices (nodes, links, triangles, tetrahedra etc.) that have a natural geometric interpretation. As such simplicial complexes are widely used in quantum gravity approaches that involve a ...