5 research outputs found
Machine learning meets complex networks via coalescent embedding in the hyperbolic space
Complex network topologies and hyperbolic geometry seem specularly connected,
and one of the most fascinating and challenging problems of recent complex
network theory is to map a given network to its hyperbolic space. The
Popularity Similarity Optimization (PSO) model represents - at the moment - the
climax of this theory. It suggests that the trade-off between node popularity
and similarity is a mechanism to explain how complex network topologies emerge
- as discrete samples - from the continuous world of hyperbolic geometry. The
hyperbolic space seems appropriate to represent real complex networks. In fact,
it preserves many of their fundamental topological properties, and can be
exploited for real applications such as, among others, link prediction and
community detection. Here, we observe for the first time that a
topological-based machine learning class of algorithms - for nonlinear
unsupervised dimensionality reduction - can directly approximate the network's
node angular coordinates of the hyperbolic model into a two-dimensional space,
according to a similar topological organization that we named angular
coalescence. On the basis of this phenomenon, we propose a new class of
algorithms that offers fast and accurate coalescent embedding of networks in
the hyperbolic space even for graphs with thousands of nodes