Machine learning meets network science: dimensionality reduction for fast and efficient embedding of networks in the hyperbolic space

TL;DR

This paper introduces a machine learning approach for fast and accurate embedding of complex networks into hyperbolic space, preserving topological properties for applications like link prediction and community detection.

Contribution

It demonstrates that topological-based machine learning algorithms can directly approximate hyperbolic node coordinates, enabling efficient network embedding.

Findings

Machine learning algorithms can approximate hyperbolic node coordinates.

The proposed method achieves fast embedding for large networks.

Embedding preserves key topological properties of networks.

Abstract

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.