Spherical Graph Drawing by Multi-dimensional Scaling

TL;DR

This paper introduces a scalable method for embedding graphs onto spherical surfaces using a generalized multi-dimensional scaling approach optimized with stochastic gradient descent, outperforming Euclidean and hyperbolic embeddings in certain cases.

Contribution

It presents a novel spherical graph embedding technique based on a generalized stress function and demonstrates its scalability and effectiveness through evaluations.

Findings

The method is scalable to large graphs.

Spherical embeddings can have lower distortion for certain graph families.

The approach outperforms Euclidean and hyperbolic embeddings in some scenarios.

Abstract

We describe an efficient and scalable spherical graph embedding method. The method uses a generalization of the Euclidean stress function for Multi-Dimensional Scaling adapted to spherical space, where geodesic pairwise distances are employed instead of Euclidean distances. The resulting spherical stress function is optimized by means of stochastic gradient descent. Quantitative and qualitative evaluations demonstrate the scalability and effectiveness of the proposed method. We also show that some graph families can be embedded with lower distortion on the sphere, than in Euclidean and hyperbolic spaces.