The spring bounces back: introducing the strain elevation tension spring embedding algorithm for network representation

Jonathan Bourne

doi:10.1007/s41109-020-00329-4

Abstract

This paper introduces the strain elevation tension spring embedding (SETSe) algorithm. SETSe is a novel graph embedding method that uses a physical model to project feature-rich networks onto a manifold with semi-Euclidean properties. Due to its method, SETSe avoids the tractability issues faced by traditional force-directed graphs, having an iteration time and memory complexity that is linear to the number of edges in the network. SETSe is unusual as an embedding method as it does not reduce dimensionality or explicitly attempt to place similar nodes close together in the embedded space. Despite this, the algorithm outperforms five common graph embedding algorithms, on graph classification and node classification tasks, in low-dimensional space. The algorithm is also used to embed 100 social networks ranging in size from 700 to over 40,000 nodes and up to 1.5 million edges. The social network embeddings show that SETSe provides a more expressive alternative to the popular assortativity metric and that even on large complex networks, SETSe’s classification ability outperforms the naive baseline and the other embedding methods in low-dimensional representation. SETSe is a fast and flexible unsupervised embedding algorithm that integrates node attributes and graph topology to produce interpretable results.

Highlights

With the rise of social media and e-commerce, graph and complex networks have become a common concept in society
The strain elevation tension spring embedding (SETSe) algorithm acts as a hybrid between the advanced techniques of the machine learning graph embedders used for analysis and the intuitive simplicity of the spring embedders used for graph drawing
SETSe acts as a hybrid between the advanced techniques of the graph embedders used for analysis and the intuitive simplicity of the spring embedders used for graph drawing

Summary

Introduction

With the rise of social media and e-commerce, graph and complex networks have become a common concept in society. There is a range of algorithms that can perform supervised learning directly on graphs (Cao et al 2016; Kipf and Welling 2016; Seo et al 2018; Scarselli et al 2009) [see Wu et al (2020) for a recent survey on the subject], a more common approach is to create embeddings in a latent vector space that traditional supervised learning techniques can use. Like other spring embedders (Fruchterman and Reingold 1991; Kamada and Kawai 1989; Quigley and Eades 2001), SETSe is subject to the n-body problem (Aarseth 2003; Springel et al 2005) and must be solved iteratively

Results

Discussion

Conclusion