Graph Drawing by Stochastic Gradient Descent

TL;DR

This paper introduces a stochastic gradient descent method for force-directed graph drawing that achieves lower stress levels faster, handles constraints more easily, and scales efficiently to large graphs compared to traditional methods.

Contribution

The authors develop a stochastic gradient descent algorithm for graph layout optimization that improves speed, scalability, and constraint handling over existing approaches.

Findings

SGD reaches lower stress faster than majorization.

SGD handles constrained layouts more easily.

Algorithm scales to large graphs using sparse stress approximation.

Abstract

A popular method of force-directed graph drawing is multidimensional scaling using graph-theoretic distances as input. We present an algorithm to minimize its energy function, known as stress, by using stochastic gradient descent (SGD) to move a single pair of vertices at a time. Our results show that SGD can reach lower stress levels faster and more consistently than majorization, without needing help from a good initialization. We then show how the unique properties of SGD make it easier to produce constrained layouts than previous approaches. We also show how SGD can be directly applied within the sparse stress approximation of Ortmann et al. [1], making the algorithm scalable up to large graphs.