2017/10/12 by Jonathan X. Zheng, Zheng, Jonathan X., Samraat Pawar +3
Computer Science · #Computational Geometry (cs.CG) #Data Visualization and Analytics #FOS: Computer and information sciences #Graph Theory and Algorithms #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1710.04626
openalex publication_date 2017/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.