Spaceland Embedding of Sparse Stochastic Graphs

We introduce SG-t-SNE, a nonlinear method for embedding stochastic graphs/networks into d-dimensional spaces, d = 1, 2, 3, without requiring vertex features to reside in, or be transformed into, a metric space. Graphs/networks are relational data, prevalent in real-world applications. Graph embedding is fundamental to many graph analysis tasks, besides graph visualization. SG-t-SNE follows and builds upon the core principle of t-SNE, which is a widely used method for visualizing high-dimensional data. We also introduce SG-t-SNE-Π, a high-performance software for rapid d-dimensional embedding of large, sparse, stochastic graphs on personal computers with superior efficiency. It empowers SG-t-SNE with modern computing techniques exploiting matrix structures in tandem with memory architectures. We present elucidating graph embedding results with several synthetic graphs and real-world networks in this paper and its Supplementary Material.¹¹Supplementary Material is at http://t-sne-pi.cs.duke.edu.