# Spaceland Embedding of Sparse Stochastic Graphs

## TL;DR

This paper presents SG-t-SNE, a novel nonlinear embedding method for large sparse stochastic graphs, enabling effective visualization and analysis without requiring metric space vertex features, along with a high-performance software implementation.

## Contribution

The paper introduces SG-t-SNE, a new graph embedding technique inspired by t-SNE, and provides a software tool for efficient 2D/3D embedding of large sparse graphs.

## Key findings

- Successful embedding of synthetic and real-world graphs.
- Enhanced efficiency in graph visualization on personal computers.
- Demonstrated effectiveness of the method on large sparse networks.

## Abstract

We introduce a nonlinear method for directly embedding large, sparse, stochastic graphs into low-dimensional spaces, without requiring vertex features to reside in, or be transformed into, a metric space. Graph data and models are prevalent in real-world applications. Direct graph embedding is fundamental to many graph analysis tasks, in addition to graph visualization. We name the novel approach SG-t-SNE, as it is inspired by and builds upon the core principle of t-SNE, a widely used method for nonlinear dimensionality reduction and data visualization. We also introduce t-SNE-$\Pi$, a high-performance software for 2D, 3D embedding of large sparse graphs on personal computers with superior efficiency. It empowers SG-t-SNE with modern computing techniques for exploiting in tandem both matrix structures and memory architectures. We present elucidating embedding results on one synthetic graph and four real-world networks.