📝 SummarXiv

Abstract

Manifolds are complex topological spaces that can be used to represent datasets of real-world measurements. Visualizing such manifolds can help with illustrating their topological characteristics (e.g., curvature) and providing insights into important properties of the underlying data (e.g., anomalies in the measurements). In this paper, we describe a new methodology and system for generating and visualizing manifolds that are inferred from actual Internet latency measurements between different cities and are projected over a 2D Euclidean space (e.g., a geographic map). Our method leverages a series of graphs that capture critical information contained in the data, including well-defined locations (for vertices) and Ricci curvature information (for edges). Our visualization approach then generates a curved surface (manifold) in which (a) geographical locations of vertices are maintained and (b) the Ricci curvature values of the graph edges determine the curvature properties of the manifold. The resulting manifold highlights areas of critical connectivity and defines an instance of "Internet delay space" where latency measurements manifest as geodesics. We describe details of our method and its implementation in a tool, which we call Matisse, for generating, visualizing and manipulating manifolds projected onto a base map. We illustrate Matisse with two case studies: a simple example to demonstrate key concepts, and visualizations of the US public Internet to show Matisse's utility.