Matisse: Visualizing Measured Internet Latencies as Manifolds

2025-09-09

AI Summary

Internet latency data exhibit complex topological structures that are difficult to interpret intuitively. Method: This paper proposes a manifold-based geometric visualization framework that models real-world latency measurements as a geography-aware manifold embedded in a 2D Euclidean space. It employs geodesic distance as the intrinsic metric and—novelty introduced herein—uses Forman–Ricci curvature to quantify local connectivity and detect anomalies. The approach integrates graph neural networks, nonlinear dimensionality reduction (t-SNE/UMAP), and GIS projection to enable curvature-driven interactive rendering. Contribution/Results: Implemented as the Matisse system, the method successfully identifies high-curvature anomalous regions in U.S. public Internet latency data, demonstrating the efficacy of geometric representation for uncovering performance bottlenecks and topological vulnerabilities. Its core innovation lies in incorporating Ricci curvature into latency-space modeling, establishing a tri-coupled visualization paradigm linking latency, geometry, and geography.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Machine Learning: Learning with Manifolds
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Web data visualization
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• Visualizing Internet latency manifolds from measurements
• Projecting latency data onto 2D geographic maps
• Identifying critical connectivity through curvature analysis

Innovation

• Visualizing Internet latencies as 2D manifolds
• Leveraging graph Ricci curvature for manifold curvature
• Projecting latency manifolds onto geographic maps