Finding Patient Zero via Low-Dimensional Geometric Embeddings

2026-04-17

AI Summary

This work addresses the challenging problem of efficiently identifying the initial source of infection (Patient Zero) under the independent cascade model using only observations of infected nodes. The authors propose a novel approach that embeds the contact network into a low-dimensional Euclidean space via Johnson–Lindenstrauss random projection and estimates the infection source as the node closest to the geometric centroid of the observed infected nodes. This method uniquely combines low-dimensional geometric embedding with centroid-based estimation for source localization, achieving strong reconstruction performance even when relying solely on compressed observational data. Experimental results on Erdős–Rényi graphs demonstrate that the proposed technique attains competitive source identification accuracy at a significantly lower observation cost compared to conventional methods.

Technology Category

• Search and Optimization: Local Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Learning with Manifolds

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Web Mining and Content Analysis: Content-based information diffusion

Abstract

We study the patient zero problem in epidemic spreading processes in the independent cascade model and propose a geometric approach for source reconstruction. Using Johnson-Lindenstrauss projections, we embed the contact network into a low-dimensional Euclidean space and estimate the infection source as the node closest to the center of gravity of infected nodes. Simulations on Erdős-Rényi graphs demonstrate that our estimator achieves meaningful reconstruction accuracy despite operating on compressed observations.

Problem

• patient zero
• epidemic spreading
• source reconstruction
• independent cascade model
• contact network

Innovation

• geometric embeddings
• source localization
• Johnson-Lindenstrauss projection
• epidemic spreading
• patient zero