Finding Patient Zero via Low-Dimensional Geometric Embeddings

TL;DR

This paper introduces a geometric method using Johnson-Lindenstrauss projections to identify the initial infection source in epidemic models by embedding contact networks into low-dimensional space.

Contribution

It presents a novel low-dimensional embedding approach for source detection in epidemic spreading, improving accuracy with compressed network observations.

Findings

Estimator achieves meaningful accuracy on Erdős-Rényi graphs

Embedding reduces dimensionality while preserving source information

Method effective despite operating on compressed data

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 Erd\H{o}s-R\'enyi graphs demonstrate that our estimator achieves meaningful reconstruction accuracy despite operating on compressed observations.