Infection Analysis on Irregular Networks through Graph Signal Processing

TL;DR

This paper introduces graph signal processing techniques, including graph wavelets and machine learning, to analyze and distinguish epidemic infections from random failures in irregular networks.

Contribution

It develops novel graph wavelet methods and a machine learning framework for macro and micro infection analysis on irregular networks.

Findings

Effective detection metrics based on GFT and neighborhood features.

Distance-based graph wavelets improve infection localization.

Algorithms outperform existing methods in simulation tests.

Abstract

In a networked system, functionality can be seriously endangered when nodes are infected, due to internal random failures or a contagious virus that develops into an epidemic. Given a snapshot of the network representing the nodes' states (infected or healthy), infection analysis refers to distinguishing an epidemic from random failures and gathering information for effective countermeasure design. This analysis is challenging due to irregular network structure, heterogeneous epidemic spreading, and noisy observations. This paper treats a network snapshot as a graph signal, and develops effective approaches for infection analysis based on graph signal processing. For the macro (network-level) analysis aiming to distinguish an epidemic from random failures, 1) multiple detection metrics are defined based on the graph Fourier transform (GFT) and neighborhood characteristics of the graph signal; 2) a new class of graph wavelets, distance-based graph wavelets (DBGWs), are developed; and 3) a machine learning-based framework is designed employing either the GFT spectrum or the graph wavelet coefficients as features for infection analysis. DBGWs also enable the micro (node-level) infection analysis, through which the performance of epidemic countermeasures can be improved. Extensive simulations are conducted to demonstrate the effectiveness of all the proposed algorithms in various network settings.