Detecting Low Pass Graph Signals via Spectral Pattern: Sampling Complexity and Applications

TL;DR

This paper introduces a spectral pattern-based method for detecting low pass graph signals without knowing the graph topology, analyzing sample complexity and demonstrating applications in graph learning, opinion dynamics, and power systems.

Contribution

It presents a novel spectral pattern approach for blind detection of low pass graph signals on modular graphs, with theoretical analysis and practical applications.

Findings

Spectral pattern effectively detects low pass signals without graph knowledge.

Sample complexity depends on filter properties and graph parameters.

Method improves robustness in graph learning and anomaly detection.

Abstract

This paper proposes a blind detection problem for low pass graph signals. Without assuming knowledge of the exact graph topology, we aim to detect if a set of graph signal observations are generated from a low pass graph filter. Our problem is motivated by the widely adopted assumption of low pass (a.k.a.~smooth) signals required by many existing works in graph signal processing (GSP), as well as the longstanding problem of network dynamics identification. Focusing on detecting low pass graph signals on modular graphs whose cutoff frequency coincides with the number of clusters in the graph, we propose to leverage the unique spectral pattern exhibited by such low pass graph signals. We analyze the sample complexity of these detectors considering the effects of graph filter's properties, random delays, and other parameters. We show novel applications of the blind detector on robustifying graph learning, identifying antagonistic ties in opinion dynamics, and detecting anomalies in power systems. Numerical experiments validate our findings.