Recovering Graph-Structured Activations using Adaptive Compressive Measurements

TL;DR

This paper introduces a hierarchical adaptive sensing method for localizing clusters of activated vertices in graphs, achieving effective detection at lower signal-to-noise ratios than traditional methods.

Contribution

It proposes a novel hierarchical partitioning approach combined with adaptive measurements for graph activation localization, with theoretical guarantees and practical validation.

Findings

Localization at weaker SNR than unstructured methods

Theoretical lower bounds on SNR for successful localization

Simulation results demonstrating algorithm effectiveness

Abstract

We study the localization of a cluster of activated vertices in a graph, from adaptively designed compressive measurements. We propose a hierarchical partitioning of the graph that groups the activated vertices into few partitions, so that a top-down sensing procedure can identify these partitions, and hence the activations, using few measurements. By exploiting the cluster structure, we are able to provide localization guarantees at weaker signal to noise ratios than in the unstructured setting. We complement this performance guarantee with an information theoretic lower bound, providing a necessary signal-to-noise ratio for any algorithm to successfully localize the cluster. We verify our analysis with some simulations, demonstrating the practicality of our algorithm.