Federated Myopic Community Detection with One-shot Communication

TL;DR

This paper introduces a federated learning approach for community detection in networks, enabling the central server to recover the network structure efficiently from limited client observations with one-shot communication.

Contribution

It proposes an efficient algorithm for federated myopic community detection, analyzes conditions for exact recovery, and establishes information-theoretic limits and a new Cheeger-type inequality.

Findings

Exact network recovery is achievable in polynomial time under certain conditions.

The analysis delineates topological and signal-noise conditions for successful recovery.

A novel Cheeger-type inequality for signed weighted graphs is introduced.

Abstract

In this paper, we study the problem of recovering the community structure of a network under federated myopic learning. Under this paradigm, we have several clients, each of them having a myopic view, i.e., observing a small subgraph of the network. Each client sends a censored evidence graph to a central server. We provide an efficient algorithm, which computes a consensus signed weighted graph from clients evidence, and recovers the underlying network structure in the central server. We analyze the topological structure conditions of the network, as well as the signal and noise levels of the clients that allow for recovery of the network structure. Our analysis shows that exact recovery is possible and can be achieved in polynomial time. We also provide information-theoretic limits for the central server to recover the network structure from any single client evidence. Finally, as a byproduct of our analysis, we provide a novel Cheeger-type inequality for general signed weighted graphs.