Distribution-Free Model for Community Detection

TL;DR

This paper introduces a Distribution-Free Model for weighted networks that generalizes stochastic blockmodels, enabling consistent community detection without prior distribution assumptions, supported by theoretical guarantees and experimental validation.

Contribution

It proposes a novel Distribution-Free Model for weighted networks, extending stochastic blockmodels, with theoretical guarantees for spectral clustering and a new data generation process.

Findings

Spectral clustering achieves consistent community detection under DFM.

The proposed data generation process effectively simulates weighted networks.

Benchmark algorithms can recover communities in simulated and real datasets.

Abstract

Community detection for unweighted networks has been widely studied in network analysis, but the case of weighted networks remains a challenge. This paper proposes a general Distribution-Free Model (DFM) for weighted networks in which nodes are partitioned into different communities. DFM can be seen as a generalization of the famous stochastic blockmodels from unweighted networks to weighted networks. DFM does not require prior knowledge of a specific distribution for elements of the adjacency matrix but only the expected value. In particular, signed networks with latent community structures can be modeled by DFM. We build a theoretical guarantee to show that a simple spectral clustering algorithm stably yields consistent community detection under DFM. We also propose a four-step data generation process to generate adjacency matrices with missing edges by combining DFM, noise matrix, and a model for unweighted networks. Using experiments with simulated and real datasets, we show that some benchmark algorithms can successfully recover community membership for weighted networks generated by the proposed data generation process.