Adaptive Weights Community Detection

TL;DR

This paper introduces a new adaptive weights community detection algorithm that improves theoretical and practical performance, especially on sparse graphs, by addressing biases and achieving near-optimal consistency.

Contribution

It presents a modified algorithm that overcomes limitations of previous methods, providing both theoretical guarantees and practical effectiveness for community detection.

Findings

Achieves nearly optimal strong consistency on stochastic block models.

Addresses biases in estimators and improves performance on sparse graphs.

Validated through numerical experiments on artificial and real data.

Abstract

Due to the technological progress of the last decades, Community Detection has become a major topic in machine learning. However, there is still a huge gap between practical and theoretical results, as theoretically optimal procedures often lack a feasible implementation and vice versa. This paper aims to close this gap and presents a novel algorithm that is both numerically and statistically efficient. Our procedure uses a test of homogeneity to compute adaptive weights describing local communities. The approach was inspired by the Adaptive Weights Community Detection (AWCD) algorithm by Adamyan et al. (2019). This algorithm delivered some promising results on artificial and real-life data, but our theoretical analysis reveals its performance to be suboptimal on a stochastic block model. In particular, the involved estimators are biased and the procedure does not work for sparse graphs. We propose significant modifications, addressing both shortcomings and achieving a nearly optimal rate of strong consistency on the stochastic block model. Our theoretical results are illustrated and validated by numerical experiments.