Title: Simplify to Amplify: Achieving Information-Theoretic Bounds with Fewer Steps in Spectral Community Detection
Primary area: learning on graphs and other geometries & topologies
Keywords: stochastic block model, spectral algorithm, community detection, eigen value, graph clustering

Abstract: We propose a streamlined spectral algorithm for community detection in the two-community stochastic block model (SBM) under constant edge density assumptions. By reducing algorithmic complexity through the elimination of non-essential preprocessing steps, our method directly leverages the spectral properties of the adjacency matrix. We demonstrate that our algorithm exploits specific characteristics of the second eigenvalue to achieve improved error bounds that approach information-theoretic limits, representing a significant improvement over existing methods. Theoretical analysis establishes that our error rates are tighter than previously reported bounds in the literature. Comprehensive experimental validation confirms our theoretical findings and demonstrates the practical effectiveness of the simplified approach. Our results suggest that algorithmic simplification, rather than increasing complexity, can lead to both computational efficiency and enhanced performance in spectral community detection.

TL;DR: We made a spectral community detection algorithm simpler by removing unnecessary steps, and surprisingly it works better, achieving near-optimal error rates with less computation