Scalable and Robust Community Detection with Randomized Sketching

TL;DR

This paper introduces a scalable randomized framework for community detection in large graphs, improving computational efficiency and accuracy, especially with unbalanced clusters, using novel sampling techniques and matrix completion.

Contribution

It proposes a new randomized sketching method for clustering large graphs, including novel sampling algorithms that enhance performance and theoretical guarantees for community detection.

Findings

Random node sampling improves computational complexity for balanced clusters.

Degree-based sampling significantly enhances clustering performance for unbalanced clusters.

The framework nearly eliminates dimension dependence in low inter-cluster connectivity regimes.

Abstract

This article explores and analyzes the unsupervised clustering of large partially observed graphs. We propose a scalable and provable randomized framework for clustering graphs generated from the stochastic block model. The clustering is first applied to a sub-matrix of the graph's adjacency matrix associated with a reduced graph sketch constructed using random sampling. Then, the clusters of the full graph are inferred based on the clusters extracted from the sketch using a correlation-based retrieval step. Uniform random node sampling is shown to improve the computational complexity over clustering of the full graph when the cluster sizes are balanced. A new random degree-based node sampling algorithm is presented which significantly improves upon the performance of the clustering algorithm even when clusters are unbalanced. This framework improves the phase transitions for matrix-decomposition-based clustering with regard to computational complexity and minimum cluster size, which are shown to be nearly dimension-free in the low inter-cluster connectivity regime. A third sampling technique is shown to improve balance by randomly sampling nodes based on spatial distribution. We provide analysis and numerical results using a convex clustering algorithm based on matrix completion.