Scalable and Robust Community Detection with Randomized Sketching

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.

References in corpus (6)

• Stochastic blockmodels and community structure in networks
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• Robust and computationally feasible community detection in the presence of arbitrary outlier nodes
• Identifying Outliers in Large Matrices via Randomized Adaptive Compressive Sampling
• Spatial Random Sampling: A Structure-Preserving Data Sketching Tool
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Cited by in corpus (2)

• Distributed Community Detection for Large Scale Networks Using Stochastic Block Model
• Sketch-based community detection in evolving networks