A Compressive Sensing Approach to Community Detection with Applications
Ming-Jun Lai, Daniel Mckenzie

TL;DR
This paper introduces a novel compressive sensing-based algorithm for community detection in graphs, capable of efficiently identifying individual clusters with theoretical guarantees and outperforming traditional spectral clustering in speed.
Contribution
The paper develops a two-stage compressive sensing approach for community detection that efficiently finds individual clusters and provides robustness guarantees under the Stochastic Block Model.
Findings
Algorithm finds a single cluster in O(nlog(n)n_0) operations.
All k clusters can be found in fewer than O(n^2ln(n)) operations.
The method outperforms spectral clustering in speed and provides robustness guarantees.
Abstract
The community detection problem for graphs asks one to partition the n vertices V of a graph G into k communities, or clusters, such that there are many intracluster edges and few intercluster edges. Of course this is equivalent to finding a permutation matrix P such that, if A denotes the adjacency matrix of G, then PAP^T is approximately block diagonal. As there are k^n possible partitions of n vertices into k subsets, directly determining the optimal clustering is clearly infeasible. Instead one seeks to solve a more tractable approximation to the clustering problem. In this paper we reformulate the community detection problem via sparse solution of a linear system associated with the Laplacian of a graph G and then develop a two-stage approach based on a thresholding technique and a compressive sensing algorithm to find a sparse solution which corresponds to the community containing…
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Taxonomy
TopicsSparse and Compressive Sensing Techniques · Complex Network Analysis Techniques · Distributed Sensor Networks and Detection Algorithms
MethodsSpectral Clustering
