Hierarchical community detection by recursive partitioning
This provides a more interpretable and accurate method for hierarchical community detection in networks, such as gene co-occurrence or academic paper analysis, though it is incremental as it builds on spectral clustering.
The authors tackled community detection in networks by proposing a hierarchical tree construction method using recursive spectral partitioning, which outperforms K-way spectral clustering in certain regimes and correctly recovers community trees under mild assumptions in a binary tree stochastic block model. They applied it to a gene network, identifying six hierarchical clusters, and a statistics paper dataset.
The problem of community detection in networks is usually formulated as finding a single partition of the network into some "correct" number of communities. We argue that it is more interpretable and in some regimes more accurate to construct a hierarchical tree of communities instead. This can be done with a simple top-down recursive partitioning algorithm, starting with a single community and separating the nodes into two communities by spectral clustering repeatedly, until a stopping rule suggests there are no further communities. This class of algorithms is model-free, computationally efficient, and requires no tuning other than selecting a stopping rule. We show that there are regimes where this approach outperforms K-way spectral clustering, and propose a natural framework for analyzing the algorithm's theoretical performance, the binary tree stochastic block model. Under this model, we prove that the algorithm correctly recovers the entire community tree under relatively mild assumptions. We apply the algorithm to a gene network based on gene co-occurrence in 1580 research papers on anemia, and identify six clusters of genes in a meaningful hierarchy. We also illustrate the algorithm on a dataset of statistics papers.