Year: 2018
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Li, Tianxi, Lei, Lihua, Bhattacharyya, Sharmodeep, Berge, Koen Van den, Sarkar, Purnamrita, Bickel, Peter J., Levina, Elizaveta
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: High-resolution differential expression analysis for single-cell RNA-seq data, Collaborative Research: Inference for Network Models with Covariates: Leveraging Local Information for Statistically and Computationally Efficient Estimation of Global Parameters, G5199906080, Collaborative Research: Inference for Network Models with Covariates: Leveraging Local Information for Statistically and Computationally Efficient Estimation of Global Parameters, Collaborative Research: Inference for Networks: Bridging the Gap between Metric Spaces and Graphs, Statistical Tools for Analyzing Multiple Networks, Multivariate Analysis for Samples of Networks
OpenAlex ID: W2894887458