Computing the statistical significance of optimized communities in networks

Abstract

In scientific problems involving systems that can be modeled as a network (or “graph”), it is often of interest to find network communities - strongly connected node subsets - for unsupervised learning, feature discovery, anomaly detection, or scientific study. The vast majority of community detection methods proceed via optimization of a quality function, which is possible even on random networks without communities. Therefore there is usually not an easy way to tell if a community is “significant”, in this context meaning more internally connected than would be expected under a random graph model without communities. This paper generalizes existing null models and statistical tests for this purpose to bipartite graphs, and introduces a new significance scoring algorithm called Fast Optimized Community Significance (FOCS) that is highly scalable and agnostic to the type of graph. Compared with existing methods on unipartite graphs, FOCS is more numerically stable and better balances the trade-off between detection power and false positives. On a large-scale bipartite graph derived from the Internet Movie Database (IMDB), the significance scores provided by FOCS correlate strongly with meaningful actor/director collaborations on serial cinematic projects.

Calculation of centralities in protein kinase A

“…Complex network studies belong to a young and quickly developing field of science with a long list of questions still waiting to be answered. Statistical significance of network characteristics (72,73) and properties of networks with negative connections (74,75) are, to name a few, among most essential problems. Consequently, the results presented here are far from the definitive solution of the network centrality problem in proteins.…”

Generating Ensembles of Gene Regulatory Networks to Assess Robustness of Disease Modules

“…However, evaluating the robustness and significance of changes in network structure remains a challenge. Gene regulatory networks are often inferred from transcriptomic data using imperfect inference tools, with no easy way of assessing their underlying variance ( Lancichinetti et al, 2011 ; Menche et al, 2015 ; Choobdar et al, 2019 ; Palowitch, 2019 ). Moreover, community detection algorithms can lead to multiple solutions corresponding to local optima of the fitness function ( Newman, 2006 ; Blondel et al, 2008 ; Campigotto et al, 2014 ).…”

“…Moreover, community detection algorithms can lead to multiple solutions corresponding to local optima of the fitness function ( Newman, 2006 ; Blondel et al, 2008 ; Campigotto et al, 2014 ). Two types of approaches are often used to judge the quality of network communities: consensus clustering and statistical significance ( Lancichinetti et al, 2011 ; Lancichinetti and Fortunato, 2012 ; Menche et al, 2015 ; Zitnik and Leskovec, 2018 ; Palowitch, 2019 ). The consensus approach combines multiple solutions from the optimization algorithm to find the most likely assignment of genes to communities ( Lancichinetti and Fortunato, 2012 ; Choobdar et al, 2019 ).…”

Generating Ensembles of Gene Regulatory Networks to Assess Robustness of Disease Modules

“…However, determining the robustness and significance of changes in network structure remains a challenge. Gene regulatory networks are often inferred from transcriptomic data using imperfect inference tools, with no easy way of assessing their underlying variance [13][14][15][16]. Moreover, community detection algorithms can lead to a wide range of possible solutions corresponding to local optima of the fitness function [17][18][19].…”

“…Moreover, community detection algorithms can lead to a wide range of possible solutions corresponding to local optima of the fitness function [17][18][19]. Two types of approaches have been used to judge the quality of network communities in the past: consensus clustering and statistical significance [15,16,[20][21][22]. The consensus approach combines multiple solutions from the optimization algorithm to find the most likely assignment of genes to communities [14,20].…”