Introduction to correlation networks: Interdisciplinary approaches beyond thresholding

Abstract

Many empirical networks originate from correlational data, arising in domains as diverse as psychology, neuroscience, genomics, microbiology, finance, and climate science. Specialized algorithms and theory have been developed in different application domains for working with such networks, as well as in statistics, network science, and computer science, often with limited communication between practitioners in different fields. This leaves significant room for cross-pollination across disciplines. A central challenge is that it is not always clear how to best transform correlation matrix data into networks for the application at hand, and probably the most widespread method, i.e., thresholding on the correlation value to create either unweighted or weighted networks, suffers from multiple problems. In this article, we review various methods of constructing and analyzing correlation networks, ranging from thresholding and its improvements to weighted networks, regularization, dynamic correlation networks, threshold-free approaches, comparison with null models, and more. Finally, we propose and discuss recommended practices and a variety of key open questions currently confronting this field.

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References in corpus (98)

• Community detection in graphs
• The architecture of complex weighted networks
• The structure and dynamics of multilayer networks
• A Tutorial on Regularized Partial Correlation Networks
• Temporal Networks
• High-dimensional graphs and variable selection with the Lasso
• Spatial Networks
• Machine learning and the physical sciences
• Community Structure in Time-Dependent, Multiscale, and Multiplex Networks
• Dynamic reconfiguration of human brain networks during learning
• Networks beyond pairwise interactions: structure and dynamics
• Detrended Cross-Correlation Analysis: A New Method for Analyzing Two Non-stationary Time Series
• Scale-free brain functional networks
• The Gaussian Graphical Model in Cross-sectional and Time-series Data
• Detecting rich-club ordering in complex networks
• Weight-conserving characterization of complex functional brain networks
• The physics of higher-order interactions in complex systems
• A high-bias, low-variance introduction to Machine Learning for physicists
• A tool for filtering information in complex systems
• Extracting the multiscale backbone of complex weighted networks
• Covariance regularization by thresholding
• Are biological systems poised at criticality?
• A roadmap for the computation of persistent homology
• Dynamics of market correlations: Taxonomy and portfolio analysis
• Generalizations of the clustering coefficient to weighted complex networks
• Activity driven modeling of time varying networks
• Extended Bayesian Information Criteria for Gaussian Graphical Models
• A dynamic network approach for the study of human phenotypes
• Modern temporal network theory: A colloquium
• Shrinkage Algorithms for MMSE Covariance Estimation
• High-dimensional Ising model selection using ${\ell }_1$-regularized logistic regression
• The backbone of the climate network
• Topology of correlation based minimal spanning trees in real and model markets
• Class of correlated random networks with hidden variables
• Clique topology reveals intrinsic geometric structure in neural correlations
• Graph analysis of functional brain networks: practical issues in translational neuroscience
• Uncovering space-independent communities in spatial networks
• Clustering and information in correlation based financial networks
• Network information and connected correlations
• Optimal rates of convergence for covariance matrix estimation
• Network exploration via the adaptive LASSO and SCAD penalties
• Analysis of community structure in networks of correlated data
• Inverse statistical problems: from the inverse Ising problem to data science
• Self-organization of collaboration networks
• Operator norm consistent estimation of large-dimensional sparse covariance matrices
• Learning and comparing functional connectomes across subjects
• Persistent Homology of Complex Networks
• Cleaning large correlation matrices: tools from random matrix theory
• Brain Network Analysis: Separating Cost from Topology using Cost-integration
• Detrended partial cross-correlation analysis of two nonstationary time series influenced by common external forces
• Introduction to Random Matrices - Theory and Practice
• Dynamic asset trees and portfolio analysis
• Regularized rank-based estimation of high-dimensional nonparanormal graphical models
• Covariance Estimation: The GLM and Regularization Perspectives
• Statistical physics approaches to the complex Earth system
• Brain covariance selection: better individual functional connectivity models using population prior
• Inverse Ising inference using all the data
• Mapping multiplex hubs in human functional brain network
• Collective dynamics of social annotation
• Spanning Trees and bootstrap reliability estimation in correlation based networks
• Community detection for correlation matrices
• Energy landscape analysis of neuroimaging data
• Clustering coefficients for correlation networks
• A topological criterion for filtering information in complex brain networks
• Nonparametric weighted stochastic block models
• Unveiling the higher-order organization of multivariate time series
• Geographical threshold graphs with small-world and scale-free properties
• Scaling It Up: Stochastic Search Structure Learning in Graphical Models
• Identification of clusters of investors from their real trading activity in a financial market
• Enhanced detectability of community structure in multilayer networks through layer aggregation
• Climate Dynamics: A Network-Based Approach for the Analysis of Global Precipitation
• Unbiased sampling of network ensembles
• Pseudolikelihood Decimation Algorithm Improving the Inference of the Interaction Network in a General Class of Ising Models
• Bayesian inference of network structure from unreliable data
• Core-periphery structure requires something else in the network
• Node-weighted measures for complex networks with spatially embedded, sampled, or differently sized nodes
• Analysis of scale-free networks based on a threshold graph with intrinsic vertex weights
• VIP-club phenomenon: emergence of elites and masterminds in social networks
• Topological structures in the equities market network
• Mesoscopic Community Structure of Financial Markets Revealed by Price and Sign Fluctuations
• Multilayer Network Science: from Cells to Societies
• Thresholding normally distributed data creates complex networks
• Configuration model for correlation matrices preserving the node strength
• Super-resolution community detection for layer-aggregated multilayer networks
• Construction of Minimum Spanning Trees from Financial Returns using Rank Correlation
• Geodesic distance on optimally regularized functional connectomes uncovers individual fingerprints
• Dynamics of Investor Spanning Trees Around Dot-Com Bubble
• Irreducible network backbones: unbiased graph filtering via maximum entropy
• Gene communities in co-expression networks across different tissues
• Constructing networks by filtering correlation matrices: A null model approach
• Measuring topological descriptors of complex networks under uncertainty
• Uncovering functional brain signature via random matrix theory
• Beyond normality: Learning sparse probabilistic graphical models in the non-Gaussian setting
• Simplicial faces of the set of correlation matrices
• Uncovering the mesoscale structure of the credit default swap market to improve portfolio risk modelling
• Learning non-Gaussian graphical models via Hessian scores and triangular transport
• The Role of Network Analysis in Industrial and Applied Mathematics
• Statistically validated projection of bipartite signed networks