Comparison of co-expression measures: mutual information, correlation, and model based indices
Open accessAbstract
Background: Co-expression measures are often used to define networks among genes. Mutual information (MI) is often used as a generalized correlation measure. It is not clear how much MI adds beyond standard (robust) correlation measures or regression model based association measures. Further, it is important to assess what transformations of these and other co-expression measures lead to biologically meaningful modules (clusters of genes). Results: We provide a comprehensive comparison between mutual information and several correlation measures in 8 empirical data sets and in simulations. We also study different approaches for transforming an adjacency matrix, e.g. using the topological overlap measure. Overall, we confirm close relationships between MI and correlation in all data sets which reflects the fact that most gene pairs satisfy linear or monotonic relationships. We discuss rare situations when the two measures disagree. We also compare correlation and MI based approaches when it comes to defining co-expression network modules. We show that a robust measure of correlation (the biweight midcorrelation transformed via the topological overlap transformation) leads to modules that are superior to MI based modules and maximal information coefficient (MIC) based modules in terms of gene ontology enrichment. We present a function that relates correlation to mutual information which can be used to approximate the mutual information from the corresponding correlation coefficient. We propose the use of polynomial or spline regression models as an alternative to MI for capturing non-linear relationships between quantitative variables. Conclusion: The biweight midcorrelation outperforms MI in terms of elucidating gene pairwise relationships. Coupled with the topological overlap matrix transformation, it often leads to more significantly enriched co-expression modules. Spline and polynomial networks form attractive alternatives to MI in case of non-linear relationships. Our results indicate that MI networks can safely be replaced by correlation networks when it comes to measuring co-expression relationships in stationary data.
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WGCNA's reliance on linear correlations and scale-free assumptions has drawn criticism for oversimplifying the nonlinear and heterogeneous nature of molecular interactions.
“However, WGCNA's reliance on linear correlations and scale-free assumptions has drawn criticism for oversimplifying the nonlinear and heterogeneous nature of molecular interactions300.”
From Artificial intelligence-driven multi-omics approaches in Alzheimer's disease: Progress, challenges, and future directions (2025) · cites this paper as [300]
The Results section ('Polynomial and spline regression models as alternatives to mutual information'; page unavailable) shows that correlation-based networks missed nonlinear relationships in simulated gene data. But the paper says most gene pairs in its empirical studies satisfied linear relationships, and it does not substantiate criticism based on scale-free assumptions or heterogeneous molecular interactions. Its software section also describes nonlinear measures implemented in the WGCNA package. (LLM, conf=0.86)
Experimental — accuracy not yet measuredAt currently available sample sizes, networks are most reproducible at module level, then hub gene level, and least at precise gene connectivity rankings or module memberships.
“At currently available sample sizes, networks are most reproducible at a module level35,38,39, then at the hub gene level41,223 and, last, at the level of precise gene connectivity rankings or precise module memberships of genes40,49.”
From Systems biology and gene networks in neurodevelopmental and neurodegenerative disorders (2015) · cites this paper as [38]
Weighted networks constructed with topological overlap, such as WGCNA, have similar sensitivity and specificity for detecting true network structure for monotonic relationships as networks constructed with nonlinear association measures such as mutual information, such as ARACNE.
“weighted networks constructed with the topological overlap of correlation (for example, by weighted gene co-expression network analysis (WGCNA)42,44) have similar sensitivity and specificity for detecting true network structure for experiments involving monotonic relationships as do networks constructed with nonlinear association measures such as mutual information (for example, by the Algorithm”
From Systems biology and gene networks in neurodevelopmental and neurodegenerative disorders (2015) · cites this paper as [38]
Signed networks are more predictive of protein interactions and shared pathway relationships than unsigned networks.
“signed networks are more predictive of protein interactions and shared pathway relationships than unsigned networks38,42,43”
From Systems biology and gene networks in neurodevelopmental and neurodegenerative disorders (2015) · cites this paper as [38]
There was no pathway or PPI enrichment in these modules, probably owing to inclusion of both positive and negative correlations when computing co-expression relationships (unsigned networks), which is less sensitive to pathway and protein interaction detection.
“Interestingly, there was no pathway or PPI enrichment in these modules, probably owing to the inclusion of both positive and negative correlations when computing co-expression relationships (unsigned networks), which is a method that is less sensitive to pathway and protein interaction detection38,43.”
From Systems biology and gene networks in neurodevelopmental and neurodegenerative disorders (2015) · cites this paper as [38]
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- Authors
- Song, L., Langfelder, P., & Horvath, S.
- Affiliations
- University of California, Los Angeles (US)
- Corresponding author
- Horvath, Steve
- Venue
- BMC Bioinformatics
- Published
- 2012-12
- Volume
- 13
- Issue
- 1
- Pages
- 328-328
- ISSN
- 1471-2105 (ISSN-L)
- PMC
- PMC3586947
- OpenAlex
- W2133254377
- Cited by
- 460
- References
- 78
- Citations by year
- 2026: 9 · 2025: 27 · 2024: 34 · 2023: 35 · 2022: 48 · 2021: 49 · 2020: 51 · 2019: 47 · 2018: 36 · 2017: 33 · 2016: 38 · 2015: 25 · 2014: 18 · 2013: 8 · 2012: 2
- FWCI
- 6.82
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- cc-by
- Locations
- BMC Bioinformatics (publishedVersion, cc-by)
- Europe PMC (PubMed Central) (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
- eScholarship (California Digital Library) (submittedVersion)
- Funders
- National Institute on Drug Abuse (R01DA030913)
- National Cancer Institute (P50CA092131)
- National Institute of Neurological Disorders and Stroke (R01NS058980)
- Clinical and Translational Science Institute, University of California, Los Angeles
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Bioinformatics and Genomic Networks
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Gene expression and cancer classification
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Gene Regulatory Network Analysis
- Keywords
- mutual information, gene co-expression network, correlation measures, gene modules, maximal information coefficient, spline regression, polynomial regression, gene ontology enrichment
- MeSH terms
- Algorithms, Multigene Family, Humans, Models, Genetic, Statistics as Topic, Gene Expression Profiling, Gene Regulatory Networks
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