{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T06:14:00Z","timestamp":1772172840441,"version":"3.50.1"},"reference-count":33,"publisher":"Public Library of Science (PLoS)","issue":"10","license":[{"start":{"date-parts":[[2021,10,20]],"date-time":"2021-10-20T00:00:00Z","timestamp":1634688000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>There has been a spate of interest in association networks in biological and medical research, for example, genetic interaction networks. In this paper, we propose a novel method, the extended joint hub graphical lasso (EDOHA), to estimate multiple related interaction networks for high dimensional omics data across multiple distinct classes. To be specific, we construct a convex penalized log likelihood optimization problem and solve it with an alternating direction method of multipliers (ADMM) algorithm. The proposed method can also be adapted to estimate interaction networks for high dimensional compositional data such as microbial interaction networks. The performance of the proposed method in the simulated studies shows that EDOHA has remarkable advantages in recognizing class-specific hubs than the existing comparable methods. We also present three applications of real datasets. Biological interpretations of our results confirm those of previous studies and offer a more comprehensive understanding of the underlying mechanism in disease.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1008794","type":"journal-article","created":{"date-parts":[[2021,10,20]],"date-time":"2021-10-20T23:37:39Z","timestamp":1634773059000},"page":"e1008794","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":0,"title":["Extended graphical lasso for multiple interaction networks for high dimensional omics data"],"prefix":"10.1371","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3135-7793","authenticated-orcid":true,"given":"Yang","family":"Xu","sequence":"first","affiliation":[]},{"given":"Hongmei","family":"Jiang","sequence":"additional","affiliation":[]},{"given":"Wenxin","family":"Jiang","sequence":"additional","affiliation":[]}],"member":"340","published-online":{"date-parts":[[2021,10,20]]},"reference":[{"issue":"5586","key":"pcbi.1008794.ref001","doi-asserted-by":"crossref","first-page":"1551","DOI":"10.1126\/science.1073374","article-title":"Hierarchical organization of modularity in metabolic networks","volume":"297","author":"E Ravasz","year":"2002","journal-title":"science"},{"key":"pcbi.1008794.ref002","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1007\/978-1-59745-243-4_7","article-title":"Detecting hierarchical modularity in biological networks","author":"E Ravasz","year":"2009","journal-title":"Computational Systems Biology"},{"issue":"3","key":"pcbi.1008794.ref003","doi-asserted-by":"crossref","first-page":"1436","DOI":"10.1214\/009053606000000281","article-title":"High-dimensional graphs and variable selection with the lasso","volume":"34","author":"N Meinshausen","year":"2006","journal-title":"The annals of statistics"},{"issue":"3","key":"pcbi.1008794.ref004","doi-asserted-by":"crossref","first-page":"432","DOI":"10.1093\/biostatistics\/kxm045","article-title":"Sparse inverse covariance estimation with the graphical lasso","volume":"9","author":"Jerome Friedman","year":"2008","journal-title":"Biostatistics"},{"issue":"2","key":"pcbi.1008794.ref005","first-page":"521","article-title":"Network exploration via the adaptive LASSO and SCAD penalties","volume":"3","author":"J Fan","year":"2009","journal-title":"The annals of applied statistics"},{"issue":"2","key":"pcbi.1008794.ref006","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1111\/rssb.12033","article-title":"The joint graphical lasso for inverse covariance estimation across multiple classes","volume":"76","author":"P Danaher","year":"2014","journal-title":"Journal of the Royal Statistical Society: Series B (Statistical Methodology)"},{"issue":"20","key":"pcbi.1008794.ref007","doi-asserted-by":"crossref","first-page":"3470","DOI":"10.1093\/bioinformatics\/bty354","article-title":"JRmGRN: joint reconstruction of multiple gene regulatory networks with common hub genes using data from multiple tissues or conditions","volume":"34","author":"W Deng","year":"2018","journal-title":"Bioinformatics"},{"key":"pcbi.1008794.ref008","article-title":"Proteome-wide Data Analysis Reveals Tissue-specific Network Associated with SARS-CoV-2 Infection","author":"L Feng","year":"2020","journal-title":"Journal of Molecular Cell Biology"},{"key":"pcbi.1008794.ref009","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198522195.001.0001","volume-title":"Graphical models","author":"SL Lauritzen","year":"1996"},{"issue":"1","key":"pcbi.1008794.ref010","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1561\/2200000016","article-title":"Distributed optimization and statistical learning via the alternating direction method of multipliers","volume":"3","author":"S Boyd","year":"2010","journal-title":"Machine learning"},{"issue":"8","key":"pcbi.1008794.ref011","doi-asserted-by":"crossref","first-page":"2172","DOI":"10.1162\/NECO_a_00379","article-title":"Alternating direction methods for latent variable Gaussian graphical model selection","volume":"25","author":"S Ma","year":"2013","journal-title":"Neural computation"},{"key":"pcbi.1008794.ref012","doi-asserted-by":"crossref","unstructured":"Tang Q, Yang C, Peng J, Xu J. 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