{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,25]],"date-time":"2026-01-25T00:39:11Z","timestamp":1769301551058,"version":"3.49.0"},"reference-count":30,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2024,12,28]],"date-time":"2024-12-28T00:00:00Z","timestamp":1735344000000},"content-version":"vor","delay-in-days":2,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,12,26]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:sec>\n                  <jats:title>Motivation<\/jats:title>\n                  <jats:p>Non-negative matrix factorization (NMF) is a powerful tool often applied to genomic data to identify non-negative latent components that constitute linearly mixed samples. It is useful when the observed signal combines contributions from multiple sources, such as cell types in bulk measurements of heterogeneous tissue. NMF accounts for two types of variation between samples \u2014 disparities in the proportions of sources and observation noise. However, in many settings, there is also a non-trivial variation between samples in the contribution of each source to the mixed data. This variation cannot be accurately modeled using the NMF framework.<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Results<\/jats:title>\n                  <jats:p>We present VarNMF, a probabilistic extension of NMF that explicitly models this variation in source values. We show that by modeling sources as non-negative distributions, we can recover source variation directly from mixed samples without observing any of the sources directly. We apply VarNMF to a cell-free ChIP-seq dataset of two cancer cohorts and a healthy cohort, demonstrating that VarNMF provides a better estimation of the data distribution. Moreover, VarNMF extracts cancer-associated source distributions that decouple the tumor characteristics from the amount of tumor contribution, and identify patient-specific disease behaviors. This decomposition highlights the inter-tumor variability that is obscured in the mixed samples.<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Availability and implementation<\/jats:title>\n                  <jats:p>Code is available at https:\/\/github.com\/Nir-Friedman-Lab\/VarNMF.<\/jats:p>\n               <\/jats:sec>","DOI":"10.1093\/bioinformatics\/btae758","type":"journal-article","created":{"date-parts":[[2024,12,28]],"date-time":"2024-12-28T17:37:05Z","timestamp":1735407425000},"source":"Crossref","is-referenced-by-count":2,"title":["VarNMF: non-negative probabilistic factorization with source variation"],"prefix":"10.1093","volume":"41","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-0758-688X","authenticated-orcid":false,"given":"Ela","family":"Fallik","sequence":"first","affiliation":[{"name":"School of Computer Science and Engineering, The Hebrew University of Jerusalem , Jerusalem, 9190401,","place":["Israel"]},{"name":"Lautenberg Center for Immunology and Cancer Research, Faculty of Medicine, The Hebrew University of Jerusalem , Jerusalem, 9112102,","place":["Israel"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9678-3550","authenticated-orcid":false,"given":"Nir","family":"Friedman","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering, The Hebrew University of Jerusalem , Jerusalem, 9190401,","place":["Israel"]},{"name":"Lautenberg Center for Immunology and Cancer Research, Faculty of Medicine, The Hebrew University of Jerusalem , Jerusalem, 9112102,","place":["Israel"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2024,12,28]]},"reference":[{"key":"2025040911041882500_btae758-B1","first-page":"R106","article-title":"Differential expression analysis for sequence count data","volume":"11","author":"Anders","year":"2010","journal-title":"Nat Prec"},{"key":"2025040911041882500_btae758-B2","doi-asserted-by":"crossref","first-page":"6106","DOI":"10.1038\/s41467-021-26328-2","article-title":"Bayesian log-normal deconvolution for enhanced in silico microdissection of bulk gene expression data","volume":"12","author":"Andrade Barbosa","year":"2021","journal-title":"Nat. Comm"},{"key":"2025040911041882500_btae758-B3","first-page":"1","author":"Arora","year":"2012"},{"key":"2025040911041882500_btae758-B4","doi-asserted-by":"crossref","first-page":"1649","DOI":"10.1111\/brv.12413","article-title":"The diverse origins of circulating cell-free DNA in the human body: a critical re-evaluation of the literature","volume":"93","author":"Aucamp","year":"2018","journal-title":"Biol Rev Camb Philos Soc"},{"key":"2025040911041882500_btae758-B5","doi-asserted-by":"publisher","author":"Brouwer","year":"2017","DOI":"10.48550\/arXiv.1712.00288"},{"key":"2025040911041882500_btae758-B6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/1471-2105-14-S18-S1","article-title":"Enrichr: interactive and collaborative html5 gene list enrichment analysis tool","volume":"14","author":"Chen","year":"2013","journal-title":"BMC Bioinf"},{"key":"2025040911041882500_btae758-B7","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/0165-1684(94)90029-9","article-title":"Independent component analysis, a new concept?","volume":"36","author":"Comon","year":"1994","journal-title":"Signal Process"},{"key":"2025040911041882500_btae758-B8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.2517-6161.1977.tb01600.x","article-title":"Maximum likelihood from incomplete data via the EM algorithm","volume":"39","author":"Dempster","year":"1977","journal-title":". J R Statist Soc Ser B Methodol"},{"key":"2025040911041882500_btae758-B9","author":"Fialkoff","year":"2022"},{"key":"2025040911041882500_btae758-B10","author":"Fialkoff","year":"2023"},{"key":"2025040911041882500_btae758-B11","first-page":"326","author":"Gopalan"},{"key":"2025040911041882500_btae758-B12","doi-asserted-by":"crossref","first-page":"995","DOI":"10.1200\/PO.20.00016","article-title":"Systematic assessment of tumor purity and its clinical implications","volume":"4","author":"Haider","year":"2020","journal-title":"JCO Precision Oncology"},{"key":"2025040911041882500_btae758-B13","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1038\/ng1966","article-title":"Distinct and predictive chromatin signatures of transcriptional promoters and enhancers in the human genome","volume":"39","author":"Heintzman","year":"2007","journal-title":"Nat Genet"},{"key":"2025040911041882500_btae758-B14","first-page":"20150202","article-title":"Principal component analysis: a review and recent developments","volume":"374","author":"Jolliffe","year":"2016","journal-title":"Philos Trans A Math Phys Eng Sci"},{"key":"2025040911041882500_btae758-B15","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1038\/jhg.2013.66","article-title":"Histone modifications for human epigenome analysis","volume":"58","author":"Kimura","year":"2013","journal-title":"J Hum Genet"},{"key":"2025040911041882500_btae758-B16","doi-asserted-by":"crossref","first-page":"788","DOI":"10.1038\/44565","article-title":"Learning the parts of objects by non-negative matrix factorization","volume":"401","author":"Lee","year":"1999","journal-title":"Nature"},{"key":"2025040911041882500_btae758-B17","article-title":"Algorithms for non-negative matrix factorization","volume":"13","author":"Lee","year":"2000","journal-title":"Advances in Neural Information Processing Systems"},{"key":"2025040911041882500_btae758-B18","doi-asserted-by":"publisher","author":"Lu","year":"2022","DOI":"10.48550\/arXiv.2205.11025"},{"key":"2025040911041882500_btae758-B19","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1007\/s00018-009-0180-6","article-title":"RNA-seq: from technology to biology","volume":"67","author":"Marguerat","year":"2010","journal-title":"Cell Mol Life Sci"},{"key":"2025040911041882500_btae758-B20","doi-asserted-by":"crossref","first-page":"5068","DOI":"10.1038\/s41467-018-07466-6","article-title":"Comprehensive human cell-type methylation atlas reveals origins of circulating cell-free DNA in health and disease","volume":"9","author":"Moss","year":"2018","journal-title":"Nat. Comm"},{"key":"2025040911041882500_btae758-B21","doi-asserted-by":"crossref","first-page":"3417","DOI":"10.1038\/s41467-019-11052-9","article-title":"Cell-type-specific resolution epigenetics without the need for cell sorting or single-cell biology","volume":"10","author":"Rahmani","year":"2019","journal-title":"Nat Commun"},{"key":"2025040911041882500_btae758-B22","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1038\/s41568-019-0133-9","article-title":"Molecular subtypes of small cell lung cancer: a synthesis of human and mouse model data","volume":"19","author":"Rudin","year":"2019","journal-title":"Nat Rev Cancer"},{"key":"2025040911041882500_btae758-B23","doi-asserted-by":"crossref","first-page":"586","DOI":"10.1038\/s41587-020-00775-6","article-title":"Chip-seq of plasma cell-free nucleosomes identifies gene expression programs of the cells of origin","volume":"39","author":"Sadeh","year":"2021","journal-title":"Nat Biotechnol"},{"key":"2025040911041882500_btae758-B24","first-page":"540","author":"Schmidt"},{"key":"2025040911041882500_btae758-B25","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1016\/j.coi.2013.09.015","article-title":"Computational deconvolution: extracting cell type-specific information from heterogeneous samples","volume":"25","author":"Shen-Orr","year":"2013","journal-title":"Curr Opin Immunol"},{"key":"2025040911041882500_btae758-B26","first-page":"177","author":"Smaragdis","year":"2003"},{"key":"2025040911041882500_btae758-B27","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1016\/j.molcel.2017.10.013","article-title":"Determinants of histone H3K4 methylation patterns","volume":"68","author":"Soares","year":"2017","journal-title":"Mol Cell"},{"key":"2025040911041882500_btae758-B28","doi-asserted-by":"crossref","first-page":"1807","DOI":"10.1101\/gr.268722.120","article-title":"Bayesian estimation of cell type\u2013specific gene expression with prior derived from single-cell data","volume":"31","author":"Wang","year":"2021","journal-title":"Genome Res"},{"key":"2025040911041882500_btae758-B29","doi-asserted-by":"crossref","first-page":"1336","DOI":"10.1109\/TKDE.2012.51","article-title":"Nonnegative matrix factorization: a comprehensive review","volume":"25","author":"Wang","year":"2013","journal-title":"IEEE Trans Knowl Data Eng"},{"key":"2025040911041882500_btae758-B30","doi-asserted-by":"crossref","first-page":"3528","DOI":"10.1158\/1078-0432.CCR-17-3837","article-title":"The landscape of actionable genomic alterations in cell-free circulating tumor DNA from 21,807 advanced cancer patients","volume":"24","author":"Zill","year":"2018","journal-title":"Clin Cancer Res"}],"container-title":["Bioinformatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/bioinformatics\/advance-article-pdf\/doi\/10.1093\/bioinformatics\/btae758\/61290454\/btae758.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article-pdf\/41\/1\/btae758\/61290454\/btae758.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article-pdf\/41\/1\/btae758\/61290454\/btae758.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,9]],"date-time":"2025-04-09T11:12:53Z","timestamp":1744197173000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article\/doi\/10.1093\/bioinformatics\/btae758\/7934143"}},"subtitle":[],"editor":[{"given":"Inanc","family":"Birol","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2024,12,26]]},"references-count":30,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,12,26]]}},"URL":"https:\/\/doi.org\/10.1093\/bioinformatics\/btae758","relation":{},"ISSN":["1367-4811"],"issn-type":[{"value":"1367-4811","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2025,1]]},"published":{"date-parts":[[2024,12,26]]},"article-number":"btae758"}}