Convex Analysis of Mixtures for Separating Non-negative Well-grounded Sources

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dc.contributor.authorZhu, Yitanen
dc.contributor.authorWang, Niyaen
dc.contributor.authorMiller, David J.en
dc.contributor.authorWang, Yueen
dc.contributor.departmentElectrical and Computer Engineeringen
dc.date.accessioned2019-01-18T15:45:12Zen
dc.date.available2019-01-18T15:45:12Zen
dc.date.issued2016-12-06en
dc.description.abstractBlind Source Separation (BSS) is a powerful tool for analyzing composite data patterns in many areas, such as computational biology. We introduce a novel BSS method, Convex Analysis of Mixtures (CAM), for separating non-negative well-grounded sources, which learns the mixing matrix by identifying the lateral edges of the convex data scatter plot. We propose and prove a sufficient and necessary condition for identifying the mixing matrix through edge detection in the noise-free case, which enables CAM to identify the mixing matrix not only in the exact-determined and over-determined scenarios, but also in the under-determined scenario. We show the optimality of the edge detection strategy, even for cases where source well-groundedness is not strictly satisfied. The CAM algorithm integrates plug-in noise filtering using sector-based clustering, an efficient geometric convex analysis scheme, and stability-based model order selection. The superior performance of CAM against a panel of benchmark BSS techniques is demonstrated on numerically mixed gene expression data of ovarian cancer subtypes. We apply CAM to dissect dynamic contrast-enhanced magnetic resonance imaging data taken from breast tumors and time-course microarray gene expression data derived from in-vivo muscle regeneration in mice, both producing biologically plausible decomposition results.en
dc.description.notesThe authors would like to thank Eric P. Hoffman of the Children's National Medical Center and Peter L. Choyke of the National Cancer Institute for providing biomedical data and expert advice. This work was funded in part by the National Institutes of Health under Grants HL133932, CA160036, CA184902, ES024988.en
dc.description.sponsorshipNational Institutes of Health [HL133932, CA160036, CA184902, ES024988]en
dc.format.extent13en
dc.format.mimetypeapplication/pdfen
dc.identifier.doihttps://doi.org/10.1038/srep38350en
dc.identifier.issn2045-2322en
dc.identifier.other38350en
dc.identifier.pmid27922124en
dc.identifier.urihttp://hdl.handle.net/10919/86754en
dc.identifier.volume6en
dc.language.isoenen
dc.publisherSpringer Natureen
dc.rightsCreative Commons Attribution 4.0 Internationalen
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/en
dc.subjectmatrix factorizationen
dc.subjectblind separationen
dc.subjectdynamic contrasten
dc.subjectexpressionen
dc.subjectalgorithmen
dc.subjectoptimizationen
dc.subjectselectionen
dc.subjectcellen
dc.titleConvex Analysis of Mixtures for Separating Non-negative Well-grounded Sourcesen
dc.title.serialScientific Reportsen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten

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