title: Convex Analysis of Mixtures for Separating Non-negative Well-grounded Sources.
abstract: Blind 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.
authors.affiliation: The Bradley Department of Electrical and Computer Engineering, Virginia Polytechnic Institute and State University, Arlington, VA 22203, USA.|The Program of Computational Genomics and Medicine, NorthShore University HealthSystem, Evanston, IL 60201, USA.
authors.forename: Yitan
authors.initials: Y
authors.lastname: Zhu
authors.affiliation: The Bradley Department of Electrical and Computer Engineering, Virginia Polytechnic Institute and State University, Arlington, VA 22203, USA.
authors.forename: Niya
authors.initials: N
authors.lastname: Wang
authors.affiliation: The Department of Electrical Engineering, Pennsylvania State University, University Park, PA 16802, USA.
authors.forename: David J
authors.initials: DJ
authors.lastname: Miller
authors.affiliation: The Bradley Department of Electrical and Computer Engineering, Virginia Polytechnic Institute and State University, Arlington, VA 22203, USA.
authors.forename: Yue
authors.initials: Y
authors.lastname: Wang
mesh_terms: D000465:Algorithms; D000818:Animals; D001943:Breast Neoplasms / Q000098:blood supply / Q000000981:diagnostic imaging* / Q000235:genetics / Q000473:pathology; D016000:Cluster Analysis; D003198:Computer Simulation; D066264:Datasets as Topic; D005260:Female; D015870:Gene Expression; D020869:Gene Expression Profiling / Q000706:statistics & numerical data*; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods / Q000706:statistics & numerical data*; D008279:Magnetic Resonance Imaging; D051379:Mice; D009124:Muscle Proteins / Q000235:genetics* / Q000378:metabolism; D018482:Muscle, Skeletal / Q000293:injuries / Q000378:metabolism; D009389:Neovascularization, Pathologic / Q000000981:diagnostic imaging* / Q000235:genetics / Q000473:pathology; D012333:RNA, Messenger / Q000235:genetics / Q000378:metabolism; D012038:Regeneration / Q000235:genetics
chemical_list: D009124:Muscle Proteins; D012333:RNA, Messenger