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

Yitan Zhu, Niya Wang, David J. Miller, Yue Wang

    Research output: Contribution to journalArticle

    3 Citations (Scopus)

    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.

    Original languageEnglish (US)
    Article number38350
    JournalScientific reports
    Volume6
    DOIs
    StatePublished - Dec 6 2016

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    Noise
    Gene Expression
    Benchmarking
    Computational Biology
    Ovarian Neoplasms
    Cluster Analysis
    Regeneration
    Magnetic Resonance Imaging
    Breast Neoplasms
    Muscles

    All Science Journal Classification (ASJC) codes

    • General

    Cite this

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    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.",
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    Convex Analysis of Mixtures for Separating Non-negative Well-grounded Sources. / Zhu, Yitan; Wang, Niya; Miller, David J.; Wang, Yue.

    In: Scientific reports, Vol. 6, 38350, 06.12.2016.

    Research output: Contribution to journalArticle

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