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arXiv · 1406.7349

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

Yitan Zhu·Niya Wang·David J. Miller·Yue Wang
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Abstract

Blind Source Separation (BSS) has proven to be a powerful tool for the analysis of composite patterns in engineering and science. We introduce 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 prove a sufficient and necessary condition for identifying the mixing matrix through edge detection, which also serves as the foundation for CAM to be applied not only to the exact-determined and over-determined cases, but also to the under-determined case. 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. We demonstrate the principle of CAM on simulated data and numerically mixed natural images. The superior performance of CAM against a panel of benchmark BSS techniques is demonstrated on numerically mixed gene expression data. We then 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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Yitan Zhu, Niya Wang, David J. Miller, Yue Wang. 2015-12-10. Convex Analysis of Mixtures for Separating Non-negative Well-grounded Sources. https://arxiv.org/abs/1406.7349

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