Convex Analysis of Mixtures for Separating Non-negative Well-grounded Sources
This work addresses source separation in fields like biomedical imaging and genomics, offering a method that handles under-determined cases, but it is incremental as it builds on existing BSS techniques with geometric optimizations.
The paper tackles the problem of Blind Source Separation (BSS) for non-negative well-grounded sources by introducing Convex Analysis of Mixtures (CAM), which learns the mixing matrix through edge detection in convex data plots, and demonstrates superior performance against benchmark techniques on simulated and real-world datasets like gene expression and MRI data.
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.