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Airborne gamma-ray surveys are useful for many applications, ranging from geology and mining to public health and nuclear security. In all these contexts, the ability to decompose a measured spectrum into a linear combination of background source terms can provide useful insights into the data and lead to improvements over techniques that use spectral energy windows. Multiple methods for the linear decomposition of spectra exist but are subject to various drawbacks, such as allowing negative photon fluxes or requiring detailed Monte Carlo modeling. We propose using Non-negative Matrix Factorization (NMF) as a data-driven approach to spectral decomposition. Using aerial surveys that include flights over water, we demonstrate that the mathematical approach of NMF finds physically relevant structure in aerial gamma-ray background, namely that measured spectra can be expressed as the sum of nearby terrestrial emission, distant terrestrial emission, and radon and cosmic emission. These NMF background components are compared to the background components obtained using Noise-Adjusted Singular Value Decomposition (NASVD), which contain negative photon fluxes and thus do not represent emission spectra in as straightforward a way. Finally, we comment on potential areas of research that are enabled by NMF decompositions, such as new approaches to spectral anomaly detection and data fusion.
The Baum-Welsh algorithm together with its derivatives and variations has been the main technique for learning Hidden Markov Models (HMM) from observational data. We present an HMM learning algorithm based on the non-negative matrix factorization (NM
Extracting genetic information from a full range of sequencing data is important for understanding diseases. We propose a novel method to effectively explore the landscape of genetic mutations and aggregate them to predict cancer type. We used multin
In this paper we explore avenues for improving the reliability of dimensionality reduction methods such as Non-Negative Matrix Factorization (NMF) as interpretive exploratory data analysis tools. We first explore the difficulties of the optimization
In the non-negative matrix factorization (NMF) problem, the input is an $mtimes n$ matrix $M$ with non-negative entries and the goal is to factorize it as $Mapprox AW$. The $mtimes k$ matrix $A$ and the $ktimes n$ matrix $W$ are both constrained to h
Modeling of headway/spacing between two consecutive vehicles has many applications in traffic flow theory and transport practice. Most known approaches only study the vehicles running on freeways. In this paper, we propose a model to explain the spac