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Results for “nonnegative matrix factorization”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Randomized Algorithms for Symmetric Nonnegative Matrix Factorization

Symmetric Nonnegative Matrix Factorization (SymNMF) is a technique in data analysis and machine learning that approximates a matrix with a product of a nonnegative, low-rank matrix and it transpose. To design faster and more scalable algorithms for SymNMF we develop two randomized algorithms for its computation. The first method uses randomized matrix sketching to compute an initial low-rank approximation to the input matrix and proceeds to uses this as a low-rank input to rapidly compute a SymNMF. The second methods uses randomized leverage score sampling to approximately solve constrained least squares problems. Many successful methods for SymNMF rely on (approximately) solving sequences of constrained least squares problems. Here, we prove theoretically that leverage score sampling can approximately solve constrained least squares problems to e-accuracy. Finally we demonstrate both methods work in practice by applying them to graph clustering tasks on large real world data sets. These experiments show that our methods approximately maintain solution quality and achieve significant speed ups for both large dense and large sparse problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

On Rank Selection for Nonnegative Matrix Factorization

Rank selection, i.e. the choice of factorization rank, is the first step in constructing Nonnegative Matrix Factorization (NMF) models. It is a long-standing problem which is not unique to NMF, but arises in most models which attempt to decompose data into its underlying components. Since these models are often used in the unsupervised setting, the rank selection problem is further complicated by the lack of ground truth labels. In this paper, we review and empirically evaluate the most commonly used schemes for NMF rank selection.

Eswar, Srinivas [Argonne National Laboratory]↗
DOE OSTI2026

Using Filter Methods to Guide Convergence for ADMM, with Applications to Nonnegative Matrix Factorization Problems

Nonconvex, nonlinear optimization problems arise naturally in parameter fitting and machine learning. While augmented Lagrangian methods have demonstrated robust convergence for classes of these problems, their convergence for block updates has been relatively unexplored outside of the context of the alternating direction method of multipliers (ADMM). ADMM has seen extensive use in these applications, but may exhibit uncertain convergence behavior in many practical nonconvex settings, and struggles with general nonlinear constraints. In contrast, filter methods have proved effective in enforcing convergence for sequential quadratic programming methods and interior point methods with feasibility criteria. We develop an ADMM-filter method for highly nonlinear and nonconvex problems. Here, we show convergence under mild assumptions for several types of coordinate descent schemes, and demonstrate our algorithm on nonnegative matrix factorization and completion problems in imaging and chemical spectrum analysis.

Nonconvex optimization↗
DOE OSTI2026

Fast Active-Set Thresholding Method for Nonnegative Least Squares

Nonnegative Least Squares (NNLS) is a fundamental constrained optimization problem encountered in many applications such as image deblurring, signal processing, nonnegative matrix factorization, magnetic microscopy, and hyperspectral imaging. Active-set based methods are a common class of algorithms for solving NNLS which identify the optimal variable set of the NNLS solution. They do so by iteratively solving a series of unconstrained least squares problems, identifying which variables violate the nonnegativity constraints, and then swapping variables in/out of consideration until the optimal set of variables is found. Several variations improving upon this method exist in the literature. In this work, we propose an active-set swap heuristic which further improves upon existing active-set based methods for NNLS. Our optimizations are based upon adding multiple variables to the passive set within a threshold of the smallest gradient value and removing variables within a similar threshold of the closest boundary constraint. We leverage these optimizations to yield a Fast Active-Set Thresholding NNLS (FAST-NNLS) algorithm which significantly outperforms the existing state-of-the-art NNLS algorithms for a wide range of problems. Rigorous convergence guarantees are proven for the proposed method. We demonstrate the effectiveness of our proposed method on multiple synthetic datasets and two realworld text analysis applications. In doing so, we present the most comprehensive NNLS solver comparison in the literature to date.

Cobb, Benjamin [Georgia Institute of Technology]↗
DOE OSTI2025

Unsupervised Clustering of Microseismic Events and Focal Mechanism Analysis at the CO 2 Injection Site in Decatur, Illinois

Characterization of induced microseismicity at a carbon dioxide (CO 2 ) storage site is critical for preserving reservoir integrity and mitigating seismic hazards. We apply a multilevel machine learning (ML) approach that combines the nonnegative matrix factorization and hidden Markov model to extract spectral representations of microseismic events and cluster them to identify seismic patterns at the Illinois Basin-Decatur Project. Unlike traditional waveform correlation methods, this approach leverages spectral characteristics of first arrivals to improve event classification and detect previously undetected planes of weakness. By integrating ML-based clustering with focal mechanism analysis, we resolve small-scale fault structures that are below the detection limits of conventional seismic imaging. Our findings reveal temporal bursts of microseismicity associated with brittle failure, providing insights into the spatio-temporal evolution of fault reactivation during CO 2 injection. This approach enhances seismic monitoring capabilities at CO 2 injection sites by improving fault characterization beyond the resolution of standard geophysical surveys.

Willis, Rachel Marie [Sandia National Laboratories↗
DOE OSTI2024

New Measurements of the Lyα Forest Continuum and Effective Optical Depth with LyCAN and DESI Y1 Data

Abstract We present the Ly α Continuum Analysis Network (LyCAN), a convolutional neural network that predicts the unabsorbed quasar continuum within the rest-frame wavelength range of 1040–1600 Å based on the red side of the Ly α emission line (1216–1600 Å). We developed synthetic spectra based on a Gaussian mixture model representation of nonnegative matrix factorization (NMF) coefficients. These coefficients were derived from high-resolution, low-redshift ( z < 0.2) Hubble Space Telescope/Cosmic Origins Spectrograph (COS) quasar spectra. We supplemented this COS-based synthetic sample with an equal number of DESI Year 5 mock spectra. LyCAN performs extremely well on testing sets, achieving a median error in the forest region of 1.5% on the DESI mock sample, 2.0% on the COS-based synthetic sample, and 4.1% on the original COS spectra. LyCAN outperforms principal component analysis (PCA) and NMF-based prediction methods using the same training set by 40% or more. We predict the intrinsic continua of 83,635 DESI Year 1 spectra in the redshift range of 2.1 ≤ z ≤ 4.2 and perform an absolute measurement of the evolution of the effective optical depth. This is the largest sample employed to measure the optical depth evolution to date. We fit a power law of the form τ ( z ) = τ 0 ( 1 + z ) γ to our measurements and find τ 0 = (2.46 ± 0.14) × 10 −3 and γ = 3.62 ± 0.04. Our results show particular agreement with high-resolution, ground-based observations around z = 2, indicating that LyCAN is able to predict the quasar continuum in the forest region with only spectral information outside the forest.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Real-Time, Adaptive Radiological Anomaly Detection and Isotope Identification Using Non-Negative Matrix Factorization

Spectroscopic anomaly detection and isotope identification algorithms are integral components in nuclear nonproliferation applications such as search operations. The task is especially challenging in the case of mobile detector systems because the observed gamma-ray background changes more than for a static detector system, and a pretrained background model can easily find itself out of domain. The result is that algorithms may exceed their intended false alarm rate or sacrifice detection sensitivity to maintain the desired false alarm rate. Non-negative matrix factorization (NMF) is a powerful tool for spectral anomaly detection and identification, but, like many similar algorithms that rely on data-driven background models, in its conventional implementation, it is unable to update in real time to account for environmental changes that affect the background spectroscopic signature. Here, we have developed a novel NMF-based algorithm that periodically updates its background model to accommodate changing environmental conditions. The adaptive NMF algorithm involves fewer assumptions about its environment, making it more generalizable than existing NMF-based methods while maintaining or exceeding detection performance on simulated and real-world datasets.

Anomaly detection↗