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All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

A neural network for determination of latent dimensionality in Nonnegative Matrix Factorization

Non-negative Matrix Factorization (NMF) has proven to be a powerful unsupervised learning method for uncovering hidden features in complex and noisy datasets with applications in data mining, text recognition, dimension reduction, face recognition, anomaly detection, blind source separation, and many other fields. An important input for NMF is the latent dimensionality of the data, that is, the number of hidden features, K, present in the explored dataset. Unfortunately, and this quantity is rarely known a priori. The existing methods for determining latent dimensionality, such as Automatic Relevance Determination (ARD), are mostly heuristic and utilize different characteristics to estimate the number of hidden features. However, all of them require human presence to make a final determination of K. Here we utilize a supervised machine learning approach in combination with a recent method for model determination, called NMFk, to determine the number of hidden features automatically. NMFk performs a set of NMF simulations on an ensemble of matrices, obtained by bootstrapping the initial dataset, and estimates which K produces stable groups of latent features that reconstruct the initial dataset well. We then train a Multi-Layter Perceptron (MLP) classifier network to determine the correct number of latent features utilizing the statistics and characteristics of the NMF solution, obtained from NMFk. In order to train the MLP classifier, a training set of 58,660 matrices with predetermined latent features were factorized with NMFk. The MLP classifier in conjunction with NMFk maintains a greater than 95% success rate when applied to a held out test set. Additionally, when applied to two well-known benchmark datasets, the swimmer and MIT face data, NMFk/MLP correctly recovers the established number of hidden features. Finally, we compare the accuracy of our method to the ARD, AIC and Stability-based methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A fast two-stage algorithm for non-negative matrix factorization in smoothly varying data

This article reports the study of algorithms for non-negative matrix factorization (NMF) in various applications involving smoothly varying data such as time or temperature series diffraction data on a dense grid of points. Utilizing the continual nature of the data, a fast two-stage algorithm is developed for highly efficient and accurate NMF. In the first stage, an alternating non-negative least-squares framework is used in combination with the active set method with a warm-start strategy for the solution of subproblems. In the second stage, an interior point method is adopted to accelerate the local convergence. The convergence of the proposed algorithm is proved. The new algorithm is compared with some existing algorithms in benchmark tests using both real-world data and synthetic data. Furthermore, the results demonstrate the advantage of the algorithm in finding high-precision solutions.

interior point method↗
DOE OSTI2020

Modeling Aerial Gamma-Ray Backgrounds Using Non-negative Matrix Factorization

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 in the 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. In this work, 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 the 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. Furthermore, these NMF background components are compared with the background components obtained by noise-adjusted singular value decomposition (NASVD), which contain negative photon fluxes and, thus, do not represent the emission spectra in as straightforward a way. Finally, we comment on the potential areas of research that are enabled by NMF decompositions, such as new approaches to spectral anomaly detection and data fusion.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
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↗
DOE OSTI2024

Algorithms for Non-Negative Matrix Factorization on Noisy Data With Negative Values

Non-negative matrix factorization (NMF) is a dimensionality reduction technique that has shown promise for analyzing noisy data, especially astronomical data. For these datasets, the observed data may contain negative values due to noise even when the true underlying physical signal is strictly positive. Prior NMF work has not treated negative data in a statistically consistent manner, which becomes problematic for low signal-to-noise data with many negative values. In this paper we present two algorithms, Shift-NMF and Nearly-NMF, that can handle both the noisiness of the input data and also any introduced negativity. Both of these algorithms use the negative data space without clipping or masking and recover non-negative signals without any introduced positive offset that occurs when clipping or masking negative data. We demonstrate this numerically on both simple and more realistic examples, and prove that both algorithms have monotonically decreasing update rules.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

Poster — Thur Eve — 03: Application of the non-negative matrix factorization technique to [{sup 11}C]-DTBZ dynamic PET data for the early detection of Parkinson's disease

In this work, a class of non-negative matrix factorization (NMF) technique known as alternating non-negative least squares, combined with the projected gradient method, is used to analyze twenty-five [{sup 11}C]-DTBZ dynamic PET/CT brain data. For each subject, a two-factor model is assumed and two factors representing the striatum (factor 1) and the non-striatum (factor 2) tissues are extracted using the proposed NMF technique and commercially available factor analysis software “Pixies”. The extracted factor 1 and 2 curves represent the binding site of the radiotracer and describe the uptake and clearance of the radiotracer by soft tissues in the brain, respectively. The proposed NMF technique uses prior information about the dynamic data to obtain sample time-activity curves representing the striatum and the non-striatum tissues. These curves are then used for “warm” starting the optimization. Factor solutions from the two methods are compared graphically and quantitatively. In healthy subjects, radiotracer uptake by factors 1 and 2 are approximately 35–40% and 60–65%, respectively. The solutions are also used to develop a factor-based metric for the detection of early, untreated Parkinson's disease. The metric stratifies healthy subjects from suspected Parkinson's patients (based on the graphical method). The analysis shows that both techniques produce comparable results with similar computational time. The “semi-automatic” approach used by the NMF technique allows clinicians to manually set a starting condition for “warm” starting the optimization in order to facilitate control and efficient interaction with the data.

60 APPLIED LIFE SCIENCES↗
NASA NTRS2015

Nonnegative Matrix Factorization for Efficient Hyperspectral Image Projection

Hyperspectral imaging for remote sensing has prompted development of hyperspectral image projectors that can be used to characterize hyperspectral imaging cameras and techniques in the lab. One such emerging astronomical hyperspectral imaging technique is wide-field double-Fourier interferometry. NASA's current, state-of-the-art, Wide-field Imaging Interferometry Testbed (WIIT) uses a Calibrated Hyperspectral Image Projector (CHIP) to generate test scenes and provide a more complete understanding of wide-field double-Fourier interferometry. Given enough time, the CHIP is capable of projecting scenes with astronomically realistic spatial and spectral complexity. However, this would require a very lengthy data collection process. For accurate but time-efficient projection of complicated hyperspectral images with the CHIP, the field must be decomposed both spectrally and spatially in a way that provides a favorable trade-off between accurately projecting the hyperspectral image and the time required for data collection. We apply nonnegative matrix factorization (NMF) to decompose hyperspectral astronomical datacubes into eigenspectra and eigenimages that allow time-efficient projection with the CHIP. Included is a brief analysis of NMF parameters that affect accuracy, including the number of eigenspectra and eigenimages used to approximate the hyperspectral image to be projected. For the chosen field, the normalized mean squared synthesis error is under 0.01 with just 8 eigenspectra. NMF of hyperspectral astronomical fields better utilizes the CHIP's capabilities, providing time-efficient and accurate representations of astronomical scenes to be imaged with the WIIT.

NMF↗
NASA NTRS2021

Topic Modeling Tool for PeTaL (Periodic Table of Life)

A topic modeling tool is constructed for the purpose of providing insights from biology to the engineer within the framework of PeTaL (Periodic Table of Life). The machine learning text mining tools–latent Dirichlet allocation (LDA) and nonnegative matrix factorization (NMF) with Kullback-Leibler (KL) divergence—are used to provide topic clusters to the user. Topic clusters are the underlying themes of a paper. For the text modeling problem, NMF-KL is the equivalent of probabilistic latent semantic analysis. Both LDA and NMF-KL are top-performing modeling tools. These tools are used to identify biological specimens relevant to the user. Various organisms solve a particular survival problem in nature differently. The topic clusters allow people without domain expertise to find these cross-topic themes in the body of documents and then branch out and examine papers whose target organisms solve the engineer’s problem. Abstracts from the Journal of Experimental Biology were used as input for the clustering tool in addition to a curated set of articles for validation. The tool is able to accept alternate input sources.

Machine learning↗
DOE OSTI2015

Toward environmentally-benign utilization of nonmetallic fraction of waste printed circuit boards as modifier and precursor

Highlights: • Environmental impacts of electronic waste and specifically waste printed circuit boards. • Review of the recycling techniques of waste printed circuit boards. • Advantages of physico-mechanical recycling techniques over chemical methods. • Utilization of nonmetallic fraction of waste printed circuit boards as modifier/filler. • Recent advances in the use of nonmetallic fraction of waste printed circuit boards as precursor. - Abstract: Electronic waste, including printed circuit boards, is growing at an alarming rate due to the accelerated technological progress and the shorter lifespan of the electronic equipment. In the past decades, due to the lack of proper economic and environmentally-benign recycling technologies, a major fraction of e-waste generated was either destined to landfills or incinerated with the sole intention of its disposal disregarding the toxic nature of this waste. Recently, with the increasing public awareness over their environment and health issues and with the enaction of more stringent regulations, environmentally-benign recycling has been driven to be an alternative option partially replacing the traditional eco-unfriendly disposal methods. One of the most favorable green technologies has been the mechanical separation of the metallic and nonmetallic fraction of the waste printed circuit boards. Although metallic fraction, as the most profitable component, is used to generate the revenue of the separation process, the nonmetallic fraction (NMF) has been left isolated. Herein, the recent developments in the application of NMF have been comprehensively reviewed and an eco-friendly emerging usage of NMF as a value-added material for sustainable remediation has been introduced.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2012

Photodissociation of N-methylformamide isolated in solid parahydrogen

We report FTIR studies of the 193 nm photodecomposition of N-methylformamide (NMF) isolated in solid parahydrogen (pH{sub 2}) matrices at 1.9 K. By studying the detailed photokinetics we can distinguish between primary and secondary photoproducts. We observe single exponential decay of the NMF precursor upon irradiation and identify three competing primary dissociation channels: HCO + NHCH{sub 3}; H + CONHCH{sub 3}; and CO + CH{sub 3}NH{sub 2} with branching ratios of 0.46(7):0.032(8):0.51(6), respectively. Two of the primary photoproducts (NHCH{sub 3} and CONHCH{sub 3}) are observed for the first time using IR spectroscopy and assigned via ab initio calculations of the vibrational frequencies and intensities of these radicals. The dominant radical formation channel HCO + NHCH{sub 3} is consistent with efficient C-N peptide bond fission at this wavelength and escape of the nascent radical pair from the pH{sub 2} solvent cage. The significant branching 0.51(6) measured for the molecular channel CO + CH{sub 3}NH{sub 2} is unexpected and raises important questions about the details of the in situ photochemistry. Starting from the NMF precursor, we observe and characterize spectroscopically a wide variety of secondary photoproducts including CH{sub 2}NH, HCN, HNC, HNCO, CH{sub 3}NCO, CH{sub 4}, and NH{sub 3}.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Validation of non-negative matrix factorization for rapid assessment of large sets of atomic pair distribution function data

The use of the non-negative matrix factorization (NMF) technique is validated for automatically extracting physically relevant components from atomic pair distribution function (PDF) data from time-series data such as in situ experiments. The use of two matrix-factorization techniques, principal component analysis and NMF, on PDF data is compared in the context of a chemical synthesis reaction taking place in a synchrotron beam, applying the approach to synthetic data where the correct composition is known and on measured PDFs from previously published experimental data. The NMF approach yields mathematical components that are very close to the PDFs of the chemical components of the system and a time evolution of the weights that closely follows the ground truth. Lastly, it is discussed how this would appear in a streaming context if the analysis were being carried out at the beamline as the experiment progressed.

36 MATERIALS SCIENCE↗
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 OSTI2017

STExNMF: Spatio-Temporally Exclusive Topic Discovery for Anomalous Event Detection

Understanding newly emerging events or topics associated with a particular region of a given day can provide deep insight on the critical events occurring in highly evolving metropolitan cities. We propose herein a novel topic modeling approach on text documents with spatio-temporal information (e.g., when and where a document was published) such as location-based social media data to discover prevalent topics or newly emerging events with respect to an area and a time point. We consider a map view composed of regular grids or tiles with each showing topic keywords from documents of the corresponding region. To this end, we present a tilebased spatio-temporally exclusive topic modeling approach called STExNMF, based on a novel nonnegative matrix factorization (NMF) technique. STExNMF mainly works based on the two following stages: (1) first running a standard NMF of each tile to obtain general topics of the tile and (2) running a spatiotemporally exclusive NMF on a weighted residual matrix. These topics likely reveal information on newly emerging events or topics of interest within a region. We demonstrate the advantages of our approach using the geo-tagged Twitter data of New York City. We also provide quantitative comparisons in terms of the topic quality, spatio-temporal exclusiveness, topic variation, and qualitative evaluations of our method using several usage scenarios. In addition, we present a fast topic modeling technique of our model by leveraging parallel computing.

Shin, Sungbok↗
DOE OSTI2026

Data-Driven Performance Optimization of Gamma Spectrometers With Many Channels

In gamma spectrometers with variable spectroscopic performance across many channels (e.g., many pixels or voxels), a tradeoff exists between including data from successively worse-performing readout channels and increasing efficiency. Brute-force calculation of the optimal set of included channels is exponentially infeasible as the number of channels grows, and approximate methods are required. In this work, we present a data-driven framework for attempting to find near-optimal sets of included detector channels. The framework leverages non-negative matrix factorization (NMF) to learn the behavior of gamma spectra across the detector and clusters similarly-performing detector channels together. Performance comparisons are then made between spectra with channel clusters removed, which is more feasible than brute force. The framework is general and can be applied to arbitrary, user-defined performance metrics depending on the application. We apply this framework to optimizing gamma spectra measured by H3D M400 CdZnTe (CZT) spectrometers, which exhibit variable performance across their crystal volumes. In particular, we show several examples optimizing various performance metrics for uranium and plutonium gamma spectra in non-destructive assay (NDA) for nuclear safeguards, and explore trends in performance versus parameters such as clustering algorithm type. We also compare the NMF + clustering pipeline to several non-machine-learning (ML) algorithms, including several greedy algorithms. Although, we find that the NMF + clustering pipeline tends to find the best-performing set of detector voxels, significantly improving over the unoptimized spectra, but that a greedy accumulation of spectra segmented by detector depth can, in some cases, give similar performance improvements in much less computation time.

Energy resolution↗
DOE OSTI2017

Non-Intrusive Energy Disaggregation Using Non-Negative Matrix Factorization With Sum-to-k Constraint

Energy disaggregation or non-intrusive load monitoring addresses the issue of extracting device-level energy consumption information by monitoring the aggregated signal at one single measurement point without installing meters on each individual device. Energy disaggregation can be formulated as a source separation problem, where the aggregated signal is expressed as linear combination of basis vectors in a matrix factorization framework. In this paper, an approach based on Sum-to-k constrained non-negative matrix factorization (S2K-NMF) is proposed. By imposing the sum-to-k constraint and the non-negative constraint, S2K-NMF is able to effectively extract perceptually meaningful sources from complex mixtures. The strength of the proposed algorithm is demonstrated through two sets of experiments: Energy disaggregation in a residential smart home; and heating, ventilating, and air conditioning components energy monitoring in an industrial building testbed maintained at the Oak Ridge National Laboratory. Furthermore, extensive experimental results demonstrate the superior performance of S2K-NMF as compared to state-of-the-art decomposition-based disaggregation algorithms.

42 ENGINEERING↗
DOE OSTI2018

Partitioning and Communication Strategies for Sparse Non-negative Matrix Factorization

Non-negative matrix factorization (NMF), the problem of finding two non-negative low-rank factors whose product approximates an input matrix, is a useful tool for many data mining and scientific applications such as topic modeling in text mining and unmixing in microscopy. In this paper, we focus on scaling algorithms for NMF to very large sparse datasets and massively parallel machines by employing effective algorithms, communication patterns, and partitioning schemes that leverage the sparsity of the input matrix. We consider two previous works developed for related problems, one that uses a fine-grained partitioning strategy using a point-to-point communication pattern and one that uses a Cartesian, or checkerboard, partitioning strategy using a collective-based communication pattern. We show that a combination of the previous approaches balances the demands of the various computations within NMF algorithms and achieves high efficiency and scalability. From the experiments, we see that our proposed strategy runs up to 10x faster than the state of the art on real-world datasets.

Kaya, Oguz↗
NASA NTRS2008

Algorithms for Spectral Decomposition with Applications to Optical Plume Anomaly Detection

The analysis of spectral signals for features that represent physical phenomenon is ubiquitous in the science and engineering communities. There are two main approaches that can be taken to extract relevant features from these high-dimensional data streams. The first set of approaches relies on extracting features using a physics-based paradigm where the underlying physical mechanism that generates the spectra is used to infer the most important features in the data stream. We focus on a complementary methodology that uses a data-driven technique that is informed by the underlying physics but also has the ability to adapt to unmodeled system attributes and dynamics. We discuss the following four algorithms: Spectral Decomposition Algorithm (SDA), Non-Negative Matrix Factorization (NMF), Independent Component Analysis (ICA) and Principal Components Analysis (PCA) and compare their performance on a spectral emulator which we use to generate artificial data with known statistical properties. This spectral emulator mimics the real-world phenomena arising from the plume of the space shuttle main engine and can be used to validate the results that arise from various spectral decomposition algorithms and is very useful for situations where real-world systems have very low probabilities of fault or failure. Our results indicate that methods like SDA and NMF provide a straightforward way of incorporating prior physical knowledge while NMF with a tuning mechanism can give superior performance on some tests. We demonstrate these algorithms to detect potential system-health issues on data from a spectral emulator with tunable health parameters.

Srivastava, Askok N.↗
DOE OSTI2022

An Ensemble Approach to Computationally Efficient Radiological Anomaly Detection and Isotope Identification

Radiological source search is a challenging task involving detection and identification of weak sources in a constantly changing radiological background. As of now, many radiological source detection algorithms have been proposed; however, their computational complexity, and hence reliance on power intensive processing units inhibit low-power applications of radiological source search systems. In this work, we introduce the anomaly filter (AF) algorithm; a computationally light, yet effective time-series source detection algorithm based on exponential weighted moving average (EWMA) and Poisson deviance statistics. Then, we demonstrate that the proposed algorithm can be used in ensemble with other more computationally intensive source detection and identification algorithms to achieve both increased detection performance and reduced power consumption. The proposed AF algorithm and the ensemble algorithms were thoroughly benchmarked against several existing source detection and identification algorithms. The results show that the AF algorithm outperforms existing conventional source detection algorithms, and the ensemble approach improves the overall performance of existing source detection and isotope identification algorithms. Furthermore, the AF algorithm and the Non-negative Matrix Factorization approach based source identification (NMF-ID) algorithm were combined and implemented on a singleboard microcontroller and the power consumption was measured. This ensemble algorithm reduced the power consumption of the NMF-ID algorithm almost by a factor of 100, while improving the detection performance of the overall system.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗