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DOE OSTI2013

A Parallel EM Algorithm for Model-Based Clustering Applied to the Exploration of Large Spatio-Temporal Data

We develop a parallel EM algorithm for multivariate Gaussian mixture models and use it to perform model-based clustering of a large climate data set. Three variants of the EM algorithm are reformulated in parallel and a new variant that is faster is presented. All are implemented using the single program, multiple data (SPMD) programming model, which is able to take advantage of the combined collective memory of large distributed computer architectures to process larger data sets. Displays of the estimated mixture model rather than the data allow us to explore multivariate relationships in a way that scales to arbitrary size data. We study the performance of our methodology on simulated data and apply our methodology to a high resolution climate dataset produced by the community atmosphere model (CAM5). This article has supplementary material online.

Chen, Wei-Chen↗

NASA NTRS1982

Mixture densities, maximum likelihood, and the EM algorithm

The problem of estimating the parameters which determine a mixture density is reviewed as well as maximum likelihood estimation for it. A particular iterative procedure for numerically approximating maximum likelihood estimates for mixture density problems is considered. This EM algorithm, is a specialization to the mixture density context of a general algorithm of the same name used to approximate maximum likelihood estimates for incomplete data problems. The formulation and theoretical and practical properties of the EM algorithm for mixture densities are discussed focussing in particular on mixtures of densities from exponential families.

Redner, R. A.↗

DOE OSTI2017

Application and performance of an ML-EM algorithm in NEXT

The goal of the NEXT experiment is the observation of neutrinoless double beta decay in (136)Xe using a gaseous xenon TPC with electroluminescent amplification and specialized photodetector arrays for calorimetry and tracking. The NEXT Collaboration is exploring a number of reconstruction algorithms to exploit the full potential of the detector. This paper describes one of them: the Maximum Likelihood Expectation Maximization (ML-EM) method, a generic iterative algorithm to find maximum-likelihood estimates of parameters that has been applied to solve many different types of complex inverse problems. In particular, we discuss a bi-dimensional version of the method in which the photosensor signals integrated over time are used to reconstruct a transverse projection of the event. First results show that, when applied to detector simulation data, the algorithm achieves nearly optimal energy resolution (better than 0.5% FWHM at the Q value of (136)Xe) for events distributed over the full active volume of the TPC.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2016

Results on the neutron energy distribution measurements at the RECH-1 Chilean nuclear reactor

Neutron activations experiments has been perform at the RECH-1 Chilean Nuclear Reactor to measure its neutron flux energy distribution. Samples of pure elements was activated to obtain the saturation activities for each reaction. Using - ray spectroscopy we identify and measure the activity of the reaction product nuclei, obtaining the saturation activities of 20 reactions. GEANT4 and MCNP was used to compute the self shielding factor to correct the cross section for each element. With the Expectation-Maximization algorithm (EM) we were able to unfold the neutron flux energy distribution at dry tube position, near the RECH-1 core. In this work, we present the unfolding results using the EM algorithm.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2013

Expectation-maximization algorithms for learning a finite mixture of univariate survival time distributions from partially specified class values

Heterogeneity exists on a data set when samples from di erent classes are merged into the data set. Finite mixture models can be used to represent a survival time distribution on heterogeneous patient group by the proportions of each class and by the survival time distribution within each class as well. The heterogeneous data set cannot be explicitly decomposed to homogeneous subgroups unless all the samples are precisely labeled by their origin classes; such impossibility of decomposition is a barrier to overcome for estimating nite mixture models. The expectation-maximization (EM) algorithm has been used to obtain maximum likelihood estimates of nite mixture models by soft-decomposition of heterogeneous samples without labels for a subset or the entire set of data. In medical surveillance databases we can find partially labeled data, that is, while not completely unlabeled there is only imprecise information about class values. In this study we propose new EM algorithms that take advantages of using such partial labels, and thus incorporate more information than traditional EM algorithms. We particularly propose four variants of the EM algorithm named EM-OCML, EM-PCML, EM-HCML and EM-CPCML, each of which assumes a specific mechanism of missing class values. We conducted a simulation study on exponential survival trees with five classes and showed that the advantages of incorporating substantial amount of partially labeled data can be highly signi cant. We also showed model selection based on AIC values fairly works to select the best proposed algorithm on each specific data set. A case study on a real-world data set of gastric cancer provided by Surveillance, Epidemiology and End Results (SEER) program showed a superiority of EM-CPCML to not only the other proposed EM algorithms but also conventional supervised, unsupervised and semi-supervised learning algorithms.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

On implementation of EM-type algorithms in the stochastic models for a matrix computing on GPU

The paper discusses the main ideas of an implementation of EM-type algorithms for computing on the graphics processors and the application for the probabilistic models based on the Cox processes. An example of the GPU’s adapted MATLAB source code for the finite normal mixtures with the expectation-maximization matrix formulas is given. The testing of computational efficiency for GPU vs CPU is illustrated for the different sample sizes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

Compositing "Stand Off" Ground Penetrating Radar Scans of Differing Frequencies.

Methods have been developed to combine signals of various frequencies in a manner to produce clearer images in the presence of noise. Ground Penetrating Radar (GPR) scans at various frequencies are no exception. Methods using an optimization problem solver, the Expectation-Maximization (EM) Algorithm, define weights used to perform the task of combining GPR scans. In this paper, we explore using the Gaussian Mixture Model (GMM) feature of the EM Algorithm on GPR scans taken at various heights above ground ("Stand Off' GPR). This method demonstrates the same measured improvement toward producing a cleaner image as GPR scans taken at ground level using the same EM Algorithm method.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Expectation-maximization algorithm for amplitude estimation of saturated optical transient signals

This paper addresses parameter estimation for an optical transient signal when the received data has been right-censored. We develop an expectation-maximization (EM) algorithm to estimate the amplitude of a Poisson intensity with a known shape in the presence of additive background counts, where the measurements are subject to saturation effects. We then compare the results of our algorithm with those of an EM algorithm that is unaware of the censoring.

47 OTHER INSTRUMENTATION↗

DOE OSTI2023

Probabilistic partition of unity networks for high–dimensional regression problems

We explore the probabilistic partition of unity network (PPOU-Net) model in the context of high-dimensional regression problems and propose a general framework focusing on adaptive dimensionality reduction. With the proposed framework, the target function is approximated by a mixture of experts model on a low-dimensional manifold, where each cluster is associated with a fixed-degree polynomial. We present a training strategy that leverages the expectation maximization (EM) algorithm. During the training, we alternate between (i) applying gradient descent to update the DNN coefficients; and (ii) using closed-form formulae derived from the EM algorithm to update the mixture of experts model parameters. Under the probabilistic formulation, step (ii) admits the form of embarrassingly paralleliazable weighted least-squares solves. The PPOU-Nets consistently outperform the baseline fully-connected neural networks of comparable sizes in numerical experiments of various data dimensions. Here, we also explore the proposed model in applications of quantum computing, where the PPOU-Nets act as surrogate models for cost landscapes associated with variational quantum circuits.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

Dose impact in radiographic lung injury following lung SBRT: Statistical analysis and geometric interpretation

Purpose: To demonstrate a new method of evaluating dose response of treatment-induced lung radiographic injury post-SBRT (stereotactic body radiotherapy) treatment and the discovery of bimodal dose behavior within clinically identified injury volumes. Methods: Follow-up CT scans at 3, 6, and 12 months were acquired from 24 patients treated with SBRT for stage-1 primary lung cancers or oligometastic lesions. Injury regions in these scans were propagated to the planning CT coordinates by performing deformable registration of the follow-ups to the planning CTs. A bimodal behavior was repeatedly observed from the probability distribution for dose values within the deformed injury regions. Based on a mixture-Gaussian assumption, an Expectation-Maximization (EM) algorithm was used to obtain characteristic parameters for such distribution. Geometric analysis was performed to interpret such parameters and infer the critical dose level that is potentially inductive of post-SBRT lung injury. Results: The Gaussian mixture obtained from the EM algorithm closely approximates the empirical dose histogram within the injury volume with good consistency. The average Kullback-Leibler divergence values between the empirical differential dose volume histogram and the EM-obtained Gaussian mixture distribution were calculated to be 0.069, 0.063, and 0.092 for the 3, 6, and 12 month follow-up groups, respectively. The lower Gaussian component was located at approximately 70% prescription dose (35 Gy) for all three follow-up time points. The higher Gaussian component, contributed by the dose received by planning target volume, was located at around 107% of the prescription dose. Geometrical analysis suggests the mean of the lower Gaussian component, located at 35 Gy, as a possible indicator for a critical dose that induces lung injury after SBRT. Conclusions: An innovative and improved method for analyzing the correspondence between lung radiographic injury and SBRT treatment dose has been demonstrated. Bimodal behavior was observed in the dose distribution of lung injury after SBRT. Novel statistical and geometrical analysis has shown that the systematically quantified low-dose peak at approximately 35 Gy, or 70% prescription dose, is a good indication of a critical dose for injury. The determined critical dose of 35 Gy resembles the critical dose volume limit of 30 Gy for ipsilateral bronchus in RTOG 0618 and results from previous studies. The authors seek to further extend this improved analysis method to a larger cohort to better understand the interpatient variation in radiographic lung injury dose response post-SBRT.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2017

Compositing Ground Penetrating Radar Scans of Differing Frequencies for Better Depth Perception

Methods developed to reduce interference in a noisy environment, be it radar target responses or effective communications in the presence of noise for mobile phone users, are vital in delivering a clear usable signal. The methods used to render a cleaner signal can also be used to combine signals of various frequencies. Ground Penetrating Radar (GPR) scans over the same area are no exception. This paper explores using an optimization problem solver, the Expectation Maximization (EM) Algorithm, to define the weights to use to combine multiple GPR scans at different frequencies over the same target area. This approach exploits the Gaussian Mixture Model (GMM) feature of the EM algorithm to produce a cleaner image at depth. Our method demonstrates a measured improvement toward producing a cleaner image.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2013

Test of 3D CT reconstructions by EM + TV algorithm from undersampled data

Computerized tomography (CT) plays an important role in medical imaging for diagnosis and therapy. However, CT imaging is connected with ionization radiation exposure of patients. Therefore, the dose reduction is an essential issue in CT. In 2011, the Expectation Maximization and Total Variation Based Model for CT Reconstruction (EM+TV) was proposed. This method can reconstruct a better image using less CT projections in comparison with the usual filtered back projection (FBP) technique. Thus, it could significantly reduce the overall dose of radiation in CT. This work reports the results of an independent numerical simulation for cone beam CT geometry with alternative virtual phantoms. As in the original report, the 3D CT images of 128 Multiplication-Sign 128 Multiplication-Sign 128 virtual phantoms were reconstructed. It was not possible to implement phantoms with lager dimensions because of the slowness of code execution even by the CORE i7 CPU.

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2016

TH-CD-206-01: Expectation-Maximization Algorithm-Based Tissue Mixture Quantification for Perfusion MRI

Purpose: To investigate the feasibility of estimating the tissue mixture perfusions and quantifying cerebral blood flow change in arterial spin labeled (ASL) perfusion MR images. Methods: The proposed perfusion MR image analysis framework consists of 5 steps: (1) Inhomogeneity correction was performed on the T1- and T2-weighted images, which are available for each studied perfusion MR dataset. (2) We used the publicly available FSL toolbox to strip off the non-brain structures from the T1- and T2-weighted MR images. (3) We applied a multi-spectral tissue-mixture segmentation algorithm on both T1- and T2-structural MR images to roughly estimate the fraction of each tissue type - white matter, grey matter and cerebral spinal fluid inside each image voxel. (4) The distributions of the three tissue types or tissue mixture across the structural image array are down-sampled and mapped onto the ASL voxel array via a co-registration operation. (5) The presented 4-dimensional expectation-maximization (4D-EM) algorithm takes the down-sampled three tissue type distributions on perfusion image data to generate the perfusion mean, variance and percentage images for each tissue type of interest. Results: Experimental results on three volunteer datasets demonstrated that the multi-spectral tissue-mixture segmentation algorithm was effective to initialize tissue mixtures from T1- and T2-weighted MR images. Compared with the conventional ASL image processing toolbox, the proposed 4D-EM algorithm not only generated comparable perfusion mean images, but also produced perfusion variance and percentage images, which the ASL toolbox cannot obtain. It is observed that the perfusion contribution percentages may not be the same as the corresponding tissue mixture volume fractions estimated in the structural images. Conclusion: A specific application to brain ASL images showed that the presented perfusion image analysis method is promising for detecting subtle changes in tissue perfusions, which is valuable for the early diagnosis of certain brain diseases, e.g. multiple sclerosis.

60 APPLIED LIFE SCIENCES↗

NASA NTRS2004

Symmetric normal mixtures

We consider mixture density estimation under the symmetry constraint x = Az for an orthogonal matrix A. This distributional constraint implies a corresponding constraint on the mixture parameters. Focusing on the gaussian case, we derive an expectation-maximization (EM) algorithm to enforce the constraint and show results for modeling of image feature vectors.

symmetry constraint↗

DOE OSTI2019

GPR Imaging for Deeply Buried Objects: A Comparative Study Based on Compositing of Scanning Frequencies and a Chirp Excitation Function

Compositing of ground penetrating radar (GPR) scans of differing frequencies have been found to produce cleaner images at depth using the Gaussian mixture model (GMM) feature of the expectation-maximization (EM) algorithm. GPR scans at various heights (“Stand Off”), as well as ground-based scans, have been studied. In this paper, we compare the GPR response from a chirp excitation function-based radar with the response from the EM GMM algorithm compositing process, using the same mix of frequencies. A chirp excitation pulse was found to be effective in delineating the defined buried object, but the resulting image is less sharp than the GMM EM method.

58 GEOSCIENCES↗

DOE OSTI2016

Multimodal Event Detection in Twitter Hashtag Networks

In this study, event detection in a multimodal Twitter dataset is considered. We treat the hashtags in the dataset as instances with two modes: text and geolocation features. The text feature consists of a bag-of-words representation. The geolocation feature consists of geotags (i.e., geographical coordinates) of the tweets. Fusing the multimodal data we aim to detect, in terms of topic and geolocation, the interesting events and the associated hashtags. To this end, a generative latent variable model is assumed, and a generalized expectation-maximization (EM) algorithm is derived to learn the model parameters. The proposed method is computationally efficient, and lends itself to big datasets. Lastly, experimental results on a Twitter dataset from August 2014 show the efficacy of the proposed method.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Estimating the Propagation of Interdependent Cascading Outages with Multi-Type Branching Processes

In this paper, the multi-type branching process is applied to describe the statistics and interdependencies of line outages, the load shed, and isolated buses. The offspring mean matrix of the multi-type branching process is estimated by the Expectation Maximization (EM) algorithm and can quantify the extent of outage propagation. The joint distribution of two types of outages is estimated by the multi-type branching process via the Lagrange-Good inversion. The proposed model is tested with data generated by the AC OPA cascading simulations on the IEEE 118-bus system. The largest eigenvalues of the offspring mean matrix indicate that the system is closer to criticality when considering the interdependence of different types of outages. Compared with empirically estimating the joint distribution of the total outages, good estimate is obtained by using the multitype branching process with a much smaller number of cascades, thus greatly improving the efficiency. It is shown that the multitype branching process can effectively predict the distribution of the load shed and isolated buses and their conditional largest possible total outages even when there are no data of them.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

A Load Switching Group based Feeder-level Microgrid Energy Management Algorithm for Service Restoration in Power Distribution System

This paper presents a load switching group based energy management system (LSG-EMS) for operating microgrids on a distribution feeder powered by one or multiple grid-forming distributed energy resources. Loads on a distribution feeder are divided into load switching groups that can be remotely switched on and off. The LSG-EMS algorithm, formulated as a mixed-integer linear programming (MILP) problem, has an objective function of maximizing the served loads while minimizing the total number of switching actions. A new set of topology constraints are developed for allowing multiple microgrids to be formed on the feeder and selecting the optimal supply path. Customer comfort is accounted for by maximizing the supply duration in the customer preferred service period and enforcing a minimum service duration. The proposed method is demonstrated on a modified IEEE 33-bus system using actual customer data. Simulation results show that the LSG-EMS successfully coordinates multiple grid-forming sources by selecting an optimal supply topology that maximizes the supply period of both the critical and noncritical loads while minimizing customer service interruptions in the service restoration process.

Hu, Rongxing↗