Parameters Of Mixture Model Research Articles

A learning from demonstration framework for implementation of a feeding task

In this paper, a learning from demonstration (LFD) approach is used to design an autonomous meal-assistance agent. The feeding task is modeled as a mixture of Gaussian distributions. Using the data collected via kinesthetic teaching, the parameters of the Gaussian mixture model (GMM) are learnt using Gaussian mixture regression (GMR) and expectation maximization (EM) algorithm. Reproduction of feeding trajectories for different environments is obtained by solving a constrained optimization problem. In this method we show that obstacles can be avoided by robot’s end-effector by adding a set of extra constraints to the optimization problem. Finally, the performance of the designed meal assistant is evaluated in two feeding scenario experiments: one considering obstacles in the path between the bowl and the mouth and the other without.

Calculation of the age of the first infection for skin sores and scabies in five remote communities in northern Australia.

Prevalence of skin sores and scabies in remote Australian Aboriginal communities remains unacceptably high, with Group A Streptococcus (GAS) the dominant pathogen. We aim to better understand the drivers of GAS transmission using mathematical models. To estimate the force of infection, we quantified the age of first skin sores and scabies infection by pooling historical data from three studies conducted across five remote Aboriginal communities for children born between 2001 and 2005. We estimated the age of the first infection using the Kaplan-Meier estimator; parametric exponential mixture model; and Cox proportional hazards. For skin sores, the mean age of the first infection was approximately 10 months and the median was 7 months, with some heterogeneity in median observed by the community. For scabies, the mean age of the first infection was approximately 9 months and the median was 8 months, with significant heterogeneity by the community and an enhanced risk for children born between October and December. The young age of the first infection with skin sores and scabies reflects the high disease burden in these communities.

Tomographic Image Reconstruction with a Spatially Varying Gamma Mixture Prior

A spatially varying Gamma mixture model prior is employed for tomographic image reconstruction, ensuring effective noise elimination and the preservation of region boundaries. We define a line process, modeling edges between image segments, through appropriate Markov random field smoothness terms which are based on the Student’s t-distribution. The proposed algorithm consists of two alternating steps. In the first step, the mixture model parameters are automatically estimated from the image. In the second step, the reconstructed image is estimated by optimizing the maximum-a-posteriori criterion using the one-step-late expectation–maximization and preconditioned conjugate gradient algorithms. Numerical experiments on various photon-limited image scenarios show that the proposed model outperforms the compared state-of-the-art reconstruction models.

AnaCoDa: analyzing codon data with Bayesian mixture models

AnaCoDa is an R package for estimating biologically relevant parameters of mixture models, such as selection against translation inefficiency, non-sense errors and ribosome pausing time, from genomic and high throughput datasets. AnaCoDa provides an adaptive Bayesian MCMC algorithm, fully implemented in C++ for high performance with an ergonomic R interface to improve usability. AnaCoDa employs a generic object-oriented design to allow users to extend the framework and implement their own models. Current models implemented in AnaCoDa can accurately estimate biologically relevant parameters given either protein coding sequences or ribosome foot-printing data. Optionally, AnaCoDa can utilize additional data sources, such as gene expression measurements, to aid model fitting and parameter estimation. By utilizing a hierarchical object structure, some parameters can vary between sets of genes while others can be shared. Genes may be assigned to clusters or membership may be estimated by AnaCoDa. This flexibility allows users to estimate the same model parameter under different biological conditions and categorize genes into different sets based on shared model properties embedded within the data. AnaCoDa also allows users to generate simulated data which can be used to aid model development and model analysis as well as evaluate model adequacy. Finally, AnaCoDa contains a set of visualization routines and the ability to revisit or re-initiate previous model fitting, providing researchers with a well rounded easy to use framework to analyze genome scale data. AnaCoDa is freely available under the Mozilla Public License 2.0 on CRAN (https://cran.r-project.org/web/packages/AnaCoDa/).

Young star clusters in nearby molecular clouds

The SFiNCs (Star Formation in Nearby Clouds) project is an X-ray/infrared study of the young stellar populations in 22 star forming regions with distances <=1 kpc designed to extend our earlier MYStIX survey of more distant clusters. Our central goal is to give empirical constraints on cluster formation mechanisms. Using parametric mixture models applied homogeneously to the catalog of SFiNCs young stars, we identify 52 SFiNCs clusters and 19 unclustered stellar structures. The procedure gives cluster properties including location, population, morphology, association to molecular clouds, absorption, age (AgeJX), and infrared spectral energy distribution (SED) slope. Absorption, SED slope, and AgeJX are age indicators. SFiNCs clusters are examined individually, and collectively with MYStIX clusters, to give the following results. (1) SFiNCs is dominated by smaller, younger, and more heavily obscured clusters than MYStIX. (2) SFiNCs cloud-associated clusters have the high ellipticities aligned with their host molecular filaments indicating morphology inherited from their parental clouds. (3) The effect of cluster expansion is evident from the radius-age, radius-absorption, and radius-SED correlations. Core radii increase dramatically from ~0.08 to ~0.9 pc over the age range 1--3.5 Myr. Inferred gas removal timescales are longer than 1 Myr. (4) Rich, spatially distributed stellar populations are present in SFiNCs clouds representing early generations of star formation. An Appendix compares the performance of the mixture models and nonparametric Minimum Spanning Tree to identify clusters. This work is a foundation for future SFiNCs/MYStIX studies including disk longevity, age gradients, and dynamical modeling.

Segmentation of Remotely Sensed Images using Unsupervised ‘Sampling-Resampling’ based on Hopfield Type Neural Network

In this paper we propose a technique for performing unsupervised segmentation for satellite images using a ’sampling – resampling’ based on Hopfield type Neural Network. The multi band values of the satellite images are grouped into clusters that are modeled using Gaussians. The parameters of Gaussian mixture models are learnt using Hopfield Type Neural Network. The purpose of this work is to show the effectiveness of the results obtained by using Hopfield type Neural Network rather than Bayesian parameter estimation. Each spatial position in the considered image is represented by neuron that is connected only to its neighboring units. It can be observed that the proposed technique have a better correspondence to the actual land features in the satellite images than compared with the results obtained by using the clustering technique like K-means Algorithm. The unsupervised techniques learns the class parameter by exploiting the structure of the unlabeled data .However ,the numerical integration technique that are required for implementing Bayesian learning becomes complicated for practical applications, because of involving large data’s than compared to the Hopfield type Neural Network model.

Estimating the Laplacian matrix of Gaussian mixtures for signal processing on graphs

Recent works in signal processing on graphs have been driven to estimate the precision matrix and to use it as the graph Laplacian matrix. The normalized elements of the precision matrix are the partial correlation coefficients which measure the pairwise conditional linear dependencies of the graph. However, the non-linear dependencies inherent in any non-Gaussian model cannot be captured. We propose in this paper a generalized partial correlation coefficient which is derived by assuming an underlying multivariate Gaussian Mixture Model of the observations. Exact and approximate methods are proposed to estimate the generalized partial correlation coefficients from estimates of the Gaussian Mixture Model parameters. Thus it may find application in any non-Gaussian scenario where the Laplacian matrix is to be learned from training signals.

Abstract P4-15-07: Quantifying the natural history and overtreatment rate of ductal carcinoma in situ

Abstract Background. Subsets of ductal carcinoma in situ (DCIS) are thought to be relatively indolent disease with long progression time to invasive cancer. Nevertheless, the vast majority of women diagnosed with DCIS undergo extirpative surgery, potentially leading to widespread overtreatment of patients who would not develop symptomatic breast cancer in absence of treatment. Due to a poor understanding of the natural history of untreated DCIS, it remains difficult to derive estimates of the true rate of overtreatment. The objective of this study was to quantify the natural history of untreated DCIS through synthesis of retrospective data sources and to estimate the associated rate of overtreatment. Methods. A systematic PubMed search was performed to identify published studies on ipsilateral invasive cancer-free survival in women who did not undergo surgery with curative intent after diagnosis with DCIS. Individual life histories from included studies were manually extracted and aggregated in a patient-level meta-analysis. Each lesion was assigned to one of three categories: DCIS precursor lesions, low-risk DCIS, and high-risk DCIS. Time-to-event analyses (Kaplan-Meier) and Cox proportional-hazards models were used to calculate absolute and relative progression rates for the three risk groups. For the low-risk group, overtreatment rates were estimated by means of a competing risk analysis. For this purpose, progression hazards were estimated by maximum likelihood inference of parametric mixture models, and non-breast cancer mortality rates were derived from standardized life tables (birth cohort: 1960). Results. A total of n=122 women from 3 retrospective studies were included in the patient-level meta-analysis. The median age at diagnosis was 47 years (interquartile range [IQR]: 41-57) and median follow-up was 17 years (IQR: 6-20). Compared to DCIS precursor lesions (n=38), relative rates of progression to invasive cancer were significantly higher for both low-risk DCIS (n=68; hazard ratio [HR]: 4.8, 95%-CI: 1.4-16.0) and high-risk DCIS (n=16; HR: 6.9, 95%-CI: 1.7-27.8). Among women with low-risk DCIS, the cumulative progression to ipsilateral invasive disease after 5, 10, and 20 years was found to be 16.9% (95%-CI: 9.7-28.5), 28.5% (95%-CI: 16.6-38.8) and 35.1% (95%-CI: 23.8-49.8), respectively. The corresponding overtreatment rates for low-risk DCIS were estimated to be of the order of 56%, 63% and 72% for ages at diagnosis of 55, 65 and 75 years respectively. Conclusion. To our knowledge, this study constitutes the most comprehensive quantitative analysis of the natural history of incompletely treated DCIS. The estimated propensity to progress to invasive disease suggests overtreatment among some women diagnosed with low-risk DCIS, especially in older patients with comorbidities. The extent to which this cohort resembles those currently diagnosed with DCIS is unclear. However, these results underscore the importance of clinical trials in evaluating active surveillance and/or anti-estrogen therapy as alternative management strategies for women diagnosed with low-risk DCIS. Citation Format: Ryser MD, Weaver DL, Marks JR, Hyslop T, Hwang ES. Quantifying the natural history and overtreatment rate of ductal carcinoma in situ [abstract]. In: Proceedings of the 2017 San Antonio Breast Cancer Symposium; 2017 Dec 5-9; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2018;78(4 Suppl):Abstract nr P4-15-07.

Research on Initialization on EM Algorithm Based on Gaussian Mixture Model

The EM algorithm is a very popular maximum likelihood estimation method, the iterative algorithm for solving the maximum likelihood estimator when the observation data is the incomplete data, but also is very effective algorithm to estimate the finite mixture model parameters. However, EM algorithm can not guarantee to find the global optimal solution, and often easy to fall into local optimal solution, so it is sensitive to the determination of initial value to iteration. Traditional EM algorithm select the initial value at random, we propose an improved method of selection of initial value. First, we use the k-nearest-neighbor method to delete outliers. Second, use the k-means to initialize the EM algorithm. Compare this method with the original random initial value method, numerical experiments show that the parameter estimation effect of the initialization of the EM algorithm is significantly better than the effect of the original EM algorithm.

Stochastic characterization of wind field characteristics of an arch bridge instrumented with structural health monitoring system

This paper aims to conduct a stochastic characterization of wind field characteristics nearby an arch bridge based on long-term monitoring data from an instrumented structural health monitoring (SHM) system. The fluctuating wind characteristics are first presented by analyzing the real-time wind monitoring data. A genetic algorithm (GA)-based finite mixture modeling approach is proposed to formulate the joint distribution of the wind speed and direction. For the probability density function (PDF) of the wind speed, a two-parameter Weibull distribution is applied, and a von Mises distribution is selected to present the PDF of the wind direction. The parameters of finite mixture models are estimated by the GA-based parameter estimation method. The effectiveness of the proposed direct probabilistic modeling approach is validated by use of one-year of wind monitoring data, and compared with the traditional angular-linear (AL) distribution-based indirect modeling approach in terms of the Akaike’s information criterion (AIC), Bayesian information criterion (BIC) and R2 value. Results indicate that the proposed GA-based finite mixture modeling approach fits the measured data better than the AL distribution-based indirect modeling approach. In addition, the joint distribution of the wind speed and direction will facilitate the wind-resistant design and wind-induced fatigue assessment of long-span bridges.

PLEMT: A Novel Pseudolikelihood-Based EM Test for Homogeneity in Generalized Exponential Tilt Mixture Models

ABSTRACTMotivated by analyses of DNA methylation data, we propose a semiparametric mixture model, namely, the generalized exponential tilt mixture model, to account for heterogeneity between differentially methylated and nondifferentially methylated subjects in the cancer group, and capture the differences in higher order moments (e.g., mean and variance) between subjects in cancer and normal groups. A pairwise pseudolikelihood is constructed to eliminate the unknown nuisance function. To circumvent boundary and nonidentifiability problems as in parametric mixture models, we modify the pseudolikelihood by adding a penalty function. In addition, the test with simple asymptotic distribution has computational advantages compared with permutation-based test for high-dimensional genetic or epigenetic data. We propose a pseudolikelihood-based expectation–maximization test, and show the proposed test follows a simple chi-squared limiting distribution. Simulation studies show that the proposed test controls Type I errors well and has better power compared to several current tests. In particular, the proposed test outperforms the commonly used tests under all simulation settings considered, especially when there are variance differences between two groups. The proposed test is applied to a real dataset to identify differentially methylated sites between ovarian cancer subjects and normal subjects. Supplementary materials for this article are available online.

The Precise Measurement of Vapor–Liquid Equilibrium Properties of the CO$$_{2}$$/Isopentane Binary Mixture, and Fitted Parameters for a Helmholtz Energy Mixture Model

Natural working fluid mixtures, including combinations of CO $$_{2}$$ , hydrocarbons, water, and ammonia, are expected to have applications in energy conversion processes such as heat pumps and organic Rankine cycles. However, the available literature data, much of which were published between 1975 and 1992, do not incorporate the recommendations of the Guide to the Expression of Uncertainty in Measurement. Therefore, new and more reliable thermodynamic property measurements obtained with state-of-the-art technology are required. The goal of the present study was to obtain accurate vapor–liquid equilibrium (VLE) properties for complex mixtures based on two different gases with significant variations in their boiling points. Precise VLE data were measured with a recirculation-type apparatus with a 380 cm $$^{3}$$ equilibration cell and two windows allowing observation of the phase behavior. This cell was equipped with recirculating and expansion loops that were immersed in temperature-controlled liquid and air baths, respectively. Following equilibration, the composition of the sample in each loop was ascertained by gas chromatography. VLE data were acquired for CO $$_{2}$$ /ethanol and CO $$_{2}$$ /isopentane binary mixtures within the temperature range from 300 K to 330 K and at pressures up to 7 MPa. These data were used to fit interaction parameters in a Helmholtz energy mixture model. Comparisons were made with the available literature data and values calculated by thermodynamic property models.

Interference Modeling for Cellular Networks Under Beamforming Transmission

We propose analytical models for the interference power distribution in a cellular system employing MIMO beamforming in rich and limited scattering environments, which capture non line-of-sight signal propagation in the microwave and mmWave bands, respectively. Two candidate models are considered: the Inverse Gaussian and the Inverse Weibull, both are two-parameter heavy tail distributions. We further propose a mixture of these two distributions as a model with three parameters. To estimate the parameters of these distributions, three approaches are used: moment matching, individual distribution maximum likelihood estimation (MLE), and mixture distribution MLE with a designed expectation maximization algorithm. We then introduce simple fitted functions for the mixture model parameters as polynomials of the channel path loss exponent and shadowing variance. To measure the goodness of these models, the information-theoretic metric relative entropy is used to capture the distance from the model distribution to a reference one. The interference models are tested against data obtained by simulating a cellular network based on stochastic geometry. The results show that the three-parameter mixture model offers remarkably good fit to simulated interference power. The mixture model is further used to analyze the capacity of a cellular network employing joint transmit and receive beamforming and confirms a good fit with simulation.

Statistical modeling of Optical Coherence Tomography images by asymmetric Normal Laplace mixture model.

Optical Coherence Tomography (OCT) is known as a non-invasive and high resolution imaging modality in ophthalmology. Effecting noise on the OCT images as well as other reasons cause a random behavior in these images. In this study, we introduce a new statistical model for retinal layers in healthy OCT images. This model, namely asymmetric Normal Laplace (NL), fits well the advent of asymmetry and heavy-tailed in intensity distribution of each layer. Due to the layered structure of retina, a mixture model is addressed. It is proposed to evaluate the fitness criteria called Kull-back Leibler Divergence (KLD) and chi-square test along visual results. The results express the well performance of proposed model in fitness of data except for 6th and 7th layers. Using a complicated model, e.g. a mixture model with two component, seems to be appropriate for these layers. The mentioned process for train images can then be devised for a test image by employing the Expectation Maximization (EM) algorithm to estimate the values of parameters in mixture model.

A Gaussian mixture model based adaptive classifier for fNIRS brain–computer interfaces and its testing via simulation

Objective. Functional near infra-red spectroscopy (fNIRS) is a promising brain imaging technology for brain–computer interfaces (BCI). Future clinical uses of fNIRS will likely require operation over long time spans, during which neural activation patterns may change. However, current decoders for fNIRS signals are not designed to handle changing activation patterns. The objective of this study is to test via simulations a new adaptive decoder for fNIRS signals, the Gaussian mixture model adaptive classifier (GMMAC). Approach. GMMAC can simultaneously classify and track activation pattern changes without the need for ground-truth labels. This adaptive classifier uses computationally efficient variational Bayesian inference to label new data points and update mixture model parameters, using the previous model parameters as priors. We test GMMAC in simulations in which neural activation patterns change over time and compare to static decoders and unsupervised adaptive linear discriminant analysis classifiers. Main results. Our simulation experiments show GMMAC can accurately decode under time-varying activation patterns: shifts of activation region, expansions of activation region, and combined contractions and shifts of activation region. Furthermore, the experiments show the proposed method can track the changing shape of the activation region. Compared to prior work, GMMAC performed significantly better than the other unsupervised adaptive classifiers on a difficult activation pattern change simulation: 99% versus <54% in two-choice classification accuracy. Significance. We believe GMMAC will be useful for clinical fNIRS-based brain–computer interfaces, including neurofeedback training systems, where operation over long time spans is required.

Scattering statistics of glacially quarried rock outcrops: Bayesian inversions for mixture model parameters

Knowledge of the probability distribution of the scattered amplitude return from the seafloor in reverberation measurements and seafloor sonar images is a prerequisite to designing effective target detection systems and predicting their performance. Previous measurements have revealed that the distribution is often heavier tailed than the Rayleigh distribution, and may be modeled by the K, Weibull, and log-normal distributions, among others. Recent measurements of the scattering statistics from rock seafloors resulted in a bimodal distribution, which is poorly modeled by many commonly used distributions. The rock surfaces were formed from glacial quarrying and exhibit a stepped structure. The observed distribution is hypothesized to result from a mixture, where the scattered field from vertically oriented facets is modeled as a K distribution, and the scattered field due to the horizontally oriented facets is modeled as a Rayleigh distribution. If this hypothesis is true, then roughness parameters may be estimated from scattering data. A Bayesian technique for estimating the distribution of mixture parameters from the probability distribution of the scattered field is presented. This technique, while computationally expensive, reveals the relationship between the mixture model parameters, and can reveal any degeneracies that could lead to problems during inversions.

EXIT Chart-Based IRA Code Design for TDMR Turbo-Equalization System

We present an extrinsic information transfer (EXIT) chart-based design technique for irregular repeat-accumulate (IRA) codes used in 2-D magnetic recording (TDMR) turbo-equalization systems. The channel model includes Voronoi magnetic grains, 2-D intersymbol interference (2D-ISI) and additive white Gaussian noise (AWGN). The receiver uses a 2D-ISI BCJR equalizer and an IRA decoder. For one outer equalizer-decoder iteration, we propose theory and simulation-based methods for computing EXIT curves. The simulation method calculates experimental EXIT curves for the check node decoder (CND) and the combination of the variable node decoder (VND) and an equalizer. The theoretical approach recursively calculates CND and VND Gaussian mixture model parameters in order to calculate EXIT curves. We then fit the VND and CND EXIT curves to find optimized variable node degree distributions. Simulation results show that the TDMR-optimized IRA codes achieve up to a 6.2% density increase in user bits/grain (U/G) compared with IRA codes designed for AWGN channels. The theory-based code designs achieve the same or better U/G as the simulation-based designs, but require 98% less design computation time. We also derive optimized IRA codes for iterative turbo-equalization; these codes can achieve simultaneous U/G gains and SNR savings compared with AWGN-optimized codes.

Bayesian Analysis of two Censored Shifted Gompertz Mixture Distributions using Informative and Noninformative Priors

This study deals with Bayesian analysis of shifted Gompertz mixture model under type-I censored samples assuming both informative and noninformative priors. We have discussed the Bayesian estimation of parameters of shifted Gompertz mixture model under the uniform, and gamma priors assuming three loss functions. Further, some properties of the model with some graphs of the mixture density are discussed. These properties include Bayes estimators, posterior risks and reliability function under simulation scheme. Bayes estimates are obtained considering two cases: (a) when the shape parameter is known and (b) when all parameters are unknown. We analyzed some simulated sets in order to investigate the effect of prior belief, loss functions, and performance of the proposed set of estimators of the mixture model parameters.

A variable step learning algorithm for Gaussian mixture models based on the Bhattacharyya coefficient and correlation coefficient criterion

The expectation maximization (EM) algorithm is one of the most enduring ways to estimate the parameters of Gaussian mixture models. However, the EM algorithm needs to know in advance the true number of mixing components, and its performance highly depends on the initial parameters, which leads to use it difficultly in practice. To overcome the above two drawbacks, a variable step learning algorithm is proposed for learning a Gaussian mixture models. The novelty of the algorithm is that a variable step search strategy is proposed to find the actual number of Gaussian mixture components, or slightly above it. This number is obtained by maximizing the Bhattacharyya coefficient criterion, which in turn quantifies how close the Gaussian mixtures models fit the observed data. Furthermore, the initialization parameters are determined by the correlation coefficient criterion representing the shape characteristics between the new GMM and the histograms of the data. Based on these two criteria, the proposed algorithm can make both parameter learning and model selection more efficient, as shown by the conducted experiments.

An Interactive Image Segmentation Method in Hand Gesture Recognition.

In order to improve the recognition rate of hand gestures a new interactive image segmentation method for hand gesture recognition is presented, and popular methods, e.g., Graph cut, Random walker, Interactive image segmentation using geodesic star convexity, are studied in this article. The Gaussian Mixture Model was employed for image modelling and the iteration of Expectation Maximum algorithm learns the parameters of Gaussian Mixture Model. We apply a Gibbs random field to the image segmentation and minimize the Gibbs Energy using Min-cut theorem to find the optimal segmentation. The segmentation result of our method is tested on an image dataset and compared with other methods by estimating the region accuracy and boundary accuracy. Finally five kinds of hand gestures in different backgrounds are tested on our experimental platform, and the sparse representation algorithm is used, proving that the segmentation of hand gesture images helps to improve the recognition accuracy.