Gamma Mixture Research Articles

Segmentation Approach for a Noisy Iris Images Based on Block Statistical Parameters

The Iris localization plays a big role in the performance of an iris recognition system. This is due to the dependent of the next steps up on it, and the incorrect segmentation might lead to inexact normalization and improper feature extraction from less discriminatory parts (eyelids, eyelashes, pupil, etc.) so the execution of system will diminish. An effective method for locating the iris of the eye is suggested in this paper. At first a mixture of gamma transform and contrast enhancing mechanisms are used to guarantee a precise renovation of eye image to become an iris area easy to isolate. The next step is relayed on calculating the statistical image parameters (i.e., the mean and standard deviation) which are employed as a feature to detect outer iris boundary. The integro-differential operational technique is used with further pre-processing processes to detect the inner boundaries of iris. The noisy iris UBIRIS.v1 dataset was used in the experiment. Thee conducted results indicated that the proposed technique has a good performance, which is improved accuracy of iris localization step for noisy dataset.

Dealing with highly skewed hospital length of stay distributions: The use of Gamma mixture models to study delivery hospitalizations.

The increased focus on addressing severe maternal morbidity and maternal mortality has led to studies investigating patient and hospital characteristics associated with longer hospital stays. Length of stay (LOS) for delivery hospitalizations has a strongly skewed distribution with the vast majority of LOS lasting two to three days in the United States. Prior studies typically focused on common LOSs and dealt with the long LOS distribution tail in ways to fit conventional statistical analyses (e.g., log transformation, trimming). This study demonstrates the use of Gamma mixture models to analyze the skewed LOS distribution. Gamma mixture models are flexible and, do not require data transformation or removal of outliers to accommodate many outcome distribution shapes, these models allow for the analysis of patients staying in the hospital for a longer time, which often includes those women experiencing worse outcomes. Random effects are included in the model to account for patients being treated within the same hospitals. Further, the role and influence of differing placements of covariates on the results is discussed in the context of distinct model specifications of the Gamma mixture regression model. The application of these models shows that they are robust to the placement of covariates and random effects. Using New York State data, the models showed that longer LOS for childbirth hospitalizations were more common in hospitals designated to accept more complicated deliveries, across hospital types, and among Black women. Primary insurance also was associated with LOS. Substantial variation between hospitals suggests the need to investigate protocols to standardize evidence-based medical care.

A Methodology for Efficient Sketch Based Image Retrievals Based on Correlation Based Matching and Generalized Gamma Mixture Model (GGMM)

The huge developments in touch screen devices and used in Computer vision developed the methodologies for recovering the images based on content. However in certain situations narration is the best suitable way to express and hence in the views of narration sketch based images are thus developed and utilized. These sketch based images are most useful in identifying face in criminal investigations. This paper provides a methodology for retrieving such sketch based images using the correlation based matching and generalized gamma mixture models. Performance is measured using precision and recall.

Application of CT images in the diagnosis of lung cancer based on finite mixed model.

ObjectiveInvestigating the application of CT images when diagnosing lung cancer based on finite mixture model is the objective. Method: 120 clean healthy rats were taken as the research objects to establish lung cancer rat model and carry out lung CT image examination. After the successful CT image data preprocessing, the image is segmented by different methods, which include lung nodule segmentation on the basis of Adaptive Particle Swarm Optimization – Gaussian mixture model (APSO-GMM), lung nodule segmentation on the basis of Adaptive Particle Swarm Optimization – gamma mixture model (APSO-GaMM), lung nodule segmentation based on statistical information and self-selected mixed distribution model, and lung nodule segmentation based on neighborhood information and self-selected mixed distribution model. The segmentation effect is evaluated. Results: Compared with the results of lung nodule segmentation based on statistical information and self-selected mixed distribution model, the Dice coefficient of lung nodule segmentation based on neighborhood information and self-selected mixed distribution model is higher, the relative final measurement accuracy is smaller, the segmentation is more accurate, but the running time is longer. Compared with APSO-GMM and APSO-GaMM, the dice value of self-selected mixed distribution model segmentation method is larger, and the final measurement accuracy is smaller. Conclusion: Among the five methods, the dice value of the self-selected mixed distribution model based on neighborhood information is the largest, and the relative accuracy of the final measurement is the smallest, indicating that the segmentation effect of the self-selected mixed distribution model based on neighborhood information is the best.

A Mechanism for Sketch Based Image Retrievals using Generalized Gamma Mixture Model (GGMM) and Relevance Feedback Mechanism

The exponential growth of multimedia technologies facilitated the ease of developing various images having different shapes and scales. With the advent of mobile technologies, these messages so generated are being transmitted across the globe in different formats for different purposes. With these advancements methodologies thus developed for identifying or expressing subjects (individuals) their views by means of sketches. These sketch based images have many advantages, in particular, these images can be well considered in situations where the narration and capturing becomes difficult. The present article underlines a mechanism to interpret the images and also addresses the retrieval of such sketch based images using Generalized Gamma Mixture Model. The relevance feedback mechanism is utilized to retrieve more relevant to sketch based images based on the query image. The efficiency of the proposed word is evaluated using metrics like precision, recall, error rate, and retrieval accuracy.

A Novel Methodology for Efficient Retrievals of Sketch Based Images using Local Binary Patterns and Generalized Gamma Mixture Models (GGMM)

The enormous work in Information technology sector met towards the development of methodologies for identifying or retrieving the images based on content. However in specific conditions narration is the best suitable way to express and hence basing the views of narration sketch based images are thus developed and utilized. These sketch based images are most useful in criminal investigations. The present article portrays a methodology for retrieving such sketch based images using the statistical modeling approaches.

Fitting Gamma Mixture Density Networks with Expectation-Maximization Algorithm

We discuss how mixtures of Gamma distributions with mixing probabilities, shape and rate parameters depending on features can be fitted with neural networks. We develop two versions of the EM algorithm for fitting so-called Gamma Mixture Density Networks, which we call the EM network boosting algorithm and the EM forward network algorithm, and we test their implementation together with the choices of hyperparameters. A simulation study shows that our algorithms perform very well on synthetic data sets. We further illustrate the application of the Gamma Mixture Density Network on a real data set of motor insurance claim amounts and conclude that Gamma Mixture Density Networks can improve the fit of the regression model and the predictions of the claim severities used for rate-making compared to classical actuarial techniques.

A new extreme value copula and new families of univariate distributions based on Freund’s exponential model

Abstract The use of the exponential distribution and its multivariate generalizations is extremely popular in lifetime modeling. Freund’s bivariate exponential model (1961) is based on the idea that the remaining lifetime of any entity in a bivariate system is shortened when the other entity defaults. Such a model can be quite useful for studying systemic risk, for instance in financial systems. Guzmics and Pflug (2019) revisited Freund’s model, deriving the corresponding bivariate copula and examined some characteristics of it; furthermore, we opened the door for a multivariate setting. Now we present further investigations in the bivariate model: we compute the tail dependence coefficients, we examine the marginal and joint distributions of the componentwise maxima, which leads to an extreme value copula, which – to the best of our knowledge – has not been investigated in the literature yet. The original bivariate model of Freund has been extended to more variables by several authors. We also turn to the multivariate setting, and our focus is different from that of the previous generalizations, and therefore it is novel: examining the distribution of the sum and of the average of the lifetime variables (provided that the shock parameters are all the same) leads to new families of univariate distributions, which we call Exponential Gamma Mixture Type I and Type II (EGM) distributions. We present their basic properties, we provide asymptotics for them, and finally we also provide the limiting distribution for the EGM Type II distribution.

Shannon Entropy for the $\mathcal {G}^0_I$ Model: A New Segmentation Approach

Synthetic aperture radar (SAR) has been successfully used as a remote sensing tool. However, SAR images are contaminated by speckle noise and require specialized postprocessing procedures; e.g, tailored segmenters. The G <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sup> distribution is a flexible model for SAR intensities because of its ability at describing heterogeneous clutters. Furthermore, applying information theory measures (e.g., entropy) to extract features in SAR imagery processing has achieved a prominent position. In this article, we derive both a closed-form expression for the G <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sup> Shannon entropy and some of its mathematical properties. Consequently new entropy-based segmentation procedures for multidimensional SAR intensities-assuming independence or some dependence pattern-are also proposed. Finally, applications to real SAR imagery point out the proposed entropy-based segmenters can be more efficient than other well-defined methods, like the clustering by gamma mixture models.

Sparse Travel Time Estimation from Streaming Data

We address two shortcomings in online travel time estimation methods for congested urban traffic. The first shortcoming is related to the determination of the number of mixture modes, which can change dynamically within a day and from day to day. The second shortcoming is the widespread use of Gaussian probability densities as mixture components. Gaussian densities fail to capture the positive skew in travel time distributions, and consequently, large numbers of mixture components are needed for reasonable fitting accuracy when applied as mixture components. They also assign positive probabilities to negative travel times. To address these issues, this paper derives a mixture distribution with Gamma component densities, which are asymmetric and supported on the positive numbers. We use sparse estimation techniques to ensure parsimonious models and propose a generalization of Gamma mixture densities using Mittag–Leffler functions that provides enhanced fitting flexibility and improved parsimony. In order to accommodate within-day variability and allow for online implementation of the proposed methodology (i.e., fast computations on streaming travel time data), we introduce a recursive algorithm that efficiently updates the fitted distribution whenever new data become available. Experimental results using real-world travel time data illustrate the efficacy of the proposed methods.

Advanced spatial modulation for efficient MIMO‐based B2B communications in sporting activities

In this study, advanced multiple-input multiple-output (MIMO) techniques for body-to-body (B2B) sensor-based communication for sporting activities like running and cycling under different scenarios have been proposed. Enhanced spatial modulation and spatial media-based modulation have been investigated for efficient MIMO-based B2B communication. Special sensors have been proposed to deploy such techniques. Lognormal (LN) mixture model has been used because it can address the shadowing effects in B2B communication for such activities. Since LN mixture cannot yield closed-form expressions, it has been approximated using mixture of gamma (MG) distribution to achieve closed-form expressions for bit error rate (BER) in MIMO-based B2B communication for the first time. The system performance for the proposed methods has been analysed in terms of BER and theoretical upper bound expressions using MG distribution have been verified by Monte Carlo simulations.

A hierarchical Gamma Mixture Model-based method for estimating the number of clusters in complex data

This paper proposes a new method for estimating the true number of clusters and initial cluster centers in a dataset with many clusters. The observation points are assigned to the data space to observe the clusters through the distributions of the distances between the observation points and the objects in the dataset. A Gamma Mixture Model (GMM) is built from a distance distribution to partition the dataset into subsets, and a GMM tree is obtained by recursively partitioning the dataset. From the leaves of the GMM tree, a set of initial cluster centers are identified and the true number of clusters is estimated. This method is implemented in the new GMM-Tree algorithm. Two GMM forest algorithms are further proposed to ensemble multiple GMM trees to handle high dimensional data with many clusters. The GMM-P-Forest algorithm builds GMM trees in parallel, whereas the GMM-S-Forest algorithm uses a sequential process to build a GMM forest. Experiments were conducted on 32 synthetic datasets and 15 real datasets to evaluate the performance of the new algorithms. The results have shown that the proposed algorithms outperformed the existing popular methods: Silhouette, Elbow and Gap Statistic, and the recent method I-nice in estimating the true number of clusters from high dimensional complex data.

Aircraft Detection for HR SAR Images in Non‐homogeneous Background Using GGMD‐Based Modeling

In the problem of aircraft detection for High resolution (HR) Synthetic aperture radar (SAR) images, the background areas commonly contain multiple land cover types, such as runways and grassland. The conventional Constant false alarm rate (CFAR) detection in these non-homogeneous backgrounds with homogeneous assumption leads to unreliable detection results. This paper constructs a one-stage detection method based on the Generalized gamma mixture distribution (GGMD), which is regarded as a competitive and applicable model for combining the advantages of the Generalized gamma distribution (GGD) and the Finite mixture model (FMM). In order to evaluate the availability of the proposed algorithm, HR SAR images for aircraft detection from different product types and with various resolutions are examined. Compared with the CFAR algorithms based on the Gamma distribution, the GGD, and the gamma mixture distribution, the proposed algorithm demonstrates its availability and effectiveness for aircraft detection in HR SAR images in non-homogeneous background.

A quantitative approach for assessing bark beetle infestations: A study of Pityokteines spinidens Reitt. egg gallery densities in windthrown Abies alba Mill.

Abstract The presented statistical method enables monitoring of bark beetles that colonise different parts of the windthrown tree stem at different densities. The bark beetle, Pityokteines spinidens Reitt. occurring in forests with the fir Abies alba Mill. was used as an example. We propose a three-step statistical procedure. In the first step, a hierarchical cluster analysis (HCA), the single gamma function, and the gamma mixture distributions are used to model the distribution of egg galleries of P. spinidens along an A. alba windthrown stem. In the second step, a generalised linear model (GLM) and a generalised additive model (GAM) are employed to analyse the relationships between the number of P. spinidens egg galleries in selected stem sections and the total P. spinidens egg gallery density on the entire A. alba windthrown stem. In the third step, the mean total P. spinidens egg gallery density in the investigated area is estimated using survey sampling with simple random sampling without replacement (SRSWOR). The first and second steps allow us to identify which sections of the A. alba windthrown stem should be evaluated to adequately estimate the total egg gallery density (to save time and money and to reduce the amount of debarking performed per tree). The third step enables the calculation of the estimated relative standard error (to analyse the precision of the proposed method). Data were collected between 1994 and 2003 (data set D1) and in 2014 (data set D2) in forests including A. alba in the Świetokrzyski National Park, Poland. D1 was used to build the GLM and GAM, while D2 was employed to validate the models and to illustrate the proposed method. Six main types of egg gallery distributions along the stem were distinguished. P. spinidens inhabited all parts of the stem of A. alba windthrowns. Validation of the models suggested that the GAM performed better than the GLM. The predicted and observed data were closely consistent. This statistical evaluation of P. spinidens egg gallery densities will aid in the assessment of the ecological roles played by this species in A. alba ecosystems. Similar statistical approaches can be developed for other bark beetles colonising tree stems.

Fumaric Acids Do Not Directly Influence Gene Expression of Neuroprotective Factors in Highly Purified Rodent Astrocytes.

(1) Background: Dimethylfumarate (DMF) has been approved for the treatment of relapsing remitting multiple sclerosis. However, the mode of action of DMF and its assumed active primary metabolite monomethylfumarate (MMF) is still not fully understood. Former reports suggest a neuroprotective effect of DMF mediated via astrocytes by reducing pro-inflammatory activation of these glial cells. We investigated potential direct effects of DMF and MMF on neuroprotective factors like neurotrophic factors and growth factors in astrocytes to elucidate further possible mechanisms of the mode of action of fumaric acids; (2) Methods: highly purified cultures of primary rat astrocytes were pre-treated in vitro with DMF or MMF and incubated with lipopolysaccharides (LPS) or a mixture of interferon gamma (IFN-γ) plus interleukin 1 beta (IL-1β) in order to simulate an inflammatory environment. The gene expression of neuroprotective factors such as neurotrophic factors (nuclear factor E2-related factor 2 (NGF), brain-derived neurotrophic factor (BDNF), glial cell-derived neurotrophic factor (GDNF)) and growth factors (fibroblast growth factor 2 (FGF2), platelet-derived growth factor subunit A (PDGFa), ciliary neurotrophic factor (CNTF)) as well as cytokines (tumor necrosis factor alpha (TNFα), interleukin 6 (IL-6), IL-1β, inducible nitric oxide synthase (iNOS)) was examined by determining the transcription level with real-time quantitative polymerase chain reaction (qPCR); (3) Results: The stimulation of highly purified astrocytes with either LPS or cytokines changed the expression profile of growth factors and pro- inflammatory factors. However, the expression was not altered by either DMF nor MMF in unstimulated or stimulated astrocytes; (4) Conclusions: There was no direct influence of fumaric acids on neuroprotective factors in highly purified primary rat astrocytes. This suggests that the proposed potential neuroprotective effect of fumaric acid is not mediated by direct stimulation of neurotrophic factors in astrocytes but is rather mediated by other pathways or indirect mechanisms via other glial cells like microglia as previously demonstrated.

A Hierarchical Gamma Mixture Model-Based Method for Classification of High-Dimensional Data

Data classification is an important research topic in the field of data mining. With the rapid development in social media sites and IoT devices, data have grown tremendously in volume and complexity, which has resulted in a lot of large and complex high-dimensional data. Classifying such high-dimensional complex data with a large number of classes has been a great challenge for current state-of-the-art methods. This paper presents a novel, hierarchical, gamma mixture model-based unsupervised method for classifying high-dimensional data with a large number of classes. In this method, we first partition the features of the dataset into feature strata by using k-means. Then, a set of subspace data sets is generated from the feature strata by using the stratified subspace sampling method. After that, the GMM Tree algorithm is used to identify the number of clusters and initial clusters in each subspace dataset and passing these initial cluster centers to k-means to generate base subspace clustering results. Then, the subspace clustering result is integrated into an object cluster association (OCA) matrix by using the link-based method. The ensemble clustering result is generated from the OCA matrix by the k-means algorithm with the number of clusters identified by the GMM Tree algorithm. After producing the ensemble clustering result, the dominant class label is assigned to each cluster after computing the purity. A classification is made on the object by computing the distance between the new object and the center of each cluster in the classifier, and the class label of the cluster is assigned to the new object which has the shortest distance. A series of experiments were conducted on twelve synthetic and eight real-world data sets, with different numbers of classes, features, and objects. The experimental results have shown that the new method outperforms other state-of-the-art techniques to classify data in most of the data sets.

A Unique Procedure for Accurate Recognition of Software Failures A Software Reliability Growth Model Based on Special Case of Generalized Gamma Mixture Model

This paper pinpoints to detect and eliminate the actual software failures efficiently. The approach fit in a particular case of Generalized Gamma Mixture Model (GGMM), namely Weibull distribution. The approach estimates two parameters using Maximum Likelihood Estimate (MLE). Standard Evaluation metrics like Mean Square Error (MSE), Coefficient of Determination (R2), Sum of Squares (SSE), and Root Means Square Error (RMSE) were calculated. For the justification of the model selection and goodness of fit various model selection frameworks like Chi-Square Goodness of Fit, Wald’s Test, Akaike Information Criteria (AIC), AICc and Schwarz criterion (SBC) were also estimated. The experimentation was carried out on five benchmark datasets which interpret the considered novel technique identifies the actual failures on par with the existing models. This paper presents a novel software reliability growth model which is more effectual in the identification of the failures significantly and help the present software organizations in the release of software free from bugs just in time.

Performance Analysis of B2B Communication for Different Sporting Activities

In this article, body-to-body (B2B) communication has been investigated for different sporting activities in different scenarios. The B2B system performance has been analyzed in terms of outage probability and average symbol error probability (ASEP). Lognormal mixture distribution has been used as the channel model since it can suitably describe the shadowing effects in B2B communication. However, closed-form expressions are not achievable, so mixture of gamma (MG) distribution has been used to obtain closed-form expressions for this system. The analytical results have been validated by means of Monte Carlo simulations.

Premium rate determination of crop insurance product based on rainfall index consideration

Crop insurance product based on rainfall index is an alternative product to minimize the risk in the agricultural sector. Rainfall index is supposed to represent crop failure in a specific area. Rainfall index is composed of parameters, trigger, and exit. The trigger is a benchmark value of rainfall that causes the partial risk and gives the right to the policyholder to begin partial benefit payment. The exit is the benchmark value of rainfall that consists of total crop failure and assigns the right to the policyholder to submit full benefit claim. The trigger and the exit in a rainfall index provide the value of the premium. A case study is carried out with cumulative rainfall data from June to August in the Dramaga area of Bogor from 1984 until 2017 to ensure paddy. The two-component Gamma Mixture distribution model is applied to determine the rate of premium that must be paid by the policyholder on the specified rainfall index.

A Censored Shifted Mixture Distribution Mapping Method to Correct the Bias of Daily IMERG Satellite Precipitation Estimates

Satellite precipitation estimates (SPE) provide useful input for hydrological modeling. However, hydrological modeling is frequently hindered by large bias and errors in SPE, inducing the necessity for bias corrections. Traditional distribution mapping bias correction of daily precipitation commonly uses Bernoulli and gamma distributions to separately model the probability and intensities of precipitation and is insufficient towards extremes. This study developed an improved distribution mapping bias correction method, which established a censored shifted mixture distribution (CSMD) as a transfer function when mapping raw precipitation to the reference data. CSMD coupled the censored shifted statistical distribution to jointly model both the precipitation occurrence probability and intensity with a mixture of gamma and generalized Pareto distributions to enhance extreme-value modeling. The CSMD approach was applied to correct the up-to-date SPE of Integrated Multi-satelliE Retrievals for Global Precipitation Measurement (GPM) with near-real-time “Early” run (IMERG-E) over the Yangtze River basin. To verify the hydrological response of bias-corrected IMERG-E, the streamflow of the Wujiang River basin was simulated using Ge´nie Rural with 6 parameters (GR6J) and Coupled Routing Excess Storage (CREST) models. The results showed that the bias correction using both BerGam (traditional bias correction combining Bernoulli with gamma distributions) and the improved CSMD could reduce the systematic errors of IMERG-E. Furthermore, CSMD outperformed BerGam in correcting overall precipitation (with the median of mean absolute errors of 2.46 mm versus 2.81 mm for CSMD and BerGam respectively, and the median of modified Nash–Sutcliffe efficiency of 0.39 versus 0.29) and especially in extreme values for uniform format and particular attention paid to extremes. In addition, the hydrological effect that CSMD correction exerted on IMERG-E, driving GR6J and CREST rainfall-runoff modeling, outperformed that of the BerGam correction. This study provides a promising integrated distribution mapping framework to correct the biased daily SPE, contributing to more reliable hydrological forecasts by informing accurate precipitation forcing.