Parameters Of Mixture Model Research Articles

Carrier phase error overbounding using Gaussian mixture model for high-precision air navigation integrity monitoring

Carrier phase measurements play a pivotal role in enabling high-precision positioning within future air traffic systems and autonomous vehicles. Current aviation navigation integrity monitoring, primarily using pseudorange measurements, cannot meet system positioning accuracy and integrity requirements, leading to limitations and false alarm risks, especially in complex urban canyons with signal reflections. This work presents a carrier phase-based positioning integrity monitoring algorithm, utilizing the expectation–maximization algorithm to compute parameters for the Gaussian mixture model (GMM) and nonparametric bootstrapping to construct an overbounding model of carrier phase residuals. It establishes a precise protection level (PL) calculation method, which is validated with static and flight data, demonstrating accurate overbounding of carrier phase residuals using GMM. Protection levels during testing remain below the alarm limit and exceed system positioning error, ensuring normal system operation without false or missed alarms, confirming the effectiveness of the established carrier phase error overbounding model.

Bayesian mixture modelling with ranked set samples.

We consider the Bayesian estimation of the parameters of a finite mixture model from independent order statistics arising from imperfect ranked set sampling designs. As a cost-effective method, ranked set sampling enables us to incorporate easily attainable characteristics, as ranking information, into data collection and Bayesian estimation. To handle the special structure of the ranked set samples, we develop a Bayesian estimation approach exploiting the Expectation-Maximization (EM) algorithm in estimating the ranking parameters and Metropolis within Gibbs Sampling to estimate the parameters of the underlying mixture model. Our findings show that the proposed RSS-based Bayesian estimation method outperforms the commonly used Bayesian counterpart using simple random sampling. The developed method is finally applied to estimate the bone disorder status of women aged 50 and older.

Dynamic simulation-assisted Gaussian mixture alignment approach for fault diagnosis of rotation machinery under small samples

Abstract Obtaining a substantial number of actual samples for rotating machinery in an industrial setting can be challenging, particularly when faulty samples are acquired under hazardous working conditions. The issue of insufficient samples hinders the effective training of reliable fault diagnosis models, impeding the industrial implementation of advanced intelligent methods. This study proposes an innovative dynamic simulation-assisted Gaussian mixture alignment model (DSGMA) to address the challenge of applying fault diagnosis technologies, with its performance mined by advanced transfer algorithms. Specifically, we establish a fault dynamics model for rotating machinery and acquire a substantial amount of simulated data as the source domain to facilitate the training of the deep neural network model. Subsequently, we propose a Gaussian mixture-guided domain alignment approach that assigns a domain-independent Gaussian distribution to each category as prior knowledge, with the parameters calculated using limited actual samples. Diagnostic knowledge is transferred from the source domain to the target domain by minimizing the Kullback–Leibler divergence between the features of the simulated samples and the Gaussian mixture priors. Furthermore, the DSGMA model incorporates Gaussian clustering loss to augment the clustering capability of samples belonging to the same category from real devices and enhances the computational stability of the parameters in the Gaussian mixture model. The efficacy of the DSGMA method is validated using three publicly available datasets and compared against five widely adopted methods. The experimental findings illustrate that DSGMA exhibits superior diagnostic and robust capabilities, facilitating efficient fault diagnosis under scenarios of small samples.

Optimum Designs for Optimum Mixtures: An Informative Review

In a mixture experiment, the measured response is assumed to depend only on the relative proportions of ingredients or components present in the mixture. Scheffe´ (1958) first systematically considered this problem, and introduced different models and suitable designs. Optimum designs for the estimation of parameters in various mixture models are available in the literature. However, in a mixture experiment, interest is likely to be more on the optimum mixing proportions of the ingredients being used. In this exposition, we take the readers on a journey through the optimum designs developed for estimating the optimum mixture combination as accurately as possible under various mixture models. International Journal of Statistical Sciences, Vol.24(1), March, 2024, pp 1-14

Principal Component Analysis Enhanced with Bootstrapped Confidence Interval for the Classification of Parkinsonian Patients Using Gaussian Mixture Model and Gait Initiation Parameters.

Parkinson's disease is one of the major neurodegenerative diseases that affects the postural stability of patients, especially during gait initiation. There is actually an increasing demand for the development of new non-pharmacological tools that can easily classify healthy/affected patients as well as the degree of evolution of the disease. The experimental characterization of gait initiation (GI) is usually done through the simultaneous acquisition of about 20 variables, resulting in very large datasets. Dimension reduction tools are therefore suitable, considering the complexity of the physiological processes involved. The principal Component Analysis (PCA) is very powerful at reducing the dimensionality of large datasets and emphasizing correlations between variables. In this paper, the Principal Component Analysis (PCA) was enhanced with bootstrapping and applied to the study of the GI to identify the 3 majors sets of variables influencing the postural control disability of Parkinsonian patients during GI. We show that the combination of these methods can lead to a significant improvement in the unsupervised classification of healthy/affected patients using a Gaussian mixture model, since it leads to a reduced confidence interval on the estimated parameters. The benefits of this method for the identification and study of the efficiency of potential treatments is not addressed in this paper but could be addressed in future works.

Retracted: Simulation of Tennis Match Scene Classification Algorithm Based on Adaptive Gaussian Mixture Model Parameter Estimation

Retracted: Simulation of Tennis Match Scene Classification Algorithm Based on Adaptive Gaussian Mixture Model Parameter Estimation

Application of the k-Means Algorithm and the Gaussian Mixture Model (GMM) – African Vulture Optimization Algorithm (AVOA) for the Resolution of Overlapping Energy-Dispersive X-Ray Fluorescence (EDXRF) Peaks

Limitations in instrument resolution mean that soil samples analysis using energy-dispersive X-ray fluorescence (EDXRF) often produced overlapping spectral peaks of heavy metals with similar energies. This overlapping of spectral peaks posed a significant problem in the quantitative analysis of heavy metals in soil samples. Therefore, it was necessary to decompose the overlapping peaks. In this paper, a new method for decomposing overlapping peaks was presented in the context of Gaussian Mixture Model (GMM) parameter estimation, combining the k-means algorithm and the African Vulture Optimization Algorithm (AVOA). The data acquired from EDXRF instruments were preprocessed before being input to the k-means algorithm, which produces the output used to initialize the parameters of the GMM. Subsequently, AVOA was employed to optimize the GMM parameters based on a fitness function derived from the data. Ultimately, the optimized GMM parameters obtained through the AVOA process yield the optimal solution for the decomposition of overlapping peaks. This approach effectively addressed the challenge of peak overlap in the determination of heavy metals in soil by EDXRF. Soil samples were obtained from national standard samples, peach gardens, and vegetable-growing regions. The results showed that the maximum absolute errors for the peak channel and peak area were 1.46% and 6.37%, respectively. A comparison of the proposed model with others models indicated that the k-means-GMM-AVOA model exhibits the best performance in terms of speed, accuracy, and stability.

An inverse fitting strategy to determine the constrained mixture model parameters: application in patient-specific aorta.

The Constrained Mixture Model (CMM) is a novel approach to describe arterial wall mechanics, whose formulation is based on a referential physiological state. The CMM considers the arterial wall as a mixture of load-bearing constituents, each of them with characteristic mass fraction, material properties, and deposition stretch levels from its stress-free state to the in-vivo configuration. Although some reports of this model successfully assess its capabilities, they barely explore experimental approaches to model patient-specific scenarios. In this sense, we propose an iterative fitting procedure of numerical-experimental nature to determine material parameters and deposition stretch values. To this end, the model has been implemented in a finite element framework, and it is calibrated using reported experimental data of descending thoracic aorta. The main results obtained from the proposed procedure consist of a set of material parameters for each constituent. Moreover, a relationship between deposition stretches and residual strain measurements (opening angle and axial stretch) has been numerically proved, establishing a strong consistency between the model and experimental data.

Mixture Model to Predict the Cumulative Incidence of Relapses in Follicular Lymphoma : Need for Longer Follow-up or Alternative Outcomes

Background: The effectiveness of treatments in follicular lymphoma is evaluated by the reduction in the rate of recurrence. One of the methodological difficulties is related to the presence of competitive events such as death or second primary malignancies. The related cumulative incidence functions (CIF) are always estimated by using the non-parametric Aalen-Johansen estimator and the associated predictors by using the Fine and Gray approach or by considering a cause-specific Cox model. In the present study, we investigated if the use of a parametric mixture model would provide additional information on the interpretation of the impact of treatments in the management of follicular lymphoma. Methods: We used the RELEVANCE study database (Morschhauser et al.NEJM 2018, JCO 2022) because of the prolonged follow-up of patients treated for follicular lymphoma. RELEVANCE study is a multicenter, phase 3 randomized clinical trial that evaluates rituximab lenalidomide (R 2) as compared to rituximab plus chemotherapy (R-chemo), in patients with previously untreated follicular lymphoma. All 1030 patients received a rituximab maintenance. Results: With a median follow up of 72 months, median progression-free survival (PFS) was not reached in both groups (Kaplan-Meier estimator): the 6-years PFS was 60% and 59% for R 2 and R-chemo, respectively (Cox model, HR = 1.03 [IC95% CI, 0.84 to 1.27]). The CIF of relapse at 72 months was 41% and 39% in the R 2 and R-chemo, respectively (Aalen-Johansen estimator, Figure 1). We did not highlight any significant difference between the treatments in terms of the CIF of relapse (Fine and Gray model, HR = 0.938 [IC95% CI, 0.754 to 1.17], for the same prognostic time, the CIF of death was 2,5% and 2,9% in the R 2 and R-chemo, respectively). We then performed the test with the mixture model, and confirmed there was no significant differences across groups at 72 months. Indeed, 64% and 96% of patients have not relapsed and died respectively. However the mixture model approach allows for extrapolation, and thus we predicted the long-term CIF of relapse to be 67% if patients were followed-up 20 years across groups. The mixture model extrapolation calculated that 60% of relapse would occurr between 72 months and 240 months (20 years). Conclusion: There was no difference at 72 months for survival across tests; but the mixture model, that allow extrapolation, suggested that a difference could be revealed with a greater follow-up. We concluded that future studies of survival in FL will require longer follow-up. This comment appears of particular importance in the context of the forthcoming immunotherapies such as bispecific and CAR-T cells. We can also propose for hematologic malignancies with a chronic evolution, FL, alternative primary outcomes not based on survival, allowing a shorter read out, such as the disability-adjusted life years (DALYs) or quality-adjusted life years (QALYs).

Smart Grid Outlier Detection Based on the Minorization-Maximization Algorithm.

Outliers can be generated in the power system due to aging system equipment, faulty sensors, incorrect line connections, etc. The existence of these outliers will pose a threat to the safe operation of the power system, reduce the quality of the data, affect the completeness and accuracy of the data, and thus affect the monitoring analysis and control of the power system. Therefore, timely identification and treatment of outliers are essential to ensure stable and reliable operation of the power system. In this paper, we consider the problem of detecting and localizing outliers in power systems. The paper proposes a Minorization-Maximization (MM) algorithm for outlier detection and localization and an estimation of unknown parameters of the Gaussian mixture model (GMM). To verify the performance of the method, we conduct simulation experiments by simulating different test scenarios in the IEEE 14-bus system. Numerical examples show that in the presence of outliers, the MM algorithm can detect outliers better than the traditional algorithm and can accurately locate outliers with a probability of more than 95%. Therefore, the algorithm provides an effective method for the handling of outliers in the power system, which helps to improve the monitoring analyzing and controlling ability of the power system and to ensure the stable and reliable operation of the power system.

Data-Weighted Multivariate Generalized Gaussian Mixture Model: Application to Point Cloud Robust Registration.

In this paper, a weighted multivariate generalized Gaussian mixture model combined with stochastic optimization is proposed for point cloud registration. The mixture model parameters of the target scene and the scene to be registered are updated iteratively by the fixed point method under the framework of the EM algorithm, and the number of components is determined based on the minimum message length criterion (MML). The KL divergence between these two mixture models is utilized as the loss function for stochastic optimization to find the optimal parameters of the transformation model. The self-built point clouds are used to evaluate the performance of the proposed algorithm on rigid registration. Experiments demonstrate that the algorithm dramatically reduces the impact of noise and outliers and effectively extracts the key features of the data-intensive regions.

ComBat Harmonization of Myocardial Radiomic Features Sensitive to Cardiac MRI Acquisition Parameters.

To investigate the effect of ComBat harmonization methods on the robustness of cardiac MRI-derived radiomic features to variations in imaging parameters. This Health Insurance Portability and Accountability Act-compliant retrospective study used a publicly available data set of 11 healthy controls (mean age, 33 years ± 16 [SD]; six men) and five patients (mean age, 52 years ± 16; four men). A single midventricular short-axis section was acquired with 3-T MRI using cine balanced steady-state free precision, T1-weighted, T2-weighted, T1 mapping, and T2 mapping imaging sequences. Each sequence was acquired using baseline parameters and after variations in flip angle, spatial resolution, section thickness, and parallel imaging. Image registration was performed for all sequences at a per-individual level. Manual myocardial contouring was performed, and 1652 radiomic features per sequence were extracted using baseline and variations in imaging parameters. Radiomic feature stability to change in imaging parameters was assessed using Cohen d sensitivity. The stability of radiomic features was assessed both without and after ComBat harmonization of radiomic features. Three ComBat methods were studied: parametric, nonparametric, and Gaussian mixture model (GMM). For all sequences combined, 51.4% of features were robust to changes in imaging parameters when no ComBat method was applied. ComBat harmonization substantially increased the number of stable features to 95.1% (95% CI: 94.9, 95.3) when parametric ComBat was used and 90.9% (95% CI: 90.6, 91.2) when nonparametric ComBat was used. GMM combat resulted in only 52.6% stable features. ComBat harmonization improved the stability of radiomic features to changes in imaging parameters across all cardiac MRI sequences.Keywords: Cardiac MRI, Radiomics, ComBat, Harmonization Supplemental material is available for this article. © RSNA, 2023.

MSR53 Bayesian Parametric Mixture Survival Models in Immuno-Oncology Applications: Leveraging Control Arm Observations to Model Heterogeneous Response in the Experimental Arm

Heterogeneous response to an intervention is a common feature of survival patterns in randomized clinical trials (RCTs) of immuno-oncology therapies. This effect is usually inadequately represented by standard parametric models. Instead, it is desirable to employ parametric mixture models (PMMs), which represent the cohort as a combination of two latent subpopulations with distinct survival curves. However, classical PMMs are often too complex to parameterize reliably given the limited observations in RCT data.

A new iterative initialization of EM algorithm for Gaussian mixture models.

The expectation maximization (EM) algorithm is a common tool for estimating the parameters of Gaussian mixture models (GMM). However, it is highly sensitive to initial value and easily gets trapped in a local optimum. To address these problems, a new iterative method of EM initialization (MRIPEM) is proposed in this paper. It incorporates the ideas of multiple restarts, iterations and clustering. In particular, the mean vector and covariance matrix of sample are calculated as the initial values of the iteration. Then, the optimal feature vector is selected from the candidate feature vectors by the maximum Mahalanobis distance as a new partition vector for clustering. The parameter values are renewed continuously according to the clustering results. To verify the applicability of the MRIPEM, we compared it with other two popular initialization methods on simulated and real datasets, respectively. The comparison results of the three stochastic algorithms indicate that MRIPEM algorithm is comparable in relatively high dimensions and high overlaps and significantly better in low dimensions and low overlaps.

Gaussian mixture modeling of acceleration-derived signal for monitoring external physical load of tennis player.

Introduction: With the widespread use of wearable sensors, various methods to evaluate external physical loads using acceleration signals measured by inertial sensors in sporting activities have been proposed. Acceleration-derived external physical loads have been evaluated as a simple indicator, such as the mean or cumulative values of the target interval. However, such a conventional simplified indicator may not adequately represent the features of the external physical load in sporting activities involving various movement intensities. Therefore, we propose a method to evaluate the external physical load of tennis player based on the histogram of acceleration-derived signal obtained from wearable inertial sensors. Methods: Twenty-eight matches of 14 male collegiate players and 55 matches of 55 male middle-aged players wore sportswear-type wearable sensors during official tennis matches. The norm of the three-dimensional acceleration signal measured using the wearable sensor was smoothed, and the rest period (less than 0.3G of at least 5s) was excluded. Because the histogram of the processed acceleration signal showed a bimodal distribution, for example, high- and low-intensity peaks, a Gaussian mixture model was fitted to the histogram, and the model parameters were obtained to characterize the bimodal distribution of the acceleration signal for each player. Results: Among the obtained Gaussian mixture model parameters, the linear discrimination analysis revealed that the mean and standard deviation of the high-intensity side acceleration value accurately classified collegiate and middle-aged players with 93% accuracy; however, the conventional method (only the overall mean) showed less accurate classification results (63%). Conclusion: The mean and standard deviation of the high-intensity side extracted by the Gaussian mixture modeling is found to be the effective parameter representing the external physical load of tennis players. The histogram-based feature extraction of the acceleration-derived signal that exhibit multimodal distribution may provide a novel insight into monitoring external physical load in other sporting activities.

Network Inference Using the Hub Model and Variants

Statistical network analysis primarily focuses on inferring the parameters of an observed network. In many applications, especially in the social sciences, the observed data is the groups formed by individual subjects. In these applications, the network is itself a parameter of a statistical model. Zhao and Weko propose a model-based approach, called the hub model, to infer implicit networks from grouping behavior. The hub model assumes that each member of the group is brought together by a member of the group called the hub. The set of members which can serve as a hub is called the hub set. The hub model belongs to the family of Bernoulli mixture models. Identifiability of Bernoulli mixture model parameters is a notoriously difficult problem. This article proves identifiability of the hub model parameters and estimation consistency under mild conditions. Furthermore, this article generalizes the hub model by introducing a model component that allows hubless groups in which individual nodes spontaneously appear independent of any other individual. We refer to this additional component as the null component. The new model bridges the gap between the hub model and the degenerate case of the mixture model—the Bernoulli product. Identifiability and consistency are also proved for the new model. In addition, a penalized likelihood approach is proposed to estimate the hub set when it is unknown. Supplementary materials for this article are available online.

Impact of Extrapolation Model Choices on the Structural Uncertainty in Economic Evaluations for Cancer Immunotherapy: A Case Study of Checkmate067.

The aim of this study was to compare the performance of different extrapolation modeling techniques and analyze their impact on structural uncertainties in the economic evaluations of cancer immunotherapy. The individual patient data was reconstructed through published Checkmate067 Kaplan Meier curves. Standard parametric models and six flexible techniques were tested, including fractional polynomial, restricted cubic splines, Royston-Parmar models, generalized additive models, parametric mixture models, and mixture cure models. Mean square errors (MSE) and bias from raw survival plots were used to test the model fitness and extrapolation performance. Variability of estimated incremental cost-effectiveness ratios (ICERs) from different models was used to inform the structural uncertainty in economic evaluations. All indicators were analyzed and compared under cut-offs of 3 years and 6.5 years, respectively, to further discuss model impact under different data maturity. R Codes for reproducing this study can be found on GitHub. The flexible techniques in general performed better than standard parametric models with smaller MSE irrespective of the data maturity. Survival outcomes projected by long-term extrapolation using immature data differed from those with mature data. Although a best-performing model was not found because several models had very similar MSE in this case, the variability of modeled ICERs significantly increased when prolonging simulation cycles. Flexible techniques show better performance in the case of Checkmate067, regardless of data maturity. Model choices affect ICERs of cancer immunotherapy, especially when dealing with immature survival data. When researchers lack evidence to identify the 'right' model, we recommend identifying and revealing the model impacts on structural uncertainty.

IoT Anomaly Detection Based on Autoencoder and Bayesian Gaussian Mixture Model

The Internet of Things (IoT) is increasingly providing industrial production objects to connect with the physical world and has been widely used in various fields. Although it has brought great industrial convenience, there are also potential security threats due to the vulnerabilities and malicious nodes in IoT. To correctly identify the traffic of malicious nodes in IoT and reduce the damage caused by malicious attacks on IoT devices, this paper proposes an autoencoder-based IoT malicious node detection method. The contributions of this paper are as follows: firstly, the high complexity multi-featured traffic data are processed and dimensionally reduced through the autoencoder to obtain the low-dimensional feature data. Then, the Bayesian Gaussian mixture model is adopted to cluster the data in a low-dimensional space to detect anomalies. Furthermore, the method of variational inference is used to estimate the parameters in the Bayesian Gaussian mixture model. To evaluate our model’s effectiveness, we used a public dataset for our experiments. As a result, in the experiment, the proposed method achieves a high accuracy rate of 99% distinguishing normal and abnormal traffic with three-dimension data reduced by the autoencoder, and it establishes our model’s better detection performance compared with previous K-means and Gaussian Mixture Model (GMM) solutions.

A deep architecture for log-Euclidean Fisher vector end-to-end learning with application to 3D point cloud classification

Point clouds are a widely used form of 3D data, which can be produced by depth sensors, such as RGB-D cameras. The classification of common elements of 3D point clouds remains an open research problem.We propose a new deep network approach for the end-to-end training of log-Euclidean Fisher vectors (LE-FVs), applied to the classification of 3D point clouds. Our method uses a log-Euclidean (LE) metric in order to extend the concept of Fisher vectors (FVs) to LE-FV encoding. The LE-FV was computed on covariance matrices of local 3D point cloud descriptors, representing multiple features. Our architecture is composed of two blocks. The first one aims to map the covariance matrices representing the 3D point cloud descriptors to the Euclidean space. The second block allows for joint and simultaneous learning of LE-FV Gaussian Mixture Model (GMM) parameters, LE-FV dimensionality reduction, and multi-label classification.Our LE-FV deep learning model is more accurate than the FV deep learning architecture. Additionally, the introduction of joint learning of 3D point cloud features in the log-Euclidean space, including LE-FV GMM parameters, LE-FV dimensionality reduction, and multi-label classification greatly improves the accuracy of classification. Our method has also been compared with the most popular methods in the literature for 3D point cloud classification, and it achieved good performance. The quantitative evidence will be shown through different experiments.

Handling parametric assumptions in principal causal effect estimation using Gaussian mixtures.

Given the latent stratum membership, principal stratification models with continuous outcomes naturally fit in the parametric estimation framework of Gaussian mixtures. However, with models that are not nonparametrically identified, relying on parametric mixture modeling has been mostly discouraged as a way of identifying principal effects. This study revisits this rather deserted use of parametric mixture modeling, which may open up various possibilities in principal stratification modeling. The main problem with using the parametric mixture modeling approach is that it is hard to assess the quality of principal effect estimates given its reliance on parametric conditions. As a way of assessing the estimation quality in this situation, this study proposes that we use parametric mixture modeling in two different ways, with and without the assurance of nonparametric identification. The key identifying assumption employed in this study is the moving exclusion restriction, a flexible version of the standard exclusion restriction assumption. This assumption is used as a temporary vehicle to help assess the quality of principal effect estimates obtained relying on parametric mixture modeling. The study presents promising results, showing the possibility of using parametric mixture modeling as an accessible tool for causal inference.