Gaussian Mixture Model Research Articles

A unified Bayesian framework for bias adjustment in multiple comparisons from clinical trials.

In clinical trials, multiple comparisons arising from various treatments/doses, subgroups, or endpoints are common. Typically, trial teams focus on the comparison showing the largest observed treatment effect, often involving a specific treatment pair and endpoint within a subgroup. These findings frequently lead to follow-up pivotal studies, many of which do not confirm the initial positive results. Selection bias occurs when the most promising treatment, subgroup, or endpoint is chosen for further development, potentially skewing subsequent investigations. Such bias can be defined as the deviation in the observed treatment effects from the underlying truth. In this article, we propose a general and unified Bayesian framework to address selection bias in clinical trials with multiple comparisons. Our approach does not require a priori specification of a parametric distribution for the prior, offering a more flexible and generalized solution. The proposed method facilitates a more accurate interpretation of clinical trial results by adjusting for such selection bias. Through simulation studies, we compared several methods and demonstrated their superior performance over the normal shrinkage estimator. We recommended the use of Bayesian Model Averaging estimator averaging over Gaussian Mixture Models as the prior distribution based on its performance and flexibility. We applied the method to a multicenter, randomized, double-blind, placebo-controlled study investigating the cardiovascular effects of dulaglutide.

A trajectory planning method for robotic arms based on improved dynamic motion primitives

Purpose Traditional robot arm trajectory planning methods have problems such as insufficient generalization performance and low adaptability. This paper aims to propose a method to plan the robot arm’s trajectory using the trajectory learning and generalization characteristics of dynamic motion primitives (DMPs). Design/methodology/approach This study aligns multiple demonstration motion primitives using dynamic time warping; use the Gaussian mixture model and Gaussian mixture regression methods to obtain the ideal primitive trajectory actions. By establishing a system model that improves DMPs, the parameters of the nonlinear function are learned based on the ideal primitive trajectory actions of the robotic arm, and the robotic arm motion trajectory is reproduced and generalized. Findings Experiments have proven that the robot arm motion trajectory learned by the method proposed in this article can not only learn to generalize and demonstrate the movement trend of the primitive trajectory, but also can better generate ideal motion trajectories and avoid obstacles when there are obstacles. The maximum Euclidean distance between the generated trajectory and the demonstration primitive trajectory is reduced by 29.9%, and the average Euclidean distance is reduced by 54.2%. This illustrates the feasibility of this method for robot arm trajectory planning. Originality/value It provides a new method for the trajectory planning of robotic arms in unstructured environments while improving the adaptability and generalization performance of robotic arms in trajectory planning.

Shoreline Extraction Methods from Sentinel-2 and PlanetScope Images

Abstract. This work aims to compare and assess the performance of certain methodologies for shoreline mapping based on the use of medium (10 m) and high resolution (3 m) multi-spectral imagery, provided by Sentinel-2 (S2) and PlanetScope (PS), respectively. Being Sentinel-2 part of the Copernicus missions, its data are freely available. PS imagery are also freely available for scientific research, upon approval by the European Space Agency of a related project proposal. Several spectral indices, including Normalized Difference Water Index (NDWI), Modified Normalized Difference Water Index (MNDWI), Automated Water Extraction Index (AWEI), and Water Index (WI), were used for shoreline detection. In particular, two unsupervised classification techniques, the Gaussian Mixture Model (GMM) and K-means clustering were deployed as shoreline extraction methods. The outcomes of such approaches were validated using reference shorelines derived from aerial orthomosaics, generated from images acquired as close as possible to the satellite imagery dates, and the ”baseline and transect” approach for accuracy verification. Three tide-less Mediterranean beaches were used as study cases for comparison: the beach between Castelldefels and Gava in Spain, Feniglia and Marina di Grosseto in Italy. The results demonstrated sub-pixel accuracy in shoreline extraction, with Mean Absolute Distances ranging from 2 m to 5 m for S2 data and 1.5 m to 2 m for PS data. These findings highlight the potential of freely available satellite data for semi-automatic shoreline detection. Results obtained by using the combination of different indices and methodologies show that the best option may change depending on the considered context, hence future investigations should be dedicated to the development of a procedure for automatically determining the context-based (close to) optimal index-classifier combination.

COSGAP: COntainerized statistical genetics analysis pipelines

Abstract The collection and analysis of sensitive data in large-scale consortia for statistical genetics is hampered by multiple challenges, due to their non-shareable nature. Time-consuming issues in installing software frequently arise due to different operating systems, software dependencies, and limited internet access. For federated analysis across sites, it can be challenging to resolve different problems, including format requirements, data wrangling, setting up analysis on high-performance computing facilities, etc. Easier, more standardized, automated protocols and pipelines can be solutions to overcome these issues. We have developed one such solution for statistical genetic data analysis using software container technologies. This solution, named COSGAP: “COntainerized Statistical Genetics Analysis Pipelines”, consists of already established software tools placed into Singularity containers, alongside corresponding code and instructions on how to perform statistical genetic analyses, such as genome-wide association studies, polygenic scoring, LD score regression, Gaussian Mixture Models, and gene-set analysis. Using provided helper scripts written in Python, users can obtain auto-generated scripts to conduct the desired analysis either on HPC facilities or on a personal computer. COSGAP is actively being applied by users from different countries and projects to conduct genetic data analyses without spending much effort on software installation, converting data formats, and other technical requirements. Availability COSGAP is freely available on GitHub (https://github.com/comorment/containers) under the GPLv3 license.

Interspecific and intraspecific difference in egg size of two mackerel (Scomber spp.) species in relation to sea surface temperature in the western North Pacific: A new approach to species identification

AbstractChub mackerel (Scomber japonicus, Scombridae) and blue mackerel (Scomber australasicus) are two important fishery resources in the western North Pacific that spawn eggs during the same season. Although estimating the total egg production (TEP) is important for evaluating the spawning stock biomass of mackerel species, it is difficult to accurately identify formalin‐preserved eggs collected during ichthyoplankton surveys. Hence, a new identification criterion that incorporates the effects of water temperature on egg size was developed in this study. The diameter of 37,304 mackerel eggs collected over 16 years (2006–2021) was measured, and frequency distributions of egg size across sea surface temperature (SST) ranges at 1°C interval were constructed. The frequency distributions were classified into two groups using a Gaussian mixture model; based on the results of DNA analysis, the small group was chub mackerel, while the large group was blue mackerel. The SST at the sampling stations and the mean egg size of both groups were negatively correlated. The new identification criterion, incorporating the relationship between SST and egg size, provided reasonable estimates of the TEP of the two mackerel species compared with the conventional criterion. The new species identification approach is applicable to other fish taxa in the western North Pacific.

Predicting suicidality with small sets of interpretable reward behavior and survey variables

AbstractThe prediction of suicidal thought and behavior has met with mixed results. This study of 3,476 de-identified participants (4,019 before data exclusion) quantified the prediction of four suicidal thought and behavior (STB) variables using a short reward/aversion judgment task and a limited set of demographic and mental health surveys. The focus was to produce a simple, quick and objective framework for assessing STB that might be automatable, without the use of big data. A balanced random forest classifier performed better than a Gaussian mixture model and four standard machine learning classifiers for predicting passive suicide ideation, active suicide ideation, suicide planning and planning for safety. Accuracies ranged from 78% to 92% (optimal area under the curve between 0.80 and 0.95) without overfitting, and peak performance was observed for predicting suicide planning. The relative importance of features for prediction showed distinct weighting across judgment variables, contributing between 40% and 64% to prediction per Gini scores. Mediation/moderation analyses showed that depression, anxiety, loneliness and age variables moderated the judgment variables, indicating that the interaction of judgment with mental health and demographic indices is fundamental for the high-accuracy prediction of STB. These findings suggest the feasibility of an efficient and highly scalable system for suicide assessment, without requiring psychiatric records or neural measures. The findings suggest that STB might be understood within a cognitive framework for judgment with quantitative variables whose unique constellation separates passive and active suicidal thought (ideation) from suicide planning and planning for safety.

Machine learning with electrocardiograms to optimize mortality risk stratification in patients with suspected acute coronary syndrome

Abstract Funding Acknowledgements Type of funding sources: Public grant(s) – National budget only. Main funding source(s): National Heart, Lung, and Blood Institute (NHLBI) and National Center for Advancing Translational Sciences (NCATS). Background The importance of risk stratification in patients with suspected acute coronary syndrome (ACS) extends beyond diagnosis and immediate treatment. It influences the precision of care delivery and the allocation of resources to those at highest risk of adverse events. Purpose We sought to evaluate the prognostic value of electrocardiogram (ECG) feature-based machine learning models to risk-stratify long-term mortality in those with suspected ACS. Methods This was a multicenter prospective observational cohort study of consecutive, non-traumatic patients evaluated at the emergency department for suspected ACS. The derivation cohort included 4,015 patients from a University Medical Center (age 59±16 years, 47% women, 80% training with 10-fold cross-validation and 20% testing). Ascertainment of all-cause death was based on numerous data sources, including the Centers for Disease Control and Prevention’s National Death Index registry. We trained six machine learning methods for survival analysis using 73 morphological ECG features from presenting prehospital 10-second 12-lead ECGs. We used predicted risk scores in a variational Bayesian Gaussian mixture model to define three risk groups corresponding to low, moderate, and high-risk and compared the resulting classification performance against the HEART score. The external testing cohort included 3,095 patients from a University (age 59±15 years, 44% women). Results The mortality rate was 20.3% in the derivation cohort after an average follow-up period of 3.53 years (IQR 1.75 - 5.32). Extra Survival Trees outperformed other forecasting models during cross-validation. In the internal testing cohort, the derived risk groups were significantly predictive of survival (Kaplan-Meier log-rank test statistic = 121.14, p<0.001), outperforming the classification performance using the HEART score (Figure 1). Our machine learning-based risk stratification model detected >90% of death events missed by low-risk HEART score (Figure 2). Ruling-out the low-risk group, it achieved a negative predictive value of 93.4% with a sensitivity of 85.9% (compared to 89.0% and 75.0%, respectively, for the HEART score). This classification performance generalized well to our external testing cohort. Compared to those in the low-risk group, patients at moderate (OR = 3.62 [1.35-9.74]) and high (OR = 6.12 [2.38-15.75]) risk had significantly higher odds of 30-day cardiovascular death (n=109, 3.5%). Conclusions Using only features from the 10-second 12-lead ECG, we derived and externally validated a machine learning model that stratifies the mortality risk of patients during long-term follow up. This model outperformed current standard of care based on the HEART score. Future work should validate the potential of this decision-support tool in influencing treatment plans and resource allocation.Figure 1.Clustering performanceFigure 2.Sankey diagram

Dimensionality reducing Gaussian mixture‐based reconstruction for fault detection in multimode processes

AbstractModern industrial processes increasingly prioritize demands for safety and reliability, spurring substantial research on process monitoring models. Among existing research subjects, concurrent multimode operating conditions are vital for effective process monitoring. This work proposes an efficient dimensionality‐reducing Gaussian mixture‐based reconstruction approach for multimode industrial process monitoring. The t‐SNE method is first employed to transform high‐dimensional data into a lower‐dimensional space that retains critical operational information. Using these reduced dimensions, a robust Gaussian mixture model is established to partition the operation data into different modes. Furthermore, the original data are assigned to the corresponding operating modes, and local variational autoencoder (VAE) reconstruction models are established, respectively. For each VAE model, two statistics are designed, termed and , to detect abnormalities. The proposed method is applied to a three‐phase flow facility, and the superiority over the comparison methods is proved.

FGO-MFI: factor graph optimization-based multi-sensor fusion and integration for reliable localization

Reliable and precise information pertaining to the position, velocity, and attitude is essential for automated driving. This paper proposes FGO-MFI, a cost-effective and robust multi-sensor fusion and integration localization framework that utilizes factor graph optimization. Firstly, a tightly coupled Global Navigation Satellite Systems (GNSS)/on-board sensor fusion localization framework is established to estimate vehicle states, including position, velocity, and attitude. To address the large drift rate of the Inertial Measurement Unit (IMU), this study introduces a novel IMU/Dynamics pre-integration method based on the vehicle dynamics model. We establish a two-degree-of-freedom vehicle dynamics model utilizing measurements from the wheel speed sensor and steering wheel angle sensor. The IMU/Dynamics factor is devised through a close integration of the model output and IMU pre-integration, enabling the construction of precise odometry with low-cost on-board sensors. Then, to address the issue of the non-Gaussian distribution of GNSS pseudorange error, this paper employs a Gaussian Mixture Model (GMM) to characterize the pseudorange noise, which is then applied to further sensor fusion. Given the time-varying nature of pseudorange noise, the expectation maximization algorithm is utilized to estimate GMM parameters online, leveraging the pseudorange residuals within a sliding window. Comprehensive experiments, inclusive of challenging scenarios such as urban canyons, tunnels, and wooded areas, have been carried out. They affirm the superior performance of the proposed method. Experiments have shown that our method demonstrates reliable localization across different statuses of GNSS signal, exhibiting a 39.4% improvement in the root mean square error of position error when compared to the state-of-the-art. Additionally, this FGO-MFI is a general sensor data fusion framework and is able to incorporate diverse sensor measurements, for example, from cameras and LiDARs to provide more reliable and accurate localization information.

Optimizing Collaborative Crowdsensing: A Graph Theoretical Approach to Team Recruitment and Fair Incentive Distribution

Collaborative crowdsensing is a team collaboration model that harnesses the intelligence of a large network of participants, primarily applied in areas such as intelligent computing, federated learning, and blockchain. Unlike traditional crowdsensing, user recruitment in collaborative crowdsensing not only considers the individual capabilities of users but also emphasizes their collaborative abilities. In this context, this paper takes a unique approach by modeling user interactions as a graph, transforming the recruitment challenge into a graph theory problem. The methodology employs an enhanced Prim algorithm to identify optimal team members by finding the maximum spanning tree within the user interaction graph. After the recruitment, the collaborative crowdsensing explored in this paper presents a challenge of unfair incentives due to users engaging in free-riding behavior. To address these challenges, the paper introduces the MR-SVIM mechanism. Initially, the process begins with a Gaussian mixture model predicting the quality of users’ tasks, combined with historical reputation values to calculate their direct reputation. Subsequently, to assess users’ significance within the team, aggregation functions and the improved PageRank algorithm are employed for local and global influence evaluation, respectively. Indirect reputation is determined based on users’ importance and similarity with interacting peers. Considering the comprehensive reputation value derived from the combined assessment of direct and indirect reputations, and integrating the collaborative capabilities among users, we have formulated a feature function for contribution. This function is applied within an enhanced Shapley value method to assess the relative contributions of each user, achieving a more equitable distribution of earnings. Finally, experiments conducted on real datasets validate the fairness of this mechanism.

SYSTEM DESIGN FOR CALCUALTING THE NUMBER AND DENSITY OF MOTORCYCLES IN PARKING AREA BASED ON BACKGROUND SUBTRACTION METHOD

There are still issues with a number of students parking their vehicles improperly in the parking spaces provided. This causes suboptimal parking capacity due to a lack of information about parking capacity. In recent years, at a certain library, vehicle detection has been implemented using a Gaussian mixture model algorithm using a Raspberry Pi. However, this library does not provide information about the density status of the parking area. Therefore, an information system was created to determine the level of density of the parking area based on the ratio of vehicles entering and exiting compared to the maximum capacity of the parking area. The system uses the Gaussian mixture model algorithm with the machine learning method of background subtraction MOG2, which can calculate the number of vehicles based on the difference between objects and the background of objects, using test data in the form of videos recorded using a camera positioned horizontally to the entrance and exit lanes of the parking area. This research resulted in an accuracy of 89.7% for Video1TA, precision of 93.2%, a crowded parking area density level, and a value of 129.12. Video2TA had a value of 101.08, precision of 100%, and accuracy of 90%, while Video3TA had an accuracy of 35%, precision of 56.7%, and a value of 49.48. The density levels of videos 2 and 3 are the same, indicating that the parking area is still empty. The test results show that the value can affect the system in detecting an object.

Distributed personalized imputation based on Gaussian mixture model for missing data

Distributed personalized imputation based on Gaussian mixture model for missing data

Semi‐supervised Gaussian mixture modelling with a missing‐data mechanism in R

Semi‐supervised Gaussian mixture modelling with a missing‐data mechanism in R

Bayesian inference of vorticity in unbounded flow from limited pressure measurements

We study the instantaneous inference of an unbounded planar flow from sparse noisy pressure measurements. The true flow field comprises one or more regularized point vortices of various strength and size. We interpret the true flow's measurements with a vortex estimator, also consisting of regularized vortices, and attempt to infer the positions and strengths of this estimator assuming little prior knowledge. The problem often has several possible solutions, many due to a variety of symmetries. To deal with this ill posedness and to quantify the uncertainty, we develop the vortex estimator in a Bayesian setting. We use Markov-chain Monte Carlo and a Gaussian mixture model to sample and categorize the probable vortex states in the posterior distribution, tailoring the prior to avoid spurious solutions. Through experiments with one or more true vortices, we reveal many aspects of the vortex inference problem. With fewer sensors than states, the estimator infers a manifold of equally possible states. Using one more sensor than states ensures that no cases of rank deficiency arise. Uncertainty grows rapidly with distance when a vortex lies outside of the vicinity of the sensors. Vortex size cannot be reliably inferred, but the position and strength of a larger vortex can be estimated with a much smaller one. In estimates of multiple vortices their individual signs are discernible because of the nonlinear coupling in the pressure. When the true vortex state is inferred from an estimator of fewer vortices, the estimate approximately aggregates the true vortices where possible.

Soft sensor development for mixed oil interface tracking in multi-product pipelines based on knowledge-informed semi-supervised Variational Bayesian Gaussian mixture regression

Sequential transportation of petroleum products in multi-product pipelines often lead to occurrence of mixed oil. The prediction of the arrival time of the mixed oil interface constitutes crucial data for the scheduling of treatment actions. However, existing soft sensors, like Gaussian mixture regression (GMR), may face challenges due to limited size of labeled data and numerical issues, leading to performance degradation or even training failure. To tackle these issues, we propose a Knowledge-informed Semi-supervised Variational Bayesian Gaussian mixture model (KI-SSVBGMR). It employs a semi-supervised fully Bayesian structure designed to address the constraints arising from the potential matrix singularity issues and shortage of labeled samples. Subsequently, we determine the crucial regression variable and establish its prior distribution based on industrial knowledge to improve model generalization. Finally, a learning procedure grounded in the Variational Inference algorithm is developed to train the KI-SSVBGMR. Through case studies, including numerical examples and real industrial datasets, our method demonstrates the effectiveness and reliability of the proposed soft sensor development method. This research can aid operators in improving mixed oil section management and provides valuable insights for integrating machine learning with industrial knowledge.

The whole and its parts: Visualizing Gaussian mixture models

Gaussian mixture models are classical but still popular machine learning models. An appealing feature of Gaussian mixture models is their tractability, that is, they can be learned efficiently and exactly from data, and also support efficient exact inference queries like soft clustering data points. Only seemingly simple, Gaussian mixture models can be hard to understand. There are at least four aspects to understanding Gaussian mixture models, namely, understanding the whole distribution, its individual parts (mixture components), the relationships between the parts, and the interplay of the whole and its parts. In a structured literature review of applications of Gaussian mixture models, we found the need for supporting all four aspects. To identify candidate visualizations that effectively aid the user needs, we structure the available design space along three different representations of Gaussian mixture models, namely as functions, sets of parameters, and sampling processes. From the design space, we implemented three design concepts that visualize the overall distribution together with its components. Finally, we assessed the practical usefulness of the design concepts with respect to the different user needs in expert interviews and an insight-based user study.

Improved GMMKNN Hybrid Recommendation Algorithm

This paper proposes a hybrid recommendation algorithm that combines the advantages of Gaussian Mixture Model (GMM) and K-Nearest Neighbors (KNN) algorithms. The algorithm first applies GMM to cluster the training data, grouping users with similar interests using clustering techniques. It then utilizes the KNN algorithm for prediction. During the KNN recommendation process for a target user, the algorithm searches for neighboring users with similar interests and features within the same cluster. This significantly reduces the search scope of the nearest neighbors, thanks to the assistance of the GMM algorithm. The algorithm then selects the K most similar neighbors from the target user’s cluster as the candidate pool for personalized recommendations. Additionally, the algorithm improves the weight calculation method by incorporating a Gaussian kernel function for weight estimation. Experimental results on the dataset demonstrate that the proposed improved algorithm effectively enhances the accuracy of prediction results.

BSEC Method for Unveiling Open Clusters and its Application to Gaia DR3: 83 New Clusters

Open clusters (OCs) are common in the Milky Way, but most of them remain undiscovered. There are numerous techniques, including some machine-learning algorithms, available for the exploration of OCs. However, each method has its limitations and therefore, different approaches to discovering OCs hold significant values. We develop a comprehensive approach method to automatically explore the data space and identify potential OC candidates with relatively reliable membership determination. This approach combines the techniques of Hierarchical Density-Based Spatial Clustering of Applications with Noise, Gaussian mixture model, and a novel cluster member identification technique, color excess constraint. The new method exhibits efficiency in detecting OCs while ensuring precise determination of cluster memberships. Because the main feature of this technique is to add an extra constraint (EC) for the members of cluster candidates using the homogeneity of color excess, compared to typical blind search codes, it is called Blind Search-Extra Constraint (BSEC) method. It is successfully applied to the Gaia Data Release 3, and 83 new OCs are found, whose color–magnitude diagrams (CMDs) are fitted well to the isochrones. In addition, this study reports 621 new OC candidates with discernible main sequence or red giant branch. It is shown that BSEC technique can discard some false negatives of previous works, which takes about three percentage of known clusters. It shows that as an EC, the color excess (or two-color) constraint is useful for removing fake cluster member stars from the clusters that are identified from the positions and proper motions of stars, and getting more precise CMDs, when differential reddening of member stars of a cluster is not large (e.g., ΔE(G BP − G RP) < 0.5 mag). It makes the CMDs of 15% clusters clearer (in particular for the region near turnoff) and therefore is helpful for CMD and stellar population studies. Our result suggests that the color excess constraint is more appropriate for clusters with small differential reddening, such as globular clusters or older OCs, and clusters that the distances of member stars cannot be determined accurately.

Reconstruction of measurement data with multiple outliers using novel domain-based RBF

Due to the high accuracy of computation, radial basis function (RBF) is widely recognized as a versatile and effective method for interpolating and approximating discrete points in various fields. However, RBF is quite sensitive to outliers, which can easily lead to distorted results. In this article, a novel overlapped domain-based RBF (ODRBF) method is proposed, in which the concept of effective domain is introduced to build a moving model, and Student’s t-regression and Gaussian mixture model (GMM) clustering are used for dealing with local anomalies. By introducing the effective domain, the estimated points and domain radius are constructed and the global model can be transformed into local estimation models. In each effective domain, a series of estimation models are iteratively generated through Student’s t-regression, and based on the distances between the estimation model and discrete points, GMM clustering is used to subsequently select the data as the input of the next regression. This iterative strategy in each effective domain ensures the removal of multiple outliers. Then, the preserved points in the processed effective domain are used to obtain local estimated value by RBF. The proposed method demonstrates strong robustness to highly contaminated dataset in the reconstruction of the simulation and experimental datasets.

Data-driven distributionally robust day-ahead dispatch for active distribution networks based on improved conditional generative adversarial network

With the increasing penetration of renewable energy generation (REG), strong uncertainty poses a significant challenge to the rationality of day-ahead dispatch plans in distribution systems. We propose a data-driven, distributionally robust day-ahead dispatch method for active distribution networks (ADNs) based on an improved conditional generative adversarial network (CGAN). First, an improved CWGAN-GP model is constructed based on three-dimensional convolution (Conv3D) and the Wasserstein distance to obtain the day-ahead REG scenarios, considering the correlation features of photovoltaic (PV) and wind turbines (WTs), which reduces the conservatism of scenario generation. Accordingly, the Gaussian mixture model (GMM) clustering method based on moment information was used to construct an ambiguity set. Moreover, a two-stage distributionally robust day-ahead dispatch model for an ADN is established, which realizes the fusion of the data-driven method and distributionally robust optimization (DRO) mechanism model. Finally, the validity of the data-driven DRO (DDRO) method is verified through a case analysis.