Parameters Of Gaussian Mixture Model Research Articles

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.

Predicting Ballast Fouling Conditions with the Gaussian Mixture Model

Railroad ballast is typically comprised of only large granular particles. However, the degradation of fresh ballast and the arrival of foreign fines result in ballast fouling. Compared with fresh ballast, fouled ballast exhibits reduced resilience and compromised drainage capabilities. To optimize track performance, maintenance activities for the ballast are frequently scheduled based on the fouling severity. An accurate assessment of ballast fouling conditions can enhance maintenance efficiency and reduce costs. Over the years, while many ballast fouling evaluation methods have been developed, their widespread adoption has been hindered by system costs and implementation challenges. This study aims to address this by developing an affordable and easily implemented approach to estimating ballast fouling conditions using the Gaussian Mixture Model (GMM). Initially, images of fouled ballast are characterized by fitting the distributions of each RGB (Red, Green, Blue) channel. Subsequently, two mathematical methods, expectation-maximization and point estimation, are employed to solve the GMM parameters. These derived GMM parameters are then used to backcalculate the sample parameters, facilitating the estimation of ballast fouling conditions. The results of this study reveal a close alignment between the ballast fouling conditions backcalculated with the GMM and those quantified through laboratory sieving analysis. This study thus presents a promising path forward, using images captured from cost-effective cameras to estimate ballast fouling conditions with minimal computational expense.

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.

Semiparametric constant false alarm rate method for radar and sonar images

AbstractThis work proposed a novel constant false alarm rate detection method based on Gaussian mixture model (GMM). The main contribution contains two aspects. First, the Gabor wavelet is used to determine the GMM component number. Second, the expression of probability of false alarm is derived based on the GMM parameter.

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.

Transfer-Learning-Based Gaussian Mixture Model for Distributed Clustering.

Distributed clustering based on the Gaussian mixture model (GMM) has exhibited excellent clustering capabilities in peer-to-peer (P2P) networks. However, more iterative numbers and communication overhead are required to achieve the consensus in existing distributed GMM clustering algorithms. In addition, the truth that it cannot find a closed form for the update of parameters in GMM causes the imprecise clustering accuracy. To solve these issues, by utilizing the transfer learning technique, a general transfer distributed GMM clustering framework is exploited to promote the clustering performance and accelerate the clustering convergence. In this work, each node is treated as both the source domain and the target domain, and these nodes can learn from each other to complete the clustering task in distributed P2P networks. Based on this framework, the transfer distributed expectation-maximization algorithm with the fixed learning rate is first presented for data clustering. Then, an improved version is designed to obtain the stable clustering accuracy, in which an adaptive transfer learning strategy is adopted to adjust the learning rate automatically instead of a fixed value. To demonstrate the extensibility of the proposed framework, a representative GMM clustering method, the entropy-type classification maximum-likelihood algorithm, is further extended to the transfer distributed counterpart. Experimental results verify the effectiveness of the presented algorithms in contrast with the existing GMM clustering approaches.

Real-Time Seismocardiogram Feature Extraction Using Adaptive Gaussian Mixture Models.

Accurate and timely cardiovascular health evaluations can be provided by wearable systems that estimate key hemodynamic indices in real-time. A number of these hemodynamic parameters can be estimated non-invasively using the seismocardiogram (SCG), a cardiomechanical signal whose features can be linked to cardiac events such as aortic valve opening (AO) and aortic valve closing (AC). However, tracking a single SCG feature is often unreliable due to physiological state changes, motion artifacts, and external vibrations. In this work, an adaptable Gaussian Mixture Model (GMM) framework is proposed to concurrently track multiple AO or AC features in quasi-real-time from the measured SCG signal. For all extrema in a SCG beat, the GMM calculates the likelihood that an extremum is an AO/AC correlated feature. The Dijkstra algorithm is then used to isolate tracked heartbeat related extrema. Finally, a Kalman filter updates the GMM parameters, while filtering the features. Tracking accuracy is tested on a porcine hypovolemia dataset with various noise levels added. In addition, blood volume decompensation status estimation accuracy is evaluated using the tracked features on a previously developed model. Experimental results showed a 4.5 ms tracking latency per beat and an average AO and AC root mean square error (RMSE) of 1.47ms and 7.67ms respectively at 10dB noise and 6.18ms and 15.3ms at -10dB noise. When analyzing the tracking accuracy of all AO or AC correlated features, combined AO and AC RMSE remained in similar ranges at 2.70ms and 11.91ms respectively at 10dB noise and 7.50 and 16.35ms at - 10dB. The low latency and RMSE of all tracked features make the proposed algorithm suitable for real-time processing. Such systems would enable accurate and timely extraction of important hemodynamic indices for a multitude of cardiovascular monitoring applications, including trauma care in field settings.

Robot Policy Improvement With Natural Evolution Strategies for Stable Nonlinear Dynamical System.

Robot learning through kinesthetic teaching is a promising way of cloning human behaviors, but it has its limits in the performance of complex tasks with small amounts of data, due to compounding errors. In order to improve the robustness and adaptability of imitation learning, a hierarchical learning strategy is proposed: low-level learning comprises only behavioral cloning with supervised learning, and high-level learning constitutes policy improvement. First, the Gaussian mixture model (GMM)-based dynamical system is formulated to encode a motion from the demonstration. We then derive the sufficient conditions of the GMM parameters that guarantee the global stability of the dynamical system from any initial state, using the Lyapunov stability theorem. Generally, imitation learning should reason about the motion well into the future for a wide range of tasks; it is significant to improve the adaptability of the learning method by policy improvement. Finally, a method based on exponential natural evolution strategies is proposed to optimize the parameters of the dynamical system associated with the stiffness of variable impedance control, in which the exploration noise is subject to stability conditions of the dynamical system in the exploration space, thus guaranteeing the global stability. Empirical evaluations are conducted on manipulators for different scenarios, including motion planning with obstacle avoidance and stiffness learning.

Deep expectation-maximization network for unsupervised image segmentation and clustering

Unsupervised learning, such as unsupervised image segmentation and clustering, are fundamental tasks in image representation learning. In this paper, we design a deep expectation-maximization (DEM) network for unsupervised image segmentation and clustering. It is based on the statistical modeling of image in its latent feature space by Gaussian mixture model (GMM), implemented in a novel deep learning framework. Specifically, in the unsupervised setting, we design an auto-encoder network and an EM module over the image latent features, for jointly learning the image latent features and GMM model of the latent features in a single framework. To construct the EM-module, we unfold the iterative operations of EM algorithm and the online EM algorithm in fixed steps to be differentiable network blocks, plugged into the network to estimate the GMM parameters of the image latent features. The proposed network parameters can be end-to-end optimized using losses based on log-likelihood of GMM, entropy of Gaussian component assignment probabilities and image reconstruction error. Extensive experiments confirm that our proposed networks achieve favorable results compared with several state-of-the-art methods in unsupervised image segmentation and clustering.

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.

3D Holoscopic Image Compression Based on Gaussian Mixture Model

We introduce a Gaussian Mixture Model (GMM) framework for 3D holoscopic image compression in this paper. The elemental-images of the 3D holoscopic image are predicted using GMM and the parameters of GMM are estimated using the common Expectation-Maximization (EM) algorithm. GMM Model Optimization (GMO) is used in this framework to select the optimal number of distributions and avoid local optimum of EM at the same time. A three-dimensional distribution-rotation based decomposition is proposed to change covariance parameters to meaningful features and improve the coding efficiency. The features and the remaining parameters of the GMM are encoded using fixed-length bits. A feature-based dictionary is proposed in this framework to match the similar Gaussian distributions utilizing the similar GMM features. And the offsets of the matched distributions are recorded as motion vectors to replace the similar areas in the elemental-images of the 3D holoscopic image. The residual between the original image and the prediction is encoded using Screen Content Coding Extension of High Efficiency Video Coding (HEVC-SCC). Experimental results show that our method performs better than HEVC-SCC, two coding methods based on pseudo-sequences and a state-of-the-art content-based compression method with Gaussian process regression.

A Joint Model Extraction and Data Detection Framework for IRS-NOMA System

This paper addresses the problem of data detection for intelligent reflecting surface (IRS) assisted non-orthogonal multiple access (NOMA) systems. Also, the phase noise, analog-to-digital converter (ADC) quantization error and imperfect channel estimation are taken into consideration. At present, IRS is designed to be deployed in a wide range of scenarios. However, the quantization error model and IRS phase error model developed for limited scenarios may not be well adapted to the complex and changing environment, which brings a new challenge for the application of IRS. Therefore, this paper investigates a new hybrid method for joint noise model extraction, device activity detection and data detection in the case of unknown noise models, to solve the aforementioned IRS problem. Firstly, the Gaussian mixture model (GMM) is used to describe the model of quantization noise and phase noise. Thus the problem of model extraction is transformed into the calculation of the key parameters of GMM. Secondly, an improved expectation maximization algorithm is used to calculate the quantization noise model parameters. Finally, utilizing the property of the structure of the problem, a message-passing based algorithm is investigated. Simulation results show the merits of the proposed hybrid algorithm.

Automated operational modal analysis using variational Gaussian mixture model

Automated operational modal analysis is essential for online structural health monitoring without human intervention. It remains a challenging issue due to the need of processing a large number of datasets and the involvement of many user-specified thresholds. This paper proposes a novel automated modal identification approach based on stochastic subspace identification and variational Gaussian mixture model that involves the analysis of the stabilization diagram to automatically identify modal parameters. Two validation criteria are first adopted to eliminate the spurious modes in the stabilization diagram. A Gaussian mixture model (GMM) is then used to probabilistically classify each pole in the stabilization diagram to a specific cluster. The parameters of GMM are estimated using variational inference, giving representatives of each mode, and the optimal number of clusters is automatically determined through the Dirichlet Process. The proposed framework automatically distinguishes physical modes from spurious modes with only two verified and widely used thresholds. Results of a four-story shear and a footbridge with continuous measurements demonstrate the efficacy and robustness of the proposed approach. It shows that the proposed approach can automatically identify modal parameters with high accuracy, including weakly excited and closely spaced modes.

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.

Red Dragon: a redshift-evolving Gaussian mixture model for galaxies

ABSTRACT Precision-era optical cluster cosmology calls for a precise definition of the red sequence (RS), consistent across redshift. To this end, we present the Red Dragon algorithm: an error-corrected multivariate Gaussian mixture model (GMM). Simultaneous use of multiple colours and smooth evolution of GMM parameters result in a continuous RS and blue cloud (BC) characterization across redshift, avoiding the discontinuities of red fraction inherent in swapping RS selection colours. Based on a mid-redshift spectroscopic sample of SDSS galaxies, an RS defined by Red Dragon selects quiescent galaxies (low specific star formation rate) with a balanced accuracy of over $90{{\ \rm per\ cent}}$. This approach to galaxy population assignment gives more natural separations between RS and BC galaxies than hard cuts in colour–magnitude or colour–colour spaces. The Red Dragon algorithm is publicly available at bitbucket.org/wkblack/red-dragon-gamma/.

Making Every Step Count: Minute-by-Minute Characterization of Step Counts Augments Remote Activity Monitoring in People With Multiple Sclerosis.

BackgroundAmbulatory disability is common in people with multiple sclerosis (MS). Remote monitoring using average daily step count (STEPS) can assess physical activity (activity) and disability in MS. STEPS correlates with conventional metrics such as the expanded disability status scale (Expanded Disability Status Scale; EDSS), Timed-25 Foot walk (T25FW) and timed up and go (TUG). However, while STEPS as a summative measure characterizes the number of steps taken over a day, it does not reflect variability and intensity of activity.ObjectivesNovel analytical methods were developed to describe how individuals spends time in various activity levels (e.g., continuous low versus short bouts of high) and the proportion of time spent at each activity level.Methods94 people with MS spanning the range of ambulatory impairment (unaffected to requiring bilateral assistance) were recruited into FITriMS study and asked to wear a Fitbit continuously for 1-year. Parametric distributions were fit to minute-by-minute step data. Adjusted R2 values for regressions between distributional fit parameters and STEPS with EDSS, TUG, T25FW and the patient-reported 12-item MS Walking scale (MSWS-12) were calculated over the first 4-weeks, adjusting for sex, age and disease duration.ResultsDistributional fits determined that the best statistically-valid model across all subjects was a 3-compartment Gaussian Mixture Model (GMM) that characterizes the step behavior within 3 levels of activity: high, moderate and low. The correlation of GMM parameters for baseline step count measures with clinical assessments was improved when compared with STEPS (adjusted R2 values GMM vs. STEPS: TUG: 0.536 vs. 0.419, T25FW: 0.489 vs. 0.402, MSWS-12: 0.383 vs. 0.378, EDSS: 0.557 vs. 0.465). The GMM correlated more strongly (Kruskal-Wallis: p = 0.0001) than STEPS and gave further information not included in STEPS.ConclusionsIndividuals' step distributions follow a 3-compartment GMM that better correlates with clinic-based performance measures compared with STEPS. These data support the existence of high-moderate-low levels of activity. GMM provides an interpretable framework to better understand the association between different levels of activity and clinical metrics and allows further analysis of walking behavior that takes step distribution and proportion of time at three levels of intensity into account.

TERMS: textual emotion recognition in multidimensional space.

Microblogs generate a vast amount of data in which users express their emotions regarding almost all aspects of everyday life. Capturing affective content from these context-dependent and subjective texts is a challenging task. We propose an intelligent probabilistic model for textual emotion recognition in multidimensional space (TERMS) that captures the subjective emotional boundaries and contextual information embedded in a text for robust emotion recognition. It is implausible with discrete label assignment;therefore, the model employs a soft assignment by mapping varying emotional perceptions in a multidimensional space and generates them as distributions via the Gaussian mixture model (GMM). To strengthen emotion distributions, TERMS integrates a probabilistic emotion classifier that captures the contextual and linguistic information from texts. The integration of these aspects, the context-aware emotion classifier and the learned GMM parameters provide a complete coverage for accurate emotion recognition. The large-scale experimentation shows that compared to baseline and state-of-the-art models, TERMS achieved better performance in terms of distinguishability, prediction, and classification performance. In addition, TERMS provide insights on emotion classes, the annotation patterns, and the models application in different scenarios.