Parameters Of Gaussian Mixture Model Research Articles

Robust spatial fuzzy GMM based MRI segmentation and carotid artery plaque detection in ultrasound images

Background and ObjectiveIn medical image analysis for disease diagnosis, segmentation is one of the challenging tasks. Owing to the inherited degradations in MRI improper segments are produced. Segmentation process is an important step in brain tissue analysis. Moreover, an early detection of plaque in carotid artery using ultrasound images may prevent serious brain strokes. Unfortunately, low quality and noisy ultrasound images are still challenges for accurate segmentation. The objective of this research is to develop a robust segmentation approach for medical images such as brain MRI and carotid artery ultrasound images. MethodsIn this paper, a novel approach is proposed to address the segmentation challenges of medical images. The proposed approach employed fuzzy intelligence and Gaussian mixture model (GMM). It comprises two phases; firstly, incorporating spatial fuzzy c-means in GMM by exploiting statistical, texture, and wavelet image features. During model development, GMM parameters are estimated in presence of noise by EM algorithm iteratively. Utilizing these parameters, brain MRI images are segmented. In next phase, developed approach is applied to solve a real problem of carotid artery plaque detection using ultrasound images. The dataset of real patients annotated by radiologists has been obtained from Radiology Department, Shifa International Hospital Islamabad, Pakistan. For this, intima-media-thickness values are computed from the proposed segmentation followed by support vector machines for plaque classification (normal/abnormal). ResultsThe obtained segmentation has been evaluated on standard brain MRI dataset and offers high segmentation accuracy of 99.2%. The proposed approach outperforms in term of segmentation performance range of 3–9% as compared to the state of the art approaches on brain MRI. Furthermore, the proposed approach shows robustness to various levels of Gaussian and Rician image noises. On carotid artery dataset, we have obtained high plaque detection rate in terms of accuracy, sensitivity, specificity, and F-score values of 98.8%, 99.3%, 98.0%, and 97.5% respectively. ConclusionsThe proposed approach segments both modalities with high precision and shows robustness at Gaussian and Rician noise levels. Results for brain MRI and ultrasound images indicate its effectiveness and can be used as second opinion in addition to the radiologists. The developed approach is straightforward, efficient, and reproducible. It may benefit to improve the clinical evaluation of the disease in both asymptomatic and symptomatic individuals.

Channel Estimation in Massive MIMO Systems Using a Modified Bayes-GMM Method

In this paper, we study the uplink channel estimation based on machine learning algorithm in massive MIMO systems. Based on the sparsity of channel gains in the beam domain, we use Gaussian mixture model (GMM) to model the channel. The expectation maximization (EM) algorithm is adopted to obtain the parameters of GMM. Bayesian algorithm is used to estimate the channel gains. The approximate message passing (AMP) algorithm is used to solve the multiple integrals in Bayesian estimation algorithm to reduce the computational load. When determining the initial values of AMP and EM algorithms, the hierarchical clustering algorithm is adopted to improve the mean square error (MSE) and convergence performance of the algorithm. Simulation results show that the performance of the proposed algorithm is better than that of the traditional least square (LS) algorithm and the existing Bayes-GMM algorithm.

Analysis of epileptic seizure detection method based on improved genetic algorithm optimization back propagation neural network

In order to improve the accuracy and efficiency of automatic seizure detection, the paper proposes a method based on improved genetic algorithm optimization back propagation (IGA-BP) neural network for epilepsy diagnosis, and uses the method to achieve detection of clinical epilepsy rapidly and effectively. Firstly, the method extracted the linear and nonlinear features of the epileptic electroencephalogram (EEG) signals and used a Gaussian mixture model (GMM) to perform cluster analysis on EEG features. Next, expectation maximization (EM) algorithm was used to estimate GMM parameters to calculate the optimal parameters for the selection operator of genetic algorithm (GA). The initial weights and thresholds of the BP neural network were obtained through using the improved genetic algorithm. Finally, the optimized BP neural network is used for the classification of the epileptic EEG signals to detect the epileptic seizure automatically. Compared with the traditional genetic algorithm optimization back propagation (GA-BP), the IGA-BP neural network can improve the population convergence rate and reduce the classification error. In the process of automatic detection of epilepsy, the method improves the detection accuracy in the automatic detection of epilepsy disorders and reduced inspection time. It has important application value in the clinical diagnosis and treatment of epilepsy.

Improved density peak clustering-based adaptive Gaussian mixture model for damage monitoring in aircraft structures under time-varying conditions

Abstract For the reliable damage monitoring of aircraft structures under Time-Varying Conditions (TVCs), Gaussian Mixture Model (GMM)-based damage monitoring methods combined with Guided Wave (GW) have been studied increasingly frequently in recent years. In this paper, to enhance the performance of the GMM-based damage monitoring method, an Improved Density Peaks Clustering (IDPC)-based Expectation Maximization (EM) algorithm is proposed to improve the constructing algorithm of the GMM. In the algorithm, the unique initial value of the GMM parameters is obtained based on an adaptive searching strategy of the probability density peaks of GW Damage Features (DFs) first. Next, the GMM is constructed simply and efficiently by the EM algorithm based on the initial parameters. The IDPC-EM algorithm can stably construct the GMM with fewer experience-dependent initialization parameters while promising the probability modelling accuracy and maintaining high computational efficiency. Based on the IDPC-EM algorithm, a new adaptive GMM-based damage monitoring method combined with the GW is established. The method is simple, stable, highly computationally efficient and less experience-dependent due to the adaptive GMM. In this method, two GMMs of the DFs obtained in the healthy state and the damage monitoring state of an aircraft structure are constructed, respectively. By measuring the similarity of the two GMMs, the variation trend of the probability distributions of the DFs between the two states is obtained to detect the damage. Finally, the method is validated in a full-scale aircraft fatigue test which is close to an in-flight load test on the ground. The cracks of the right landing gear spar and the left wing panel are monitored reliably and stably under random fatigue load conditions.

A dual EM algorithm for TV regularized Gaussian mixture model in image segmentation

A dual expectation-maximization (EM) algorithm for total variation (TV) regularized Gaussian mixture model (GMM) is proposed in this paper. The algorithm is built upon the EM algorithm with TV regularization (EM-TV) model which combines the statistical and variational methods together for image segmentation. Inspired by the projection algorithm proposed by Chambolle, we give a dual algorithm for the EM-TV model. The related dual problem is smooth and can be easily solved by a projection gradient method, which is stable and fast. Given the parameters of GMM, the proposed algorithm can be seen as a forward-backward splitting method which converges. This method can be easily extended to many other applications. Numerical results show that our algorithm can provide high quality segmentation results with fast computation speed. Compared with the well-known statistics based methods such as hidden Markov random field with EM method (HMRF-EM), the proposed algorithm has a better performance. The proposed method could also be applied to MRI segmentation such as SPM8 software and improve the segmentation results.

An Effective Fuel-Level Data Cleaning and Repairing Method for Vehicle Monitor Platform

With energy scarcity and environmental pollution becoming increasingly serious, the accurate estimation of fuel consumption of vehicles has been important in vehicle management and transportation planning toward a sustainable green transition. Fuel consumption is calculated by fuel-level data collected from high-precision fuel-level sensors. However, in the vehicle monitor platform, there are many types of error in the data collection and transmission processes, such as the noise, interference, and collision errors that are common in the high speed and dynamic vehicle environment. In this paper, an effective method for cleaning and repairing the fuel-level data is proposed, which adopts the threshold to acquire abnormal fuel data, the time quantum to identify abnormal data, and linear interpolation based algorithm to correct data errors. Specifically, a modified Gaussian mixture model (GMM) based on the synchronous iteration method is proposed to acquire the thresholds, which uses the particle swarm optimization algorithm and the steepest descent algorithm to optimize the parameters of GMM. The experiment results based on the fuel-level data of vehicles collected over one month prove that the modified GMM is superior to GMM-expectation maximization on fuel-level data, and the proposed method is effective for cleaning and repairing outliers of fuel-level data.

A Distributed Probabilistic Modeling Algorithm for the Aggregated Power Forecast Error of Multiple Newly Built Wind Farms

The extensive penetration of wind farms (WFs) presents challenges to the operation of distribution networks (DNs). Building a probability distribution of the aggregated wind power forecast error is of great value for decision making. However, as a result of recent government incentives, many WFs are being newly built with little historical data for training distribution models. Moreover, WFs with different stakeholders may refuse to submit the raw data to a data center for model training. To address these problems, a Gaussian mixture model (GMM) is applied to build the distribution of the aggregated wind power forecast error; then, the maximum a posteriori (MAP) estimation method is adopted to overcome the limited training data problem in GMM parameter estimation. Next, a distributed MAP estimation method is developed based on the average consensus filter algorithm to address the data privacy issue. The distribution control center is introduced into the distributed estimation process to acquire more precise estimation results and better adapt to the DN control architecture. The effectiveness of the proposed algorithm is empirically verified using historical data.

Modulation Mode Detection and Classification for In Vivo Nano-Scale Communication Systems Operating in Terahertz Band.

This paper initiates the efforts to design an intelligent/cognitive nano receiver operating in terahertz band. Specifically, we investigate two essential ingredients of an intelligent nano receiver-modulation mode detection (to differentiate between pulse-based modulation and carrier-based modulation) and modulation classification (to identify the exact modulation scheme in use). To implement modulation mode detection, we construct a binary hypothesis test in nano-receiver's passband and provide closed-form expressions for the two error probabilities. As for modulation classification, we aim to represent the received signal of interest by a Gaussian mixture model (GMM). This necessitates the explicit estimation of the THz channel impulse response and its subsequent compensation (via deconvolution). We then learn the GMM parameters via expectation-maximization algorithm. We then do Gaussian approximation of each mixture density to compute symmetric Kullback-Leibler divergence in order to differentiate between various modulation schemes (i.e., M -ary phase shift keying and M -ary quadrature amplitude modulation). The simulation results on mode detection indicate that there exists a unique Pareto-optimal point (for both SNR and the decision threshold), where both error probabilities are minimized. The main takeaway message by the simulation results on modulation classification is that for a pre-specified probability of correct classification, higher SNR is required to correctly identify a higher order modulation scheme. On a broader note, this paper should trigger the interest of the community in the design of intelligent/cognitive nano receivers (capable of performing various intelligent tasks, e.g., modulation prediction, and so on).

Gaussian mixture model for coarse-grained modeling from XFEL.

We explore the advantage of Gaussian mixture model (GMM) for interpretation of single particle diffraction patterns from X-ray free electron laser (XFEL) experiments. GMM approximates a biomolecular shape by the superposition of Gaussian distributions. As the Fourier transformation of GMM can be quickly performed, we can efficiently simulate XFEL diffraction patterns from approximated structure models. We report that the resolution that GMM can accurately reproduce is proportional to the cubic root of the number of Gaussians used in the modeling. This behavior can be attributed to the correspondence between the number of adjustable parameters in GMM and the amount of sampling points in diffraction space. Furthermore, GMMs can successfully be used to perform angular assignment and to detect conformational variation. These results demonstrate that GMMs serve as useful coarse-grained models for hybrid approach in XFEL single particle experiments.

Discriminative training of subject-dependent Gaussian mixture models for portable SSVEP identification

Abstract Various factors and challenges have impeded Brain Computer Interface (BCI) systems from moving outside laboratories towards real applications. Such impediments might be, reliability, information transfer rates, non-stationarity of Electroencephalogram (EEG), and subject variation. Moreover, due to the portable design requirements of our BCI systems, which consists of a wireless EEG device to record the data and an Android tablet that serves as visual stimuli, the system׳s performance is affected by the imprecise Steady-State Visual Evoked Potential (SSVEP) paradigm generation and the intermittent Android system calls. As such, we follow our previous effort, in which we introduced a signal processing solution that entailed partitioning the score spaces of Canonical Correlation Analysis (CCA) and Power Spectral Density Analysis (PSDA), extracting useful information from each partition, and augmenting them to generate a robust representation of the biased SSVEP recordings. Then, we incorporate subject specific information via Gaussian Mixture Model (GMM) training and adaptation utilizing Maximum A Posteriori (MAP) model adaptation. However, despite the robust performance of MAP, it is essentially a generative method which may not be very effective in capturing discriminative subject-specific information. As such, in this effort we introduce the Minimum Segment Classification Error (MSCE) algorithm for discriminative re-estimation of the GMM parameters in a time efficient manner by directly relating the parameters to the performance measure. Moreover, We conduct a comparison between the re-estimated subject-dependent GMMs utilizing our proposed discriminative MSCE algorithm and the standard GMM-MAP baseline model from our previous effort to demonstrate the significance of our proposed discriminative re-estimation algorithm. Additionally, we evaluate the performance of our proposed MSCE algorithm and compare it to a well-established SSVEP-identification method that utilizes Multivariate Linear Regression (MLR). Our 10-Fold Cross-Validation results demonstrated that while MLR achieved an overall 86% SSVEP identification accuracy, the GMM-MAP baseline model yielded an overall high identification accuracy of 92.9% and that accuracy is further improved to 97.41% when utilizing our proposed MSCE algorithm.

Exploration on origin–destination-based travel time variability: Insights from Seoul metropolitan area

Travel time variability can be defined as the variation in travel time over a certain time period. This study focuses on O/D-based analysis, which has been rarely studied due to the limited data in the context of travel time variability. The objectives of the study are twofold: to shed light on the O/D-based travel time variability and to get insights on travel time variability in the context of Seoul Metropolitan Area. This study utilizes the web information to obtain real-time estimated travel time data, and employs a Gaussian mixture model (GMM) to model the travel time distributions. The GMM parameters are found to be useful to fit travel time distribution, which exhibits skewness and multimodality, to identify underlying travel time states and to explain variability. The results indicate that O/D-based travel time variability can be characterized and that higher variability occurs during peak hours. In general, the selected O/D pairs are found to have four travel time states but exhibit different patterns. The existence of alternative paths seem to reduce travel time variability at the O/D level. The results suggest directions for future research and implementation of policies.

Online Modeling of Esthetic Communities Using Deep Perception Graph Analytics

Accurately detecting esthetic communities from a large number of Internet users (e.g., Flickr 1 1 www.flickr.com . or Picasa 2 2 picasa.google.com . users) is a useful technique that can facilitate several applications, such as image retargeting, visual esthetic assessment, and fashion recommendation. Conventional approaches cannot appropriately handle this task due to the following challenges: first, it is difficult to online update the detected esthetic communities since these photos may uploaded/removed frequently; second, human visual perception is essential to describe esthetic characteristics, but integrating it into an existing mining algorithm is challenging; and third, flat models cannot encode human visual perception precisely, especially for those sophisticated sceneries. To solve these problems, we propose deep perception graph analytics, an incremental pipeline where the esthetic relations among users are described by utilizing their gaze shifting paths (GSPs). Specifically, we first propose an aggregation-based deep network that formulates GSP representation into a unified framework. Afterward, the deep perception graph is constructed where the esthetic discrepancy between users is measured by their GSP distributions. Accordingly, we adopt a dense subgraph discovery algorithm that efficiently detects the communities belonging to each esthetic style. Finally, an online Gaussian mixture model (GMM) learning model is designed, which dynamically updates the GMM parameters in order to describe esthetic communities given the photos are uploaded/removed on the fly. Experiments on a million-scale image set crawled from Flickr demonstrate the efficiency and effectiveness of our method.

Gaussian mixture spline trajectory: learning from a dataset, generating trajectories without one

Most optimization-based motion planners use a naive linear initialization, which does not use previous planning experience. We present an algorithm called ‘Gaussian mixture spline trajectory’ (GMST) that leverages motion datasets for generating trajectories for new planning problems. Unlike other trajectory prediction algorithms, our method does not retrieve trajectories from a dataset. Instead, it first uses a Gaussian mixture model (GMM) to modelize the likelihood of the trajectories to be inside the dataset and then uses the GMM's parameters to generate new trajectories. As the use of the dataset is restricted only to the learning phase it can take advantage of very large datasets. Using both abstract and robot system planning problems, we show that the GMST algorithm decreases the computation time and number of iterations of optimization-based planners while increasing their success rates as compared to that obtained with linear initialization.

Bootstrap Averaging for Model-Based Source Separation in Reverberant Conditions

Recently proposed model-based methods use time-frequency (T-F) masking for source separation, where the T-F masks are derived from various cues described by a frequency domain Gaussian mixture model (GMM). These methods work well for separating mixtures recorded in low-to-medium level of reverberation, however, their performance degrades as the level of reverberation is increased. We note that the relatively poor performance of these methods under reverberant conditions can be attributed to the high variance of the frequency-dependent GMM parameter estimates. To address this limitation, a novel bootstrap-based approach is proposed to improve the accuracy of expectation maximization estimates of a frequency-dependent GMM based on an a priori chosen initialization scheme. It is shown how the proposed technique allows us to construct time-frequency masks which lead to improved model-based source separation for reverberant speech mixtures. Experiments and analysis are performed on speech mixtures formed using real room-recorded impulse responses.

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

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

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

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

A probabilistic soft alert method for abnormal glycemic event by quantitative analysis of prediction uncertainty for type 1 diabetes

Alerting abnormal glycemic event is of importance for people with type 1 diabetes mellitus (T1DM) using continuous glucose monitoring. The traditional deterministic hyper/hypoglycemia predictive alert methods do not consider the presence of prediction errors resulting from model inaccuracy and external disturbances and may lead to false positive alerts resulting in incorrect therapeutic actions. To address this problem, a probabilistic soft alert method is proposed to quantify the prediction uncertainty of hyper/hypoglycemic events. This method evaluates uncertainty caused by prediction errors and the probability density function of prediction errors is estimated using the Gaussian mixture model (GMM). Thus, a soft confidence interval can be set and the probability of the hyper/hypoglycemia alert can be calculated. The parameters of GMM can be updated to revise the probability density function and confidence interval in order to capture changes of prediction uncertainty with time. The proposed method is investigated using data collected from thirty in silico subjects and ten adults with type 1 diabetes. For the in silico subjects, the proposed method reduced missed alerts by 57.1%, false alerts by 73.3% and time delay by 42.3% for hypoglycemia alert utilizing autoregressive models with exogenous inputs model. For the adult subjects, the time delay of hyperglycemia alert was reduced by 33.2% and the time delay of hypoglycemia alert was reduced by 41.6% utilizing subject-dependent autoregressive model. The proposed method is demonstrated to be able to improve the alert performance of the abnormal glycemic events.

Memory-Efficient Parametric Semiglobal Matching

Accurate stereo matching for depth extraction requires a large memory space, which restricts its use in resource-limited systems. The problem is aggravated by the recent trend of applications requiring significantly high pixel resolution and disparity levels. To alleviate the high memory requirement, we propose to represent the aggregation costs as a Gaussian mixture model (GMM) function. Only a set of GMM parameters is stored and used instead of all the costs for each pixel. We also propose GMM parameter update-based aggregation along multiple paths. To preserve the accuracy of the disparity map, we employ a depth confidence measure and propose an update rule for the slanted surface of an object. Experimental results over the KITTI dataset show that the proposed method reduces the memory requirement to less than 5% of that of semiglobal matching, while the accuracy is maintained at the level of state-of-the-art semiglobal and local methods.

A Gaussian Mixture Model Representation of Endmember Variability in Hyperspectral Unmixing

Hyperspectral unmixing while considering endmember variability is usually performed by the normal compositional model, where the endmembers for each pixel are assumed to be sampled from unimodal Gaussian distributions. However, in real applications, the distribution of a material is often not Gaussian. In this paper, we use Gaussian mixture models (GMM) to represent endmember variability. We show, given the GMM starting premise, that the distribution of the mixed pixel (under the linear mixing model) is also a GMM (and this is shown from two perspectives). The first perspective originates from random variable transformations and gives a conditional density function of the pixels given the abundances and GMM parameters. With proper smoothness and sparsity prior constraints on the abundances, the conditional density function leads to a standard maximum a posteriori (MAP ) problem which can be solved using generalized expectation maximization. The second perspective originates from marginalizing over the endmembers in the GMM, which provides us with a foundation to solve for the endmembers at each pixel. Hence, compared to the other distribution based methods, our model can not only estimate the abundances and distribution parameters, but also the distinct endmember set for each pixel. We tested the proposed GMM on several synthetic and real datasets, and showed its potential by comparing it to current popular methods.

Travel pattern modelling and future travel behaviour prediction based on GMM and GPR

How to use historical data of public smart card to predict user behaviour attracts a lot of attention. This paper aims at modelling travel patterns and predicting future travel behaviour of metro system smart card holders. We apply Gaussian mixture model (GMM) on time series to model user behaviour. We propose a new method based on the perplexity for finite GMM and use expectation-maximisation (EM) algorithm to estimate parameters of GMM. In order to predict the future travel behaviour, we introduce the Gaussian process regression (GPR) to define distributions over GMM, which can not only tell the probability of travelling at a certain moment but also tell the reliability of the prediction. Experimental results show that our whole system in the centre of GMM and GPR can effectively mine the hidden knowledge of historical data of smart card, and thus model the travel patterns and predict future travel behaviour.