Gaussian Statistical Model Research Articles

Bounds for the estimation of matrix-valued parameters of a Gaussian random process

This paper derives and studies Bayesian Cramér-Rao lower bounds for the mean squared error of covariance matrices that are structured as weighted sums of symmetric positive definite matrices associated with a circularly-symmetric Gaussian statistical model. This model naturally appears in a number of important applications, including multivariate multifractal analysis and vector-valued additive Gaussian processes. As an intermediary result, we derive a novel expression for the expectation of compositions of Wishart random matrices. We provide extensive numerical simulation results for analyzing the derived bounds and their properties, and illustrate their use for the multifractal analysis of bivariate time series.

Caustics in turbulent aerosols form along the Vieillefosse line at weak particle inertia

Caustic singularities of the spatial distribution of particles in turbulent aerosols enhance collision rates and accelerate coagulation. Here we investigate how and where caustics form at weak particle inertia, by analysing a three-dimensional Gaussian statistical model for turbulent aerosols in the persistent limit, where the flow varies slowly compared with the particle relaxation time. In this case, correlations between particle- and fluid-velocity gradients are strong, and caustics are induced by large, strain-dominated excursions of the fluid-velocity gradients. These excursions must cross a characteristic threshold in the plane spanned by the invariants $Q$ and $R$ of the fluid-velocity gradients. Our method predicts that the most likely way to reach this threshold is by a unique ``optimal fluctuation'' that propagates along the Vieillefosse line, $27R^2/4 +Q^3=0$. We determine the shape of the optimal fluctuation as a function of time and show that it is dominant in numerical statistical-model simulations even for moderate particle inertia.

Hyperspectral Remote Sensing Benchmark Database for Oil Spill Detection With an Isolation Forest-Guided Unsupervised Detector

Oil spill detection has attracted increasing attention in recent years since marine oil spill accidents severely affect environments, natural resources, and the lives of coastal inhabitants. Hyperspectral remote sensing images provide rich spectral information which is beneficial for the monitoring of oil spills in complex ocean scenarios. However, most of the existing approaches are based on supervised and semi-supervised frameworks to detect oil spills from hyperspectral images (HSIs), which require a massive amount of effort to annotate a certain number of high-quality training sets. In this study, we make the first attempt to develop an unsupervised oil spill detection method based on isolation forest for HSIs. First, a Gaussian statistical model is designed to remove the bands corrupted by severe noise. Then, kernel principal component analysis (KPCA) is employed to reduce the high dimensionality of the HSIs. Next, the probability of each pixel belonging to one of the classes of seawater and oil spills is estimated with the isolation forest, and a set of pseudo-labeled training samples is automatically produced using the clustering algorithm on the detected probability. Finally, an initial detection map can be obtained by performing the support vector machine (SVM) on the dimension-reduced data, and the initial detection result is further optimized with the extended random walker (ERW) model so as to improve the detection accuracy of oil spills. Experiments on hyperspectral oil spill data (HOSD) created by ourselves demonstrate that the proposed method obtains superior detection performance with respect to other state-of-the-art detection approaches. We will make HOSD and our developed library for oil spill detection publicly available at https://github.com/PuhongDuan/HOSD to further promote this research topic.

Hybrid Forecasting of Wind for Air Pollution Dispersion over Complex Terrain

In case of an unplanned emission event from a nuclear power plant, the local population can be protected more efficiently when valid atmospheric dispersion model results are available. Atmospheric dispersion models use local meteorological variables as inputs. When atmospheric dispersion in the future is being predicted, a forecast of the local meteorological variables is needed. The most important variable in atmospheric dispersion modelling is wind, and accurately predicting ground level winds presents a challenge to numerical weather prediction models. We therefore develop hybrid models for forecasting local ground level wind at a single location where the terrain is complex and the average wind is weak and fluctuating. Wind speed and direction are modelled as west-east and south-north wind components. Each model is composed of a numerical weather prediction model and a Gaussian process statistical model that uses numerical weather predictions as some of its inputs and is trained on historical data to predict the output component. The most advanced Gaussian process models studied are of Gaussian process nonlinear autoregressive model with exogenous input (GPNARX) type. In addition to numerical weather predictions, they also use local meteorological variables, including the output variable, as their inputs. Numerical weather prediction results based on large scale information and fundamental knowledge of the system are thus supplemented by local measurements that better reflect the effects of local topography and land use. The models are tested by prediction and simulation. The wind components predicted by more advanced models are more accurate than raw or post-processed numerical weather prediction results. As an example, a model predicting 2D wind vector 1.5 h in advance achieves a NRMSE of 0.214 if it uses all the immediately available information. This is better than both the persistence model with NRMSE of 0.188 and post-processed NWP with NRMSE of 0.164. This demonstrates that hybrid modelling provides the best weather information for short-term and medium-term atmospheric dispersion forecasting. While the method is motivated by nuclear emission sources, it could also be applied to other pollution.

A learning-based evaluation for lane departure warning system considering driving characteristics

Misunderstanding the driver behavior in the next short time is the primary reason of the false warning for the lane departure warning system. This paper proposes a learning-based evaluation to predict whether the driver notices the deviation of the vehicle and takes corrective actions. First, statistical Gaussian model and K-means clustering method are utilized to classify driving style of drivers and determine warning areas based on key driving parameters extracted in driving scenarios. Then, according to the vehicle trajectory in the warning area and the time of lane crossing (TLC) value of the two warning area boundaries, an advanced horizontal dual-area warning (HDAW) model that is trained by bi-direction long short-term memory (BiLSTM) originated from recurrent neural network (RNN) is applied to predict the lane departure and corrective behavior of driver. The personalized warning strategy is finally developed by considering driver characteristics, which allows the warning system to adapt to different driving styles of drivers. Natural driving data from 57 drivers in the experimental driving simulator are collected to train personalized prediction and verify proposed evaluation method. The recent directional sequence of piecewise lateral slopes (DSPLS) and traditional TLC are also researched and compared. Experimental results show that the proposed approach has as low as false alarm rate of 3.97% and can improve prediction accuracy approximately 41.39% over DSPLS method.

Evaluation of Distance Error with Bluetooth Low Energy Transmission Model for Indoor Positioning

Currently, an indoor positioning is a challenge application for location-based services (LBS) and proximity-based services (PBS). However, the indoor channel has dense multipath fading, causing more distance error than outdoor positioning. In this paper, the distance error analysis model is proposed for indoor positioning. The indoor channel is modeled as the sum of path loss model and multipath fading model. The path loss model is a linear regression model (LRM) based on Friis’ transmission formula, used for estimating the distance from received signal strength (RSS). The multipath fading is a Gaussian statistical model with zero mean, used for characterizing the multipath fading effect. The normalized distance error is evaluated and defined. The indoor channel with Bluetooth low energy (BLE) beacons is measured and compared with the proposed model. From the results, the normalized distance error obtained from the proposed model corresponds very well to measurement. This proposed model can be used as a tool for designing an indoor positioning system to obtain the specific distance error.

Gaussian Distribution-Based Machine Learning Scheme for Anomaly Detection in Healthcare Sensor Cloud

Smart information systems are based on sensors that generate a huge amount of data. This data can be stored in cloud for further processing and efficient utilization. Anomalous data might be present within the sensor data due to various reasons (e.g., malicious activities by intruders, low quality sensors, and node deployment in harsh environments). Anomaly detection is crucial in some applications such as healthcare monitoring systems, forest fire information systems, and other internet of things (IoT) systems. This paper proposes a Gaussian distribution-based supervised machine learning scheme of anomaly detection (GDA) for healthcare monitoring sensor cloud, which is an integration of various body sensors of different patients and cloud. This work is implemented in Python. Use of Gaussian statistical model in the proposed scheme improves precision, throughput, and efficiency. GDA provides 98% efficiency with 3% and 4% improvements as compared to the other supervised learning-based anomaly detection schemes (e.g., support vector machine [SVM] and self-organizing map [SOM], respectively).

Seizure activity classification based on bimodal Gaussian modeling of the gamma and theta band IMFs of EEG signals

In this manuscript, EEG signals of seizure and non-seizure activities have been discussed and classified into five groups on the basis of seizure onset, seizure action and brain signal recording location. EEG signals consisting of gamma-band (40–80 Hz) and theta-band (4–8 Hz) oscillations have been captured for performing empirical mode decomposition (EMD). Dominant intrinsic mode functions (IMFs) have been selected from the consequences of EMD and a statistical model is employed upon the IMFs to summarize the information on those. Bimodal Gaussian statistical model has been found most effective to prepare feature set taking the modeling parameters of its probability density function (PDF). Plotting together bimodal Gaussian PDF and empirical PDF for pictorial scrutiny; cumulative distribution function (CDF) in probability–probability (p–p) plot and goodness of fit K–S test result justified the effectiveness of proposed bimodal Gaussian statistical model. Hence, aforementioned statistical modeling parameters have been sent to numerous classifiers and rationalization of goodness of features has been shown through inter-class separability and intra-class compactness parameters. Extensive varieties of simulations are performed using a well-established dataset. The suggested strategy reveals the capability of making higher values of sensitivity, specificity and accuracy compared to that made by some cutting-edge methods utilizing the same EEG dataset.

Correction of overlapping peaks of Pb and As spectrum based on a chaotic particle swarm optimization–Gaussian mixture statistical model

AbstractEnergy‐dispersive X‐ray fluorescence spectroscopy has been effectively applied to detect heavy metals in soil because of its fast detection speed, low cost, and high accuracy. However, overlapping peaks appear in the detection of some heavy metals, such as Pb and As, resulting in significant errors in the detection. Therefore, it is impossible to accurately predict the content of heavy metals in soil. To solve this problem, a Gaussian mixture statistical model (GMSM) is applied based on physical characteristics randomly formed by X‐rays combined with statistical ideas. Subsequently, when estimating the parameters of the GMSM, performing particle swarm optimization (PSO) causes the parameters to fall into the local optima easily. Chaos theory is introduced to the PSO algorithm to promote its weight update strategy, and the chaotic PSO (CPSO) with an anti‐premature mechanism is proposed to achieve global convergence. When using CPSO‐GMSM to analyze the overlapping peaks, the relative error compared with the actual single metal sample is less than 0.0693, and the error compared with the actual characteristic peak position is less than 0.0133. The overlapping peaks are corrected effectively, providing a foundation for the accurate quantitative analysis of heavy metals in soil.

Correcting TG 119 confidence limits.

Task Group 119 (TG-119) has been adopted for evaluating the adequacy of intensity-modulated radiation therapy (IMRT) commissioning and for establishing patient-specific IMRT quality assurance (QA) passing criteria in clinical practice. TG-119 establishes 95% confidence limits (CLs), which help clinics identify systematic IMRT QA errors and identify outliers. In TG-119, the 95% CLs are established by fitting the Gamma Γ analysis passing rate results to an assumed distribution, then calculating the limit in which 95% of the data fall. CLs for a given dataset will depend greatly on the type of distribution used, and those determined by following the TG-119 guidelines are only valid if the underlying data follows a Gaussian distribution. Gaussian distributions assume symmetry about the mean, which would imply the possibility of negative Γ analysis failing rates. This study demonstrates that the gamma distribution is a more reasonable assumption for establishing CLs than the Gaussian distribution used in TG-119. Thus, the gamma distribution is suggested as a replacement to the conventional Gaussian statistical model used in TG-119. The moments estimator (ME) for the gamma family is used to obtain the CLs of the failing rates for all Γ analysis criteria. To demonstrate the congruence of the gamma distribution, the root mean squared error and the CL values for the MEs of the gamma and the Gaussian families were compared. In this study, the empirical 95% CLs generated using 302 plans represent the ground truth, which resulted in a 91.83% passing rate using 3%/3 mm error local criteria. The gamma distribution underestimates the 95% CL by 0.09%, while the Gaussian distribution overestimates the 95% CL by 4.12%. Although IMRT QA equipment may vary between clinics, the mathematical formalism presented in this study applies to any combination of planning and delivery systems. This study has demonstrated that a gamma distribution should be favored over a Gaussian distribution when establishing CLs for IMRT QA.

Fast statistical model-based classification of epileptic EEG signals

This paper presents a supervised classification method to accurately detect epileptic brain activity in real-time from electroencephalography (EEG) data. The proposed method has three main strengths: it has low computational cost, making it suitable for real-time implementation in EEG devices; it performs detection separately for each brain rhythm or EEG spectral band, following the current medical practices; and it can be trained with small datasets, which is key in clinical problems where there is limited annotated data available. This is in sharp contrast with modern approaches based on machine learning techniques, which achieve very high sensitivity and specificity but require large training sets with expert annotations that may not be available. The proposed method proceeds by first separating EEG signals into their five brain rhythms by using a wavelet filter bank. Each brain rhythm signal is then mapped to a low-dimensional manifold by using a generalized Gaussian statistical model; this dimensionality reduction step is computationally straightforward and greatly improves supervised classification performance in problems with little training data available. Finally, this is followed by parallel linear classifications on the statistical manifold to detect if the signals exhibit healthy or abnormal brain activity in each spectral band. The good performance of the proposed method is demonstrated with an application to paediatric neurology using 39 EEG recordings from the Children's Hospital Boston database, where it achieves an average sensitivity of 98%, specificity of 88%, and detection latency of 4s, performing similarly to the best approaches from the literature.

Statistical Model for the Orientation of Nonspherical Particles Settling in Turbulence.

The orientation of small anisotropic particles settling in a turbulent fluid determines some essential properties of the suspension. We show that the orientation distribution of small heavy spheroids settling through turbulence can be accurately predicted by a simple Gaussian statistical model that takes into account particle inertia and provides a quantitative understanding of the orientation distribution on the problem parameters when fluid inertia is negligible. Our results open the way to a parametrization of the distribution of ice crystals in clouds, and potentially lead to an improved understanding of radiation reflection or particle aggregation through collisions in clouds.

A Probabilistic Cost/Benefit Analysis of Transmission and Distribution Asset Expansion Projects

The electric power industry often uses cost/benefit analysis to evaluate system expansion projects. This letter discusses a probabilistic formulation of cost/benefit analysis to incorporate uncertainty in the data used for these studies. A Gaussian statistical model is used and an example is shown relating to distribution engineering.

Frame Selection for Robust Speaker Identification: A Hybrid Approach

Identification of a person using voice is a challenging task under environmental noises. Important and reliable frame selection for feature extraction from the time-domain speech signal under noise can play a significant role in improving speaker identification accuracy. Therefore, this paper presents a frame selection method using hybrid technique, which combines two techniques, namely, voice activity detection (VAD) and variable frame rate (VFR) analysis. It efficiently captures the active speech part, the changes in the temporal characteristics of the speech signal, taking into account the signal-to-noise ratio, and thereby speaker-specific information. Experimental results on noisy speech, generated by artificially adding various noise signals to the clean YOHO speech at different SNRs have shown improved results for the frame selection by the hybrid technique in comparison with any one of the techniques used for the hybrid. The proposed hybrid technique outperformed both the VFR and the widely used Gaussian statistical model based VAD method for all noise scenarios at different SNRs, except for the Babble noise corrupted speech at 5 dB SNR, for which, VFR performed better. Considering the average identification accuracies of different noise scenarios, a relative improvement of 9.79% over the VFR, and 18.05% over the Gaussian statistical model based VAD method has been achieved.

Average BER and outage probability of the ground-to-train OWC link in turbulence with rain

The bit-error rate (BER) and outage probability of optical wireless communication (OWC) link for the ground-to-train of the curved track in turbulence with rain is evaluated. Considering the re-modulation effects of raining fluctuation on optical signal modulated by turbulence, we set up the models of average BER and outage probability in the present of pointing errors, based on the double inverse Gaussian (IG) statistical distribution model. The numerical results indicate that, for the same covered track length, the larger curvature radius increases the outage probability and average BER. The performance of the OWC link in turbulence with rain is limited mainly by the rain rate and pointing errors which are induced by the beam wander and train vibration. The effect of the rain rate on the performance of the link is more severe than the atmospheric turbulence, but the fluctuation owing to the atmospheric turbulence affects the laser beam propagation more greatly than the skewness of the rain distribution. Besides, the turbulence-induced beam wander has a more significant impact on the system in heavier rain. We can choose the size of transmitting and receiving apertures and improve the shockproof performance of the tracks to optimize the communication performance of the system.

基于后验概率和滤色阵列特性的图像篡改检测算法

针对图像采集过程中插值算法对图像三原色之间所引入的插值特性，论文提出一种基于后验概率和滤色阵列特性的图像篡改检测算法。首先提取待测图像绿色通道分量，引入二维预测滤波构建预测误差函数；然后分块提取特征，分析原始与篡改图像所提特征的直方图特性，从而建立特征的高斯混合统计模型，并借助EM算法估计模型参数；计算子块特征作为原始块的后验概率，定义似然率并应用到每个子块中，从而可得到篡改区域映射图，完成本次检测。仿真结果表明，该算法具有较强的鲁棒性，能够对图像篡改区域进行较准确地定位。 Focused on the artifacts between the three primaries of an image introduced by the interpolation algorithm during its acquisition process, an image tampering detection algorithm based on the posterior probability and the color filter array artifacts is proposed. Firstly, the green channel component of the image is extracted, and the two-dimensional predictive filter is used to construct the predictive error function. Then the histograms’ character of original and tampering images is analyzed, and then the Gaussian mixture statistical model is established. EM algorithm is applied to estimate the model parameters. Then the posterior probability of each sub-block as an original block is calculated, and the feature likelihood is defined and it is applied to every sub-block, so that the tampering-area map can be obtained to complete the detection. The simulation results show that the algorithm has strong robustness and can locate the image’s tampered region more accurately.

Generalized Sign Recognition Based on the Gaussian Statistical Color Model for Intelligent Road Sign Inventory

The rapid progress in sensor and information technologies makes it possible to develop intelligent road sign inventory (IRSI) by automatically collecting and processing vehicle-borne multisensor data. This study developed a framework for IRSI with a vehicle-borne multisensor system. The IRSI framework consists of four modules: ( a) sensor vehicle design for multisensor data collection, ( b) sign recognition, ( c) sign data integration and attribute computation, and ( d) IRSI-based applications. Within the framework, sign recognition is the key to IRSI. The study proposed a novel Gaussian statistical color model (G-SCM) for image segmentation and color feature extraction. The G-SCM has good capability to model actual sign color distributions and has fast implementation for G-SCM-based color segmentation. With color features integrated into sign texture, shape, location, and other features, a novel generalized recognition algorithm is proposed for sign inventory. The proposed G-SCM model and the sign recognition method were tested with actual video log images. The experimental results show that the G-SCM can model actual sign colors and segment sign images accurately. The fast implementation can greatly enhance computation speed compared with existing color analysis methods. The developed sign recognition algorithm was tested to recognize all speed limit signs from video log images collected along a 140-km highway segment. The algorithm recognized 30 of 31 signs and achieved a 96.8% site recognition rate. Of the 136 images containing speed limit signs, the algorithm had only eight false positives. The results demonstrate that the proposed sign recognition method is promising for the development of IRSI.

Disparity based stereo image retrieval through univariate and bivariate models

The widespread use of stereovision in various application fields has led to the constitution of very huge stereo image databases. Therefore, the design of effective content based image retrieval system devoted to stereo pairs becomes an issue of importance. To this end, we propose in this paper two retrieval methods which combine the visual contents of the stereo images with their corresponding disparity information. After modeling the distribution of their associated wavelet coefficients by the generalized Gaussian statistical model, the resulting distribution parameters are selected as salient features. While the two views are processed separately through a univariate modeling in the first method, the second one exploits the correlation between the views by resorting to a bivariate modeling. Experimental results show the benefits which can be drawn from the proposed retrieval approaches.

Bayesian Seabed Classification Using Angle-Dependent Backscatter Data From Multibeam Echo Sounders

<?Pub Dtl=""?> Acoustical seabed classification is a technology for mapping seabed sediments. Processed multibeam sonar data yield the variation of the seabed scattering strength with incidence angle, and this paper examines the effect of this on classification. A simple Gaussian statistical model is developed for the observed scattering strength, whereby an observation is represented by a piecewise constant function of incidence angle. Provided some data for which the sediment types are known (training data), the statistics for each type can be robustly estimated. Subsequently, a standard Bayesian theory is applied to classify new observations. The model was used to compute limits on classification accuracy in terms of the intrinsic scattering strength statistics of the seabed, and to predict whether a logarithmic or linear scale for the data is preferable. Systematic experiments on a North Sea data set with four sediment classes tested how the classification accuracy depends on the piecewise function approximation, incidence angle range, amount of training data, and spatial averaging (combining consecutive pings into one observation). The classifier based on Gaussian statistics performed at least as well as sophisticated algorithms with no assumptions about the data statistics. The best accuracy (95%) was attained for logarithmic data. The amount of training data needed to achieve this was about 500 pings per class; spatial averaging could be limited to 10–20 pings. Comparable across-track spatial resolution was possible by dividing the full swath into separate independent sectors, but only at reduced accuracy (87% or less). However, comparable accuracy may be possible by taking into account the spatial relationships of observations.

Quantifying networks complexity from information geometry viewpoint

We consider a Gaussian statistical model whose parameter space is given by the variances of random variables. Underlying this model we identify networks by interpreting random variables as sitting on vertices and their correlations as weighted edges among vertices. We then associate to the parameter space a statistical manifold endowed with a Riemannian metric structure (that of Fisher-Rao). Going on, in analogy with the microcanonical definition of entropy in Statistical Mechanics, we introduce an entropic measure of networks complexity. We prove that it is invariant under networks isomorphism. Above all, considering networks as simplicial complexes, we evaluate this entropy on simplexes and find that it monotonically increases with their dimension.