Enhancing microseismic/acoustic emission source localization accuracy with an outlier-robust kernel density estimation approach

Monitoring sensors in complex engineering environments often record abnormal data,leading to significant positioning errors.To reduce the influence of abnormal arrival times,we introduce an innovative,outlier-robust localization method that integrates kernel density estimation(KDE)with damping linear correction to enhance the precision of microseismic/acoustic emission(MS/AE)source positioning.Our approach systematically addresses abnormal arrival times through a three-step process:initial location by 4-arrival combinations,elimination of outliers based on three-dimensional KDE,and refinement using a linear correction with an adaptive damping factor.We validate our method through lead-breaking experiments,demonstrating over a 23%improvement in positioning accuracy with a maximum error of 9.12 mm(relative error of 15.80%)—outperforming 4 existing methods.Simulations under various system errors,outlier scales,and ratios substantiate our method’s superior performance.Field blasting experiments also confirm the practical applicability,with an average positioning error of 11.71 m(relative error of 7.59%),compared to 23.56,66.09,16.95,and 28.52 m for other methods.This research is significant as it enhances the robustness of MS/AE source localization when confronted with data anomalies.It also provides a practical solution for real-world engineering and safety monitoring applications.

Bayesian Classifier Based on Robust Kernel Density Estimation and Harris Hawks Optimisation

In real-world applications, datasets frequently contain outliers, which can hinder the generalization ability of machine learning models. Bayesian classifiers, a popular supervised learning method, rely on accurate probability density estimation for classifying continuous datasets. However, achieving precise density estimation with datasets containing outliers poses a significant challenge. This paper introduces a Bayesian classifier that utilizes optimized robust kernel density estimation to address this issue. Our proposed method enhances the accuracy of probability density distribution estimation by mitigating the impact of outliers on the training sample’s estimated distribution. Unlike the conventional kernel density estimator, our robust estimator can be seen as a weighted kernel mapping summary for each sample. This kernel mapping performs the inner product in the Hilbert space, allowing the kernel density estimation to be considered the average of the samples’ mapping in the Hilbert space using a reproducing kernel. M-estimation techniques are used to obtain accurate mean values and solve the weights. Meanwhile, complete cross-validation is used as the objective function to search for the optimal bandwidth, which impacts the estimator. The Harris Hawks Optimisation optimizes the objective function to improve the estimation accuracy. The experimental results show that it outperforms other optimization algorithms regarding convergence speed and objective function value during the bandwidth search. The optimal robust kernel density estimator achieves better fitness performance than the traditional kernel density estimator when the training data contains outliers. The Naïve Bayesian with optimal robust kernel density estimation improves the generalization in the classification with outliers.

Probability distribution of wind power volatility based on the moving average method and improved nonparametric kernel density estimation

In the process of large-scale,grid-connected wind power operations,it is important to establish an accurate probability distribution model for wind farm fluctuations.In this study,a wind power fluctuation modeling method is proposed based on the method of moving average and adaptive nonparametric kernel density estimation(NPKDE)method.Firstly,the method of moving average is used to reduce the fluctuation of the sampling wind power component,and the probability characteristics of the modeling are then determined based on the NPKDE.Secondly,the model is improved adaptively,and is then solved by using constraint-order optimization.The simulation results show that this method has a better accuracy and applicability compared with the modeling method based on traditional parameter estimation,and solves the local adaptation problem of traditional NPKDE.

Identification of crash hotspots using kernel density estimation and kriging methods:a comparison

This paper presents a study aimed at comparing the outcome of two geostatistical-based approaches, namely kernel density estimation （KDE） and kriging, for identifying crash hotspots in a road network. Aiming at locating high-risk locations for potential intervention, hotspot identification is an integral component of any comprehensive road safety management programs. A case study was conducted with historical crash data collected between 2003 and 2007 in the Hennepin County of Min- nesota, U.S. The two methods were evaluated on the basis of a prediction accuracy index （PAI） and a comparison in hotspot ranking. It was found that, based on the PAI measure, the kriging method outperformed the KDE method in its ability to detect hotspots, for all four tested groups of crash data with different times of day. Further- more, the lists of hotspots identified by the two methods were found to be moderately different, indicating the im- portance of selecting the right geostatistical method for hotspot identification. Notwithstanding the fact that the comparison study presented herein is limited to one case study, the findings have shown the promising perspective of the kriging technique for road safety analysis.

Kernel density estimation and marginalized-particle based probability hypothesis density filter for multi-target tracking

In order to improve the performance of the probability hypothesis density(PHD) algorithm based particle filter(PF) in terms of number estimation and states extraction of multiple targets, a new probability hypothesis density filter algorithm based on marginalized particle and kernel density estimation is proposed, which utilizes the idea of marginalized particle filter to enhance the estimating performance of the PHD. The state variables are decomposed into linear and non-linear parts. The particle filter is adopted to predict and estimate the nonlinear states of multi-target after dimensionality reduction, while the Kalman filter is applied to estimate the linear parts under linear Gaussian condition. Embedding the information of the linear states into the estimated nonlinear states helps to reduce the estimating variance and improve the accuracy of target number estimation. The meanshift kernel density estimation, being of the inherent nature of searching peak value via an adaptive gradient ascent iteration, is introduced to cluster particles and extract target states, which is independent of the target number and can converge to the local peak position of the PHD distribution while avoiding the errors due to the inaccuracy in modeling and parameters estimation. Experiments show that the proposed algorithm can obtain higher tracking accuracy when using fewer sampling particles and is of lower computational complexity compared with the PF-PHD.

AN EFFECTIVE IMAGE RETRIEVAL METHOD BASED ON KERNEL DENSITY ESTIMATION OF COLLAGE ERROR AND MOMENT INVARIANTS

In this paper, we propose a new method that combines collage error in fractal domain and Hu moment invariants for image retrieval with a statistical method - variable bandwidth Kernel Density Estimation (KDE). The proposed method is called CHK (KDE of Collage error and Hu moment) and it is tested on the Vistex texture database with 640 natural images. Experimental results show that the Average Retrieval Rate (ARR) can reach into 78.18%, which demonstrates that the proposed method performs better than the one with parameters respectively as well as the commonly used histogram method both on retrieval rate and retrieval time.

Anomalous Cell Detection with Kernel Density-Based Local Outlier Factor

Since data services are penetrating into our daily life rapidly, the mobile network becomes more complicated, and the amount of data transmission is more and more increasing. In this case, the traditional statistical methods for anomalous cell detection cannot adapt to the evolution of networks, and data mining becomes the mainstream. In this paper, we propose a novel kernel density-based local outlier factor(KLOF) to assign a degree of being an outlier to each object. Firstly, the notion of KLOF is introduced, which captures exactly the relative degree of isolation. Then, by analyzing its properties, including the tightness of upper and lower bounds, sensitivity of density perturbation, we find that KLOF is much greater than 1 for outliers. Lastly, KLOFis applied on a real-world dataset to detect anomalous cells with abnormal key performance indicators(KPIs) to verify its reliability. The experiment shows that KLOF can find outliers efficiently. It can be a guideline for the operators to perform faster and more efficient trouble shooting.

Diversity Sampling Based Kernel Density Estimation for Background Modeling

A novel diversity-sampling based nonparametric multi-modal background model is proposed. Using the samples having more popular and various intensity values in the training sequence, a nonparametric model is built for background subtraction. According to the related intensifies, different weights are given to the distinct samples in kernel density estimation. This avoids repeated computation using all samples, and makes computation more efficient in the evaluation phase. Experimental results show the validity of the diversity- sampling scheme and robustness of the proposed model in moving objects segmentation. The proposed algorithm can be used in outdoor surveillance systems.

Optimization Strategy of Commercial Space in Xianyukou Hutong Based on Kernel Density and Space Syntax

Beijing Xianyukou Hutong(hutong refers to historical and cultural block in Chinese)occupies an important geographical location with unique urban fabric,and after years of renewal and protection,the commercial space of Xianyukou Street and has gained some recognition.This article Xianyukou takes commercial hutong in Beijing as an example,spatial analysis was carried out using methods like GIS kernel density method,space syntax after site investigation and research.Based on the street space problems found,this paper then puts forward strategies to improve and upgrade Xianyukou Street’s commercial space and improve businesses in Xianyukou Street and other similar hutong.

Wind speed model based on kernel density estimation and its application in reliability assessment of generating systems

An accurate probability distribution model of wind speed is critical to the assessment of reliability contribution of wind energy to power systems. Most of current models are built using the parametric density estimation(PDE) methods, which usually assume that the wind speed are subordinate to a certain known distribution(e.g. Weibull distribution and Normal distribution) and estimate the parameters of models with the historical data. This paper presents a kernel density estimation(KDE) method which is a nonparametric way to estimate the probability density function(PDF) of wind speed. The method is a kind of data-driven approach without making any assumption on the form of the underlying wind speed distribution, and capable of uncovering the statistical information hidden in the historical data. The proposed method is compared with three parametric models using wind data from six sites.The results indicate that the KDE outperforms the PDE in terms of accuracy and flexibility in describing the longterm wind speed distributions for all sites. A sensitivity analysis with respect to kernel functions is presented and Gauss kernel function is proved to be the best one. Case studies on a standard IEEE reliability test system(IEEERTS) have verified the applicability and effectiveness of the proposed model in evaluating the reliability performance of wind farms.

Consistency of kernel density estimators for causal processes

Using the blocking techniques and m-dependent methods,the asymptotic behavior of kernel density estimators for a class of stationary processes,which includes some nonlinear time series models,is investigated.First,the pointwise and uniformly weak convergence rates of the deviation of kernel density estimator with respect to its mean(and the true density function)are derived.Secondly,the corresponding strong convergence rates are investigated.It is showed,under mild conditions on the kernel functions and bandwidths,that the optimal rates for the i.i.d.density models are also optimal for these processes.

Development and application of traffic accident density estimation models using kernel density estimation

Traffic accident frequency has been decreasing in Japan in recent years. Nevertheless, many accidents still occur on residential roads. Area-wide traffic calming measures including Zone 30, which discourages traffic by setting a speed limit of 30 km/h in residential areas, have been implemented. However, no objective implementation method has been established. Development of a model for traffic accident density estimation explained by GIS data can enable the determination of dangerous areas objectively and easily, indicating where area-wide traffic calming can be implemented preferentially. This study examined the relations between traffic accidents and city characteristics, such as population, road factors, and spatial factors. A model was developed to estimate traffic accident density. Kernel density estimation （KDE） techniques were used to assess the relations efficiently. Besides, 16 models were developed by combining accident locations, accident types, and data types. By using them, the applicability of traffic accident density estimation models was examined. Results obtained using Spearman rank correlation show high coefficients between the predicted number and the actual number. The model can indicate the relative accident risk in cities. Results of this study can be used for objective determination of areas where area-wide traffic calming can be implemented preferentially, even if sufficient traffic accident data are not available.

Dm-KDE： dynamical kernel density estimation by sequences of KDE estimators with fixed number of components over data streams

In many data stream mining applications, traditional density estimation methods such as kemel density estimation, reduced set density estimation can not be applied to the density estimation of data streams because of their high computational burden, processing time and intensive memory allocation requirement. In order to reduce the time and space complexity, a novel density estimation method Dm-KDE over data streams based on the proposed algorithm m-KDE which can be used to design a KDE estimator with the fixed number of kernel components for a dataset is proposed. In this method, Dm-KDE sequence entries are created by algorithm m-KDE instead of all kemels obtained from other density estimation methods. In order to further reduce the storage space, Dm-KDE sequence entries can be merged by calculating their KL divergences. Finally, the probability density functions over arbitrary time or entire time can be estimated through the obtained estimation model. In contrast to the state-of-the-art algorithm SOMKE, the distinctive advantage of the proposed algorithm Dm-KDE exists in that it can achieve the same accuracy with much less fixed number of kernel components such that it is suitable for the scenarios where higher on-line computation about the kernel density estimation over data streams is required. We compare Dm-KDE with SOMKE and M-kernel in terms of density estimation accuracy and running time for various stationary datasets. We also apply Dm-KDE to evolving data streams. Experimental results illustrate the effectiveness of the pro- posed method.

An Independent Component Analysis Algorithm through Solving Gradient Equation Combined with Kernel Density Estimation

A new algorithm for linear instantaneous independent component analysis is proposed based on maximizing the log-likelihood contrast function which can be changed into a gradient equation.An iterative method is introduced to solve this equation efficiently.The unknown probability density functions as well as their first and second derivatives in the gradient equation are estimated by kernel density method.Computer simulations on artificially generated signals and gray scale natural scene images confirm the efficiency and accuracy of the proposed algorithm.

Static Frame Model Validation with Small Samples Solution Using Improved Kernel Density Estimation and Confidence Level Method

An improved method using kernel density estimation （KDE） and confidence level is presented for model validation with small samples. Decision making is a challenging problem because of input uncertainty and only small samples can be used due to the high costs of experimental measurements. However, model validation provides more confidence for decision makers when improving prediction accuracy at the same time. The confidence level method is introduced and the optimum sample variance is determined using a new method in kernel density estimation to increase the credibility of model validation. As a numerical example, the static frame model validation challenge problem presented by Sandia National Laboratories has been chosen. The optimum bandwidth is selected in kernel density estimation in order to build the probability model based on the calibration data. The model assessment is achieved using validation and accreditation experimental data respectively based on the probability model. Finally, the target structure prediction is performed using validated model, which are consistent with the results obtained by other researchers. The results demonstrate that the method using the improved confidence level and kernel density estimation is an effective approach to solve the model validation problem with small samples.

Large Deviations and Moderate Deviations for Kernel Density Estimators of Directional Data

Let fn be the non-parametric kernel density estimator of directional data based on a kernel function K and a sequence of independent and identically distributed random variables taking values in d-dimensional unit sphere Sd-1. It is proved that if the kernel function is a function with bounded variation and the density function f of the random variables is continuous, then large deviation principle and moderate deviation principle for {sup x∈sd-1 ｜fn（x） - E（fn（x））｜, n ≥ 1} hold.

Kernel Density Estimation Based Multiphase Fuzzy Region Competition Method for Texture Image Segmentation

In this paper,we propose a multiphase fuzzy region competition model for texture image segmentation.In the functional,each region is represented by a fuzzy membership function and a probability density function that is estimated by a nonparametric kernel density estimation.The overall algorithm is very efficient as both the fuzzy membership function and the probability density function can be implemented easily.We apply the proposed method to synthetic and natural texture images,and synthetic aperture radar images.Our experimental results have shown that the proposed method is competitive with the other state-of-the-art segmentation methods.

Volumetric magnetic resonance imaging classification for Alzheimer＇s disease based on kernel density estimation of local features

Background The classification of Alzheimer＇s disease （AD） from magnetic resonance imaging （MRI） has been challenged by lack of effective and reliable biomarkers due to inter-subject variability. This article presents a classification method for AD based on kernel density estimation （KDE） of local features. Methods First, a large number of local features were extracted from stable image blobs to represent various anatomical patterns for potential effective biomarkers. Based on distinctive descriptors and locations, the local features were robustly clustered to identify correspondences of the same underlying patterns. Then, the KDE was used to estimate distribution parameters of the correspondences by weighting contributions according to their distances. Thus, biomarkers could be reliably quantified by reducing the effects of further away correspondences which were more likely noises from inter-subject variability. Finally, the Bayes classifier was applied on the distribution parameters for the classification of AD. Results Experiments were performed on different divisions of a publicly available database to investigate the accuracy and the effects of age and AD severity. Our method achieved an equal error classification rate of 0.85 for subject aged 60-80 years exhibiting mild AD and outperformed a recent local feature-based work regardless of both effects. Conclusions We proposed a volumetric brain MRI classification method for neurodegenerative disease based on statistics of local features using KDE. The method may be potentially useful for the computer-aided diagnosis in clinical settings.

Covariate balancing based on kernel density estimates for controlled experiments

Controlled experiments are widely used in many applications to investigate the causal relationship between input factors and experimental outcomes.A completely randomised design is usually used to randomly assign treatment levels to experimental units.When covariates of the experimental units are available,the experimental design should achieve covariate balancing among the treatment groups,such that the statistical inference of the treatment effects is not confounded with any possible effects of covariates.However,covariate imbalance often exists,because the experiment is carried out based on a single realisation of the complete randomisation.It is more likely to occur and worsen when the size of the experimental units is small or moderate.In this paper,we introduce a new covariate balancing criterion,which measures the differences between kernel density estimates of the covariates of treatment groups.To achieve covariate balance before the treatments are randomly assigned,we partition the experimental units by minimising the criterion,then randomly assign the treatment levels to the partitioned groups.Through numerical examples,weshow that the proposed partition approach can improve the accuracy of the difference-in-mean estimator and outperforms the complete randomisation and rerandomisation approaches.

Fast and accurate kernel density approximation using a divide-and-conquer approach

Density-based nonparametric clustering techniques,such as the mean shift algorithm,are well known for their flexibility and effectiveness in real-world vision-based problems.The underlying kernel density estimation process can be very expensive on large datasets.In this paper,the divide-and-conquer method is proposed to reduce these computational requirements.The dataset is first partitioned into a number of small,compact clusters.Components of the kernel estimator in each local cluster are then fit to a single,representative density function.The key novelty presented here is the efficient derivation of the representative density function using concepts from function approximation,such that the expensive kernel density estimator can be easily summarized by a highly compact model with very few basis functions.The proposed method has a time complexity that is only linear in the sample size and data dimensionality.Moreover,the bandwidth of the resultant density model is adaptive to local data distribution.Experiments on color image filtering/segmentation show that,the proposed method is dramatically faster than both the standard mean shift and fast mean shift implementations based on kd-trees while