Weighted Kernel Density Estimation Research Articles

An efficient analysis method for system reliability of semi-rigid base asphalt pavement structure based on direct probability integral method

The structural design parameters of asphalt pavement inherently possess randomness. Reliability theory aids in considering the stochastic nature of these parameters in asphalt pavement design. However, as the number of considered random factors increases, the complexity of reliability calculation models and the consumption of computational resources also significantly escalate. To analyze the structural reliability of semi-rigid base asphalt pavements more efficiently and accurately, a method combining Weighted Kernel Density Estimation (Weighted-KDE) with Direct Probability Integration Method (DPIM) using sampling strategies was employed. Furthermore, integrating the equivalent extreme value principle, an asphalt pavement structural system reliability analysis method was proposed, considering multiple failure mode correlations. The numerical solution steps of this method are also outlined. Based on the typical semi-rigid asphalt pavement structure in China, this study utilized the elastic layer system method (the program Apbi) and a computational program developed in MATLAB to compare the efficiency and accuracy of calculating reliability between DPIM and the Monte Carlo Simulations (MCS). The computational outcomes indicate that, under the premise of selecting 18 random parameters, DPIM can achieve the required accuracy in assessing the reliability of asphalt pavement structure and system reliability. Analyzing how the number of samples affects the computational results reveals that using weighted-KDE and DPIM only needs a few hundred sample points to limit the relative error within 4 %, compared to the results obtained from 105 samples in MCS. The research findings demonstrate that DPIM incorporating the principle of equivalent extreme value events can serve as an efficient analytical approach for assessing the system reliability of asphalt pavement structures characterized by more complex failure modes.

Large-scale Structures in COSMOS2020: Evolution of Star Formation Activity in Different Environments at 0.4 < z < 4

To study the role of environment in galaxy evolution, we reconstruct the underlying density field of galaxies based on COSMOS2020 (The Farmer catalog) and provide the density catalog for a magnitude-limited (K s < 24.5) sample of ∼210,000 galaxies at 0.4 < z < 5 within the COSMOS field. The environmental densities are calculated using a weighted kernel density estimation approach with the choice of a von Mises–Fisher kernel, an analog of the Gaussian kernel for periodic data. Additionally, we make corrections for the edge effect and masked regions in the field. We utilize physical properties extracted by LePhare to investigate the connection between star formation activity and the environmental density of galaxies in six mass-complete subsamples at different cosmic epochs within 0.4 < z < 4. Our findings confirm a strong anticorrelation between star formation rate (SFR)/specific SFR (sSFR) and environmental density out to z ∼ 1.1. At 1.1 < z < 2, there is no significant correlation between SFR/sSFR and density. At 2 < z < 4, we observe a reversal of the SFR/sSFR–density relation such that both SFR and sSFR increase by a factor of ∼10 with increasing density contrast, δ, from −0.4 to 5. This observed reversal at higher redshifts supports the scenario where an increased availability of gas supply, along with tidal interactions and a generally higher star formation efficiency in dense environments, could potentially enhance star formation activity in galaxies located in rich environments at z > 2.

INTEGRATION NEEDS AND CHALLENGES FOR GREEN AND SMART TRANSFORMATION OF PORT INDUSTRY BASED ON MULTI-SOURCE DATA

This research explores the integration needs and challenges for achieving green and smart transformation in the port industry, leveraging multi-source data and geographic information technology. The study utilizes comprehensive data, including information from the National Enterprise Credit Information Publicity System, the National Catalogue Service for Geographic Information, and road network maps of Jiangsu Province in China. Geographical analysis methods, such as weighted kernel density estimation and standard deviation ellipse analysis, are employed to identify spatial distribution patterns and changes in the port and shipping service industry. The results indicate a spatial distribution pattern with weak expansion from the center, along the "northwest-southeast" direction. Challenges such as decentralized management and competition for interests hinder port integration for sustainable development. By understanding the spatial dynamics, policymakers can make informed decisions for a greener, smarter, and more efficient port sector.

Toward Safer and Energy Efficient Global Trajectory Planning of Self-Guided Vehicles for Material Handling System in Dynamic Environment

For a sustainable operation of multiple Self-Guided Vehicles (SGVs) in a dynamic manufacturing environment, it is essential to guarantee collision-free and efficient navigation to the autonomous mobile platforms and safety to the surrounding subjects. To prevent from navigation failures, an SGV must avoid conflicts that constrain itself to abruptly brake or stop to avoid collisions. These inefficient conflicts result from unexpected changes in the configuration space or due to nearby unforeseen obstacle. In this paper, a navigation approach is proposed to adapt the global trajectory in order to reduce conflict occurrence while limiting energy consumption of the mobile platform. To generate such trajectory, first the collision risks are characterized using an objective risk perception parameter, the Time-To-Collision TTC, that rely on the kinematics of the egoSGV and the neighboring obstacles. Next, weighted Kernel Density Estimation (wKDE) defines the spatial distribution of conflict severity in configuration space. The defined zones are incorporated as a conflict layer in the global map. Then, a global trajectory planner algorithm is used to weigh between the length cost and conflict cost. Finally, to test the proposed solution, a simulation is performed in a factory-like environment, then an experiment is conducted with a real SGV. In comparison with the state-of-the-art geometrical path planning method, the results show that the proposed approach reduces navigation failures by up to 52%, while reducing the trajectory execution time by around up to 10 %. Also, the smoothness of the executed motion allowed to reduce energy consumption by over 12%.

Laws and preventive methods of collision accidents between merchant and fishing vessels in coastal area of China

With the rapid development of China's shipping trade and the large increase in the number of fishing vessels, the maritime navigation environment has become increasingly complex, resulting in more and more serious conflict accidents between merchant and fishing vessels. In order to study the characteristics and causes of collision accidents between merchant and fishing vessels in China's coastal areas, the research team conducted field research on the key areas in Shandong and Zhejiang. Then, a statistical analysis was carried out on the relevant information of collision accidents between merchant and fishing vessels released by the China Maritime Safety Administration (MSA) from 2016 to 2020, and the spatial distribution of collision accidents between merchant and fishing vessels was intuitively analyzed by using the weighted kernel density estimation method. Finally, based on the above analysis, this paper gave relevant suggestions from the perspectives of subjective, objective and intelligent maritime systems, which have important reference significance for reducing the occurrence of collision accidents.

A fully adaptive method for structural stochastic response analysis based on direct probability integral method

This paper proposes a fully adaptive method to estimate the probability density function (PDF) of the responses for stochastic structures under static and dynamic loads. The PDF is described by a recently published direct probability integral method (DPIM). In DPIM, the key smoothing parameter σ and the number of samples Ns, which have significant impacts on the determination of PDF and the efficiency of stochastic response calculation, are still difficult to determine in a completely adaptive manner. To this end, we derive a weighted kernel density estimation (weighted-KDE) method to adaptively obtain the σ by minimizing the mean integrated squared error between the estimated PDF and the real PDF. In addition, a new iterative sampling strategy is proposed to adaptively determine the Ns, in which a candidate sample pool is generated firstly, then the samples are gradually selected from the pool. This strategy ensures that the used samples in each iteration can fill the probability space in a ‘highly uniform’ manner. Based on the standard deviation calculated by the estimated PDF, a stopping criterion is presented to stop the iterative process. Moreover, the detailed steps of the proposed fully adaptive method is given by combining the weighted-KDE method and the sampling strategy. Four engineering examples validate the adaptive ability, efficiency and accuracy of the proposed method.

Intelligent monitoring and evaluation for the prefabricated construction schedule

AbstractThe prefabricated building construction (PBC) project is sensitive to uncertainties due to the highly required coordination and interdependency among the installation activities, which may cause progress delay. Hence, it is necessary to monitor the installation progress and evaluate the schedule in terms of the project duration to take proactive control actions to avoid actual project delay. This study focuses on intelligent monitoring and evaluation for the PBC schedule by combining the computer vision‐based (CVB) technology, a weighted kernel density estimation (WKDE) method, and the earned duration management (EDM) method. Intelligent and real‐time far‐field detection of the prefabricated components (PCs) and workers is achieved through the CVB technology, which is, respectively, used to measure the progress status of the PC installation works and other manual works by means of the WKDE method. The PBC project duration is then predicted based on the monitored progress status to evaluate the schedule through the EDM method. The proposed intelligent schedule monitoring and evaluation method have been illustrated and justified through a field application. This study contributes to achieving intelligent schedule monitoring and evaluation for the PBC project.

A local density-based outlier detection method for high dimension data

The researchers faced challenges in the outlier detection process, mainly when deals with the high dimensional dataset; to handle this problem, we use The principal component analysis. Outlier detection or anomaly detection, with local density-based methods, compares the density of observation with the surrounding local density neighbors. We apply the outlier score as a measure of comparison. In this research, we choose different density estimation functions and calculated different distances. Weighted kernel density estimation with adaptive bandwidth for multivariate kernel density estimation(Gaussian) considered the $KNN$ and RNN. $KNN$ is considered too for the Epanenchnikov kernel density estimation. Lastly, we estimate the LOF as a base method in detecting outliers. Extensive experiments on a synthetic dataset have shown that RKDOS and EPA are more efficient than LOF using the precision evaluation criterion.

Kernel density estimation in mixture models with known mixture proportions.

In this article, we consider the density estimation for data with a mixture structure, where the component densities are assumed unknown, but for each observation, the probabilities of its membership to the subpopulations are known or estimable from other resources. Data of this kind arise from practice and have wide applications. Motivated from the classical kernel density estimation method for a single population, we propose a weighted kernel density estimation method to estimate the component density functions nonparametrically. Within the framework of the EM algorithm, we derive an algorithm that computes our proposed estimates effectively. Via extensive simulation studies, we demonstrate that our methods outperform the existing methods in most occasions. We further compare our methods with existing methods by real data examples.

A spatial and dynamic solution for allocation of COVID-19 vaccines when supply is limited

BackgroundSince most of the global population needs to be vaccinated to reduce COVID-19 transmission and mortality, a shortage of COVID-19 vaccine supply is inevitable. We propose a spatial and dynamic vaccine allocation solution to assist in the allocation of limited vaccines to people who need them most.MethodsWe developed a weighted kernel density estimation (WKDE) model to predict daily COVID-19 symptom onset risk in 291 Tertiary Planning Units in Hong Kong from 18 January 2020 to 22 December 2020. Data of 5,409 COVID-19 onset cases were used. We then obtained spatial distributions of accumulated onset risk under three epidemic scenarios, and computed the vaccine demands to form the vaccine allocation plan. We also compared the vaccine demand under different real-time effective reproductive number (Rt) levels.ResultsThe estimated vaccine usages in three epidemiologic scenarios are 30.86% - 45.78% of the Hong Kong population, which is within the total vaccine availability limit. In the sporadic cases or clusters of onset cases scenario, when 6.26% of the total population with travel history to high-risk areas can be vaccinated, the COVID-19 transmission between higher- and lower-risk areas can be reduced. Furthermore, if the current Rt is increased to double, the vaccine usages needed will be increased by more than 7%.ConclusionsThe proposed solution can be used to dynamically allocate limited vaccines in different epidemic scenarios, thereby enabling more effective protection. The increased vaccine usages associated with increased Rt indicates the necessity to maintain appropriate control measures even with vaccines available.

Feature selection via max-independent ratio and min-redundant ratio based on adaptive weighted kernel density estimation

Feature selection based on entropy structure can be roughly divided into two types according to whether they are related to kernel density estimation (KDE). The first type is feature selection based on non-KDE entropy. The second type is feature selection based on KDE entropy. Compared with the first type, the second type avoids discretization and obtains more accurate mutual information when handling continuous data. However, existing feature selection methods based on KDE entropy neglect the fact that samples with noise have negative impacts on KDE. Besides, the feature evaluation functions don’t effectively assess relevance and redundancy of features. Thus, a feature selection method via maximizing independent and minimizing redundant classification information ratio is constructed based on adaptive weighted kernel density estimation. Firstly, an adaptive weighted kernel density estimation model is designed. Secondly, the entropy structure is defined by the adaptive weighted kernel density estimation model, and their theoretical properties are explored. Thirdly, a feature selection algorithm via maximizing independent and minimizing redundant classification information ratio is designed from the viewpoint of adaptive weighted kernel density estimation. Finally, comprehensive experiments are performed. The results illustrate that our approach has certain robustness, validity and superiority compared with other representative feature selection approaches.

Nebulosa recovers single-cell gene expression signals by kernel density estimation.

Data sparsity in single-cell experiments prevents an accurate assessment of gene expression when visualized in a low-dimensional space. Here, we introduce Nebulosa, an R package that uses weighted kernel density estimation to recover signals lost through drop-out or low expression. Nebulosa can be easily installed from www.github.com/powellgenomicslab/Nebulosa. Supplementary data are available at Bioinformatics online.

NaNOD: A natural neighbour-based outlier detection algorithm

Outlier detection is an essential task in data mining applications which include, military surveillance, tax fraud detection, telecommunication, etc. In recent years, outlier detection received significant attention compared to other problem of discoveries. The focus on this has resulted in the growth of several outlier detection algorithms, mostly concerning the strategy based on distance or density. However, each strategy has intrinsic weaknesses. The distance-based techniques have the problem of local density, while the density-based method is recognized as having an issue of a low-density pattern. Also, most of the existing outlier detection algorithms have a parameter selection problem, which leads to poor detection results. In this article, we present an unsupervised density-based outlier detection algorithm to deal with these shortcomings. The proposed algorithm uses a Natural Neighbour (NaN) concept, to obtain a parameter called Natural Value (NV) adaptively, and a Weighted Kernel Density Estimation (WKDE) method to estimate the density at the location of an object. Besides, our proposed algorithm employed two different categories of nearest neighbours, k Nearest Neighbours (kNN), and Reverse Nearest Neighbours (RNN), which make our system flexible in modelling different data patterns. A Gaussian kernel function is adopted to achieve smoothness in the measure. Further, we use an adaptive kernel width concept to enhance the discrimination power between normal and outlier samples. The formal analysis and extensive experiments carried out on both artificial and real datasets demonstrate that this technique can achieve better outlier detection performance.

인도 산업클러스터 경쟁력 분석과 시사점: 마하라슈트라 주를 중심으로 (An Analysis on the Competitiveness of Industrial Clusters in India: A case study of Maharashtra)

인도 산업클러스터 경쟁력 분석과 시사점: 마하라슈트라 주를 중심으로 (An Analysis on the Competitiveness of Industrial Clusters in India: A case study of Maharashtra)

RKDOS: A Relative Kernel Density-based Outlier Score

This article proposes a novel outlier detection algorithm called Relative Kernel Density-based Outlier Score (RKDOS) to detect local outliers. The proposed algorithm uses a weighted kernel density estimation (WKDE) method with an adaptive kernel width for density estimation at the location of an object based on its extended nearest neighbors. For density estimation, we consider both Reverse Nearest Neighbors (RNN) and k-Nearest Neighbors (kNN) of an object. To achieve smoothness in the measure, the Gaussian kernel function is adopted. Further, to improve discriminating power between normal and abnormal samples, we use an adaptive kernel width concept. Extensive experiments on both synthetic and real data sets have shown that our proposed algorithm has better detection performance over some popular existing outlier detection approaches.

Integrating Spatial and Temporal Approaches for Explaining Bicycle Crashes in High-Risk Areas in Antwerp (Belgium)

The majority of bicycle crash studies aim at determining risk factors and estimating crash risks by employing statistics. Accordingly, the goal of this paper is to evaluate bicycle–motor vehicle crashes by using spatial and temporal approaches to statistical data. The spatial approach (a weighted kernel density estimation approach) preliminarily estimates crash risks at the macro level, thereby avoiding the expensive work of collecting traffic counts; meanwhile, the temporal approach (negative binomial regression approach) focuses on crash data that occurred on urban arterials and includes traffic exposure at the micro level. The crash risk and risk factors of arterial roads associated with bicycle facilities and road environments were assessed using a database built from field surveys and five government agencies. This study analysed 4120 geocoded bicycle crashes in the city of Antwerp (CA, Belgium). The data sets covered five years (2014 to 2018), including all bicycle–motorized vehicle (BMV) crashes from police reports. Urban arterials were highlighted as high-risk areas through the spatial approach. This was as expected given that, due to heavy traffic and limited road space, bicycle facilities on arterial roads face many design problems. Through spatial and temporal approaches, the environmental characteristics of bicycle crashes on arterial roads were analysed at the micro level. Finally, this paper provides an insight that can be used by both the geography and transport fields to improve cycling safety on urban arterial roads.

Constraining kernel estimators in semiparametric copula mixture models

A novel algorithm for performing inference and/or clustering in semiparametric copula-based mixture models is presented. The standard kernel density estimator is replaced by a weighted version that permits to take into account the constraints put on the underlying marginal densities. Lower misclassification error rates and better estimates are obtained on simulations. The pointwise consistency of the weighted kernel density estimator is established under an assumption on the rate of convergence of the sample maximum.

Fast dynamic routing based on weighted kernel density estimation

SummaryCapsules as well as dynamic routing between them are most recently proposed structures for deep neural networks. A capsule groups data into vectors or matrices as poses rather than conventional scalars to represent specific properties of target instance. Based on pose, a capsule should be attached to a probability (often denoted as activation) for its presence. The dynamic routing helps capsule network achieve more generalization capacity with fewer model parameters. However, the bottleneck, which prevents widespread applications of capsule, is the expense of computation during routing. To address this problem, we generalize existing routing methods within the framework of weighted kernel density estimation, proposing two fast routing methods with different optimization strategies. Our methods prompt the time efficiency of routing by nearly 40% with negligible performance degradation. By stacking a hybrid of convolutional layers and capsule layers, we construct a network architecture to handle inputs at a resolution of 64 × 64 pixels. The proposed models achieve a parallel performance with other leading methods in multiple benchmarks.

Background–foreground interaction for moving object detection in dynamic scenes

ABSTRACT Both background subtraction and foreground extraction are the typical methods used to detect moving objects in video sequences. In order to flexibly represent the long-term state and the short-term changes in a scene, a new weighted Kernel Density Estimation (KDE) is proposed to build the long-term background (LTB) and short-term foreground (STF) models, respectively. A novel mechanism is proposed to support the interaction between the LTB and STF models. The interaction includes the weight transmission and the fusion between the LTB and STF models. In the weight transmission process between the LTB and STF models, the sample weight of one model (either the background model or the foreground model) in the current time step is updated under the guidance of the decision of the other model in the previous time step. In the background-foreground fusion stage, a unified Bayesian framework is proposed to detect objects and the detection result in any time step is given by the logarithm of the posterior ratio between the background and foreground models. This interactive approach proposed in this paper improves the robustness of moving object detection, preventing deadlocks and degeneration in the models. The experimental results demonstrate that our proposed approach outperforms previous ones.

Binary surrogates with stratified samples when weights are unknown

In clinical practice, surrogate variables are commonly used as an indirect measure when it is difficult or expensive to measure the primary outcome variable X, based on which the disease status is assessed. In this article, we consider the problem of constructing an optimal binary surrogate Y to substitute such the feature variable X. To retain samples that have rare values in X, the paired sample (X, Y) is usually selected based on stratified sampling, where the strata are constructed using the disjoint intervals with the support of X. For such a sampling design, the stratum proportions are usually unknown such that proportional allocation is infeasible and (X, Y)’s cannot be regarded as an i.i.d. sample between strata. We estimate the unknown cutoff determining higher/lower levels of X that optimally match the variable Y and provide the true positive rates (TPR) adjusted for the disproportionate stratum weights. Our approach is to estimate the underlying distribution of X, then conduct an ad-hoc estimation for the TPR and for the expected prediction errors under zero-one loss function. We develop parametric estimate of the distribution of X under exponential family assumption and a weighted-kernel density estimator when the distribution of X is unspecified. We illustrate our methods on various simulation studies and on a real example where binary surrogates were evaluated for a medical device. The simulation results indicate that our approach performs well.