Temporal Network Kernel Density Estimation

This study proposed a method for identifying traffic accident (TA) hotspots. The method combines kernel density estimation (KDE) with network kernel density estimation (NKDE). The hotspots identified through NKDE can be overlaid on the high-risk areas (hot zones) identified using planar KDE, resulting in accurate hotspot identification. The research site was Zhenjiang City in Jiangsu Province, China; data on 410 fatal traffic accidents from 2017 to 2020 were collected. An average nearest neighbour (ANN) ratio (0.563) was obtained using the global auto nearest neighbour distance method; thus, the fatal TAs had a cluster-type distribution in the city. Subsequently, the maximum clustering distance (7812.842591 m) in the research site was analysed using Ripley’s K-function, which yielded a reasonable KDE bandwidth and enabled identifying the distribution of hot zones for fatal TAs. Precise hotspot identification was achieved by overlaying the results of NKDE-based analysis in these hot zones. The proposed method was verified using data on 131 fatal TAs during January to July 2021. The results revealed that, in Zhenjiang City, the identification rate for hot zones and hotspots in hot zones was 71.75% and 38.29%, respectively, and the overall hotspot identification rate was 27.48%, demonstrating the method’s ability to relatively accurately identify hotspot locations, information that can help traffic authorities implement preventive measures.

An urban, commercial central district is often regarded as the heart of a city. Therefore, quantitative research on commercial central districts plays an important role when studying the development and evaluation of urban spatial layouts. However, conventional planar kernel density estimation (KDE) and network kernel density estimation (network KDE) do not reflect the fact that the road network density is high in urban, commercial central districts. To solve this problem, this paper proposes a new method (commercial-intersection KDE), which combines road intersections with KDE to identify commercial central districts based on point of interest (POI) data. First, we extracted commercial POIs from Amap (a Chinese commercial, navigation electronic map) based on existing classification standards for urban development land. Second, we calculated the commercial kernel density in the road intersection neighborhoods and used those values as parameters to build a commercial intersection density surface. Finally, we used the three standard deviations method and the commercial center area indicator to differentiate commercial central districts from areas with only commercial intersection density. Testing the method using Nanjing City as a case study, we show that our new method can identify seven municipal, commercial central districts and 26 nonmunicipal, commercial central districts. Furthermore, we compare the results of the traditional planar KDE with those of our commercial-intersection KDE to demonstrate our method’s higher accuracy and practicability for identifying urban commercial central districts and evaluating urban planning.

Knowledge and data engineering (KDEng) plays a pivotal role in advancing predictive modeling techniques, particularly in construction science, where accurate predictions of concrete properties such as strength, durability, and thermal conductivity are essential. This chapter explores the integration of KDEng with kernel‐based methods to model complex, nonlinear relationships inherent in construction datasets. By employing advanced kernel functions, such as the Radial Basis Function (RBF) and Gaussian kernels, Kernel Density Estimation (KDE) enables the efficient transformation of input data into high‐dimensional feature spaces, allowing machine learning models to uncover intricate patterns. The chapter highlights practical applications of support vector machines (SVM) and Kernel Ridge Regression (KRR) for predicting concrete properties, emphasizing their ability to handle nonlinear dependencies between factors like curing conditions, environmental variables, and mix proportions. Detailed discussions on feature engineering, the kernel trick, and kernel density estimation (KDE) illustrate how KDE enhances model accuracy, robustness, and scalability. Furthermore, the text addresses the challenges of high‐dimensional KDE, including computational complexity and data sparsity, offering strategies like feature selection, batch processing, and parallel computation to ensure scalability in real‐world applications. Future directions in KDEng research are also explored, including the development of adaptive bandwidth selection methods, scalable algorithms, and approaches for handling non‐IID data. This chapter provides actionable insights for researchers and practitioners, demonstrating how KDE and kernel‐based methods can improve decision‐making in construction, paving the way for safer, more sustainable concrete solutions.

An improved mean shift segmentation method featuring adaptive parameter selection is presented in this paper. We associate the bandwidths and weight for each point in a spatial-range feature space with boundary information in an image plane. Varying weight and bandwidth for each pixel are assigned according to a boundary map, which is obtained by learning multiple edge cues. We consider two groups of edge cues and two regressing modules, approach the cue combination as a supervised learning problem from the ground truth data (manually sketched boundary maps). From our preliminary results, the provided method can combine the top-down information got from regression models with the mean shift process and constrain over-clustering of pixels belonging different land objects.

Kernel density estimation is an important data smoothing technique. It has been applied most successfully for univariate data whilst for multivariate data its development and implementation have been relatively limited. The performance of kernel density estimators depends crucially on the bandwidth selection. Bandwidth selection in the univariate case involves selecting a scalar parameter which controls the amount of smoothing. In the multivariate case, the bandwidth matrix controls both the degree and direction of smoothing so its selection is more difficult. So far most of the research effort has been expended on automatic, data-driven selectors for univariate data. There is, on the other hand, a relative paucity of multivariate counterparts. Most of these multivariate bandwidth selectors are focused on the restricted case of diagonal matrices. In this thesis practical algorithms are constructed, with supporting theoretical justifications, for unconstrained bandwidth matrices. The two main classes of univariate bandwidth selectors are plug-in and cross validation. These unidimensional selectors are generalised to the multidimensional case. The univariate framework for theoretically analysing kernel density estimators is extended to a general multivariate version. This framework has at its core the quantification of the relative rates of convergence which provide a guide to the asymptotic behaviour of bandwidth selectors. Simulation studies and real data analysis are employed to illustrate their finite sample behaviour. It is found that unconstrained selectors possess good asymptotic and finite sample properties in a wide range of situations. Buoyed by this success, two extensions are embarked upon. The first is variable bandwidth selection, generalising the above case where the bandwidth is fixed throughout the sample space. The variation of the bandwidths is controlled by the local properties of the data. The novel contribution is to use non-parametric clustering to summarise these local properties, along with unconstrained bandwidth matrices. The second is in kernel discriminant analysis where unconstrained bandwidth matrices are shown to produce more accurate discrimination.

Kernel density estimation is a widely used statistical tool and bandwidth selection is critically important. The Sheather and Jones’ (SJ) selector [A reliable data-based bandwidth selection method for kernel density estimation, J. R. Stat. Soc. Ser. B 53 (1991), pp. 683–690] remains the best available data-driven bandwidth selector. It can, however, perform poorly if the true density deviates too much in shape from normal. This paper first develops an alternative selector by following ideas in Park and Marron [On the use of pilot estimators in bandwidth selection, Nonparametr. Stat. 1 (1992), pp. 231–240] to reduce the impact of the normal reference density. The selector can bring drastic improvement to less smooth densities that the SJ selector has difficulty with, but may be slightly worse off otherwise. We then propose to combine the alternative selector and SJ selector by using the smaller of the two bandwidths, which has the effect of automatically picking the better one for a particular density. In our extensive simulation, study using the 15 benchmark densities in Marron and Wand [Exact mean integrated squared error, Ann. Statist. 20 (1992), pp. 712–736], the combined selector significantly improves the SJ selector for 5 difficult densities and retains the superior performance of the SJ selector for the other 10. A ready-to-use R function is provided.

This paper proposes a wind power probabilistic model (WPPM) using the reflection method and multi-kernel function kernel density estimation (KDE). With the increasing penetration of renewable energy sources (RESs) into power systems, several probabilistic approaches have been introduced to assess the impact of RESs on the power system. A probabilistic approach requires a wind power scenario (WPS), and the WPS is generated from the WPPM. Previously, WPPM was generated using a parametric density estimation, and it had limitations in reflecting the characteristics of wind power data (WPD) due to a boundary bias problem. The paper proposes a WPPM generated using the KDE, which is a non-parametric method. Additionally, the paper proposes a reflection method correcting for the boundary bias problem caused by the double-bounded characteristic of the WPD and the multi-kernel function KDE minimizing the effect of tied values. Six bandwidth selectors are used to calculate the bandwidth for the KDE, and one is selected by analyzing the correlation between the normalized WPD and the calculated bandwidth. The results were validated by generating WPPMs with WPDs in six regions of the Republic of Korea, and it was confirmed that the accuracy and goodness-of-fit are improved when the proposed method is used.

The aim of this article is to construct and carry out an integrated evaluation of a system of indicators for regional logistic systems using an improved entropy weight method. Promoting the development of regional logistic systems is crucial for reducing logistic costs in the real economy and enhancing the endogenous component of economic development. This article establishes an evaluation system consisting of 17 indicators organized into four dimensions: result scale, operational quality, social contribution, and green development. The system reflects both the scale and efficiency of the logistic sector and its environmental impact during development. Additionally, it captures changes within the logistic sector itself as well as its contributions to other industries and to people’s livelihoods. An improved entropy-weight method and kernel density estimation were applied to assess the development level of regional logistic systems, in order to determine their spatial and temporal distribution, dynamic evolution, and regional differences. The key advantage of the improved entropy-weight system is that it utilizes indicator information in both spatial and temporal dimensions, using a global reference area, which allows for both vertical and horizontal comparisons of evaluation results. The comprehensive analysis of the characteristics of regional logistic systems in terms of spatial and temporal evolution showed that the level of regional logistic systems changed with an average annual growth rate of -0.04% between 2002 and 2024, though with significant regional and inter-provincial differences. From 2002 to 2024, based on the average annual growth rates of regional logistic systems, only the central, western, and northern regions achieved effective growth. In other words, regional logistic systems across the country and in the five main regions were bipolar or multipolar, with characteristic gradient features. To analyze the dynamics of the distribution of regional logistic systems and to clearly depict the evolutionary model of regional logistic system levels, the kernel density estimation – a nonparametric method capable of describing the distribution of a random variable in terms of a continuous density curve was used. The study revealed that, due to the full-scale military invasion, the gap between logistic systems in different regions gradually widened, showing a gradual reduction in the differentiation feature of «east–center–west».

Abstract: Home‐range estimators are commonly tested with simulated animal locational data in the laboratory before the estimators are used in practice. Although kernel density estimation (KDE) has performed well as a home‐range estimator for simulated data, several recent studies have reported its poor performance when used with data collected in the field. This difference may be because KDE and other home‐range estimators are generally tested with simulated point locations that follow known statistical distributions, such as bivariate normal mixtures, which may not represent well the space‐use patterns of all wildlife species. We used simulated animal locational data of 5 point pattern shapes that represent a range of wildlife utilization distributions to test 4 methods of home‐range estimation: 1) KDE with reference bandwidths, 2) KDE with least‐squares cross‐validation, 3) KDE with plug‐in bandwidths, and 4) minimum convex polygon (MCP). For the point patterns we simulated, MCP tended to produce more accurate area estimates than KDE methods. However, MCP estimates were markedly unstable, with bias varying widely with both sample size and point pattern shape. The KDE methods performed best for concave distributions, which are similar to bivariate normal mixtures, but still overestimated home ranges by about 40–50% even in the best cases. For convex, linear, perforated, and disjoint point patterns, KDE methods overestimated home‐range sizes by 50–300%, depending on sample size and method of bandwidth selection. These results indicate that KDE does not produce home‐range estimates that are as accurate as the literature suggests, and we recommend exploring other techniques of home‐range estimation.

As the proportion of renewable energy sources that are intermittent and variability increases, system uncertainty is increasing, and a probabilistic analysis that can reflect these characteristics is required. In this paper, we propose a method for generating a probablistic wind power generation model using kernel density estimation. The boundary bias problem caused by using kernel density estimation for wind power generation data is eliminated through the boundary correction method, and a bandwidth suitable for the data can be selected through the bandwidth selector. Scenarios were created from probabilistic models made in various ways, and the accuracy of the models was validated by comparing them with real data. As a result, the accuracy was improved when the scenario was created by generating the model directly from the wind power generation data by estimating the kernel density estimation.

In this paper, we present a Markov chain Monte Carlo (MCMC) simulation algorithm for estimating parameters in the kernel density estimation of bivariate insurance claim data via transformations. Our data set consists of two types of auto insurance claim costs and exhibits a high-level of skewness in the marginal empirical distributions. Therefore, the kernel density estimator based on original data does not perform well. However, the density of the original data can be estimated through estimating the density of the transformed data using kernels. It is well known that the performance of a kernel density estimator is mainly determined by the bandwidth, and only in a minor way by the kernel. In the current literature, there have been some developments in the area of estimating densities based on transformed data, where bandwidth selection usually depends on pre-determined transformation parameters. Moreover, in the bivariate situation, the transformation parameters were estimated for each dimension individually. We use a Bayesian sampling algorithm and present a Metropolis-Hastings sampling procedure to sample the bandwidth and transformation parameters from their posterior density. Our contribution is to estimate the bandwidths and transformation parameters simultaneously within a Metropolis-Hastings sampling procedure. Moreover, we demonstrate that the correlation between the two dimensions is better captured through the bivariate density estimator based on transformed data.

Context Despite the diversity of available home range estimators, no single method performs equally well in all circumstances. It is therefore important to understand how different estimators perform for data collected under diverse conditions. Kernel density estimation is a popular approach for home range estimation. While many studies have evaluated different kernel bandwidth selectors, few studies have compared different formulations of the bandwidth matrix using wildlife telemetry data. Additionally, few studies have compared the performance of kernel bandwidth selectors using VHF radio-telemetry data from small-bodied taxa. Aims In this study, we used eight different combinations of bandwidth selectors and matrices to evaluate their ability to meet several criteria that could be potentially used to select a home range estimator. Methods We used handheld VHF telemetry data from two species of snake displaying non-migratory and migratory movement patterns. We used subsampling to estimate each estimator’s sensitivity to sampling duration and fix rate and compared home range size, the number of disjunct volume contours and the proportion of telemetry fixes not included in those contours among estimators. Key Results We found marked differences among bandwidth selectors with regards to our criteria but comparatively little difference among bandwidth matrices for a given bandwidth selector. Least-squares cross-validation bandwidths exhibited near-universal convergence failure whereas likelihood cross-validation bandwidths showed high sensitivity to sampling duration and fix rate. The reference, plug-in and smoothed cross-validation bandwidths were more robust to variation in sampling intensity, with the former consistently producing the largest estimates of home range size. Conclusions Our study illustrates the performance of multiple kernel bandwidth estimators for estimating home ranges with datasets typical of many small-bodied taxa. The reference and plug-in bandwidths with an unconstrained bandwidth matrix generally had the best performance. However, our study concurs with earlier studies indicating that no single home range estimator performs equally well in all circumstances. Implications Although we did not find strong differences between bandwidth matrices, we encourage the use of unconstrained matrices because of their greater flexibility in smoothing data not parallel to the coordinate axes. We also encourage researchers to select an estimator suited to their study objectives and the life history of their study organism.

Particle-based transport models are widely used for simulating the movement of pollutants in environmental systems. Unlike grid-based methods, particles naturally address advective transport without numerical dispersion. However, these models require concentration reconstruction from the discrete particle information. This is computationally demanding in multidimensional problems, posing a challenge for field-scale models requiring frequent reconstruction. Grid Projected Kernel Density Estimation (GPKDE) is a cell-averaged reconstruction with improvements in computational performance compared to classical KDE. Currently, no programs implementing this method are readily integrated into particle simulators, compatible with three-dimensional domains, and particles with unequal weights. This article introduces a Fortran code for general-purpose GPKDE, with modular functionalities facilitating the integration into external software. The program implements locally adaptive kernel bandwidth selection and alternatives for the reconstruction from particles with non-uniform weights. The code is parallelized with the OpenMP library. Numerical test cases demonstrate the program’s applicability and scalability of the parallel implementation.

Diabetes mellitus poses a growing global health concern, particularly in low- and middle-income countries where early detection remains limited, demanding classification models that balance accuracy, interpretability, and adaptability to heterogeneous clinical data. This study proposes and evaluates the Adaptive Kernel Probability Model (AKPM), a novel nonparametric probabilistic classifier designed to enhance diabetes prediction by performing localized kernel density estimation with adaptive bandwidth selection via k-nearest neighbors. Implemented and tested on the Pima Indians Diabetes Dataset, AKPM outperformed conventional classifiers—Naïve Bayes and Gaussian Mixture Models (GMM)—across all evaluation metrics, achieving 87.5% accuracy, 83.3% precision, 76.9% recall, and an F1-score of 80.0% for the diabetic class, alongside 89.3% precision and 92.6% recall for the normal class. These results surpassed GMM (83.0% accuracy, 71.6% F1-score) and Naïve Bayes (80.0% accuracy, 66.6% F1-score), confirming AKPM’s superior capability to detect diabetic cases while minimizing false negatives. Offering transparent posterior inference and a modular design, AKPM emerges as a reliable and interpretable solution for clinical decision support systems and real-world healthcare applications.

Runoff prediction is crucial for water resource allocation and hydropower planning. To address low accuracy and uncertainty in runoff forecasting, this study proposes a framework integrating the Information Acquisition Optimizer (IAO), Variational Mode Decomposition (VMD), Convolutional Neural Network-Support Vector Machine (CNN-SVM), and Kernel Density Estimation (KDE) for interval prediction. An IAO-based optimized VMD (IVMD) is employed to decompose non-stationary runoff series and enhance feature extraction, with the resulting components used as inputs to the CNN-SVM model for point prediction. To quantify predictive uncertainty, KDE is applied to model the prediction error distribution, where a B-spline-based least squares cross-validation bandwidth selection method (LSCV-B) is adopted. By combining B-spline basis functions with data-driven cross-validation, LSCV-B overcomes the limited local adaptability of conventional AMISE-based bandwidth selection, enabling more accurate error density estimation and narrower prediction intervals with reliable coverage. Experiments in the Yangtze River Basin show that the IVMD-CNN-SVM framework reduces RMSE and MAPE by approximately 40–50% on the testing dataset compared with VMD-based counterparts, while producing highly reliable and compact 90% interval predictions.