Kernel Density Estimation Method Research Articles

Research on the development mode of cultural tourism industry based on the concept of low carbon and environmental protection by big data analysis

Abstract In order to build a low-carbon and environmentally friendly cultural tourism business, this research analyzes data on user characteristics, tourist attractions, and functional qualities. The clustering technique is used to examine the clustering features of the industry development, and the spatial variation characteristics of the industry development are developed with the aid of the closest neighbor index, standard ellipse, and kernel density estimation methods. In order to analyze the degree of development of this industry, the integration degree model was constructed by the entropy weighting method. The analysis shows that the growth rate of the central and western regions is 32.2% and 28.8%, respectively, while the growth rate of the eastern region is 22.7%. The integration degree of the eastern region ranges from 0.12 to 0.85, the integration degree of the western region ranges from 0.18 to 0.9, and the integration degree of the central region ranges from 0.2 to 0.8. Based on this study, the integration development of the low-carbon environmental protection concept and the cultural tourism industry is thriving.

Consistent or inconsistent? The club convergence effect and matching degree analysis on energy consumption intensity and production density: Evidence from the data of 2000–2020 in China

Clarifying the regional differences in coal production and consumption is important for the adjustment of the energy structure. To understand the spatial and temporal variability of coal production and consumption, this study examined coal consumption and production across 30 Chinese provinces over the period of 2000–2020 using the methodology introduced by Phillips and Sul. Then, we used the kernel density estimation method to analyze the dynamic changes. Finally, the Gini coefficient and coefficient of variation methods were used to quantify the unevenness in the production and consumption of coal. The analytical results strongly support the existence of convergence clubs. We find five convergent clubs for coal consumption and six convergent clubs for coal production. There are significant differences in the geographic distribution of convergence clubs for coal consumption and coal production. In addition, the difference in coal consumption levels between provinces widened, while the difference in coal production narrowed during the study period. The unevenness of the regional distribution and matching of coal production and consumption increased. Overall, the regional unevenness of coal production and consumption should be given sufficient attention. This study provides a reference on how to differentiate and adjust the production and consumption of coal in each region.

Analysis of the coupled and coordinated development of sports and tourism industries and the driving factors

The Yellow River Basin has a wealth of tourism resources, a long history of folk sports, and strong legislative support, all of which are advantages for the growth of the sports tourism sector. This study constructs an evaluation index system based on panel data from nine provinces and regions in the Yellow River Basin from 2011 to 2020, and then measures the development index and analyzes the driving factors using the entropy method, coupling coordination degree model, kernel density estimation method, and grey correlation analysis method. The findings demonstrate that (1) the Yellow River Basin's overall level of growth in the sports and tourist sectors exhibits a consistent and upward trend and that Shandong and Henan provinces clearly have an edge over other provinces in terms of development. (2) The geographical development pattern was lower Yellow River > upper Yellow River > middle Yellow River, and the coupling coordination status shifted from slight disorder to good coordination. (3) There is a close connection between sports tourism and variables including population density, financial prowess, and infrastructure growth. The employment population index has the smallest link with invention patent authorization. The macro-policy framework should therefore be strengthened in the future, the sports tourism infrastructure should be improved, and the Yellow River basin's unique sports tourism resources should be fully utilized in order to increase brand influence. In addition, new sports tourism products should be developed in response to market demand and consumer preferences, and enterprise innovation and research and development efforts should be increased in order to achieve high-quality development transformation.

Probabilistic short-term wind speed forecasting using a novel ensemble QRNN

Neural Networks are widely used as the intelligent tool for short-term wind speed forecasting. Owing to the inherent randomness and intermittency of the wind, it is hard to ensure sufficient forecasting precision when using single conventional Network models to conduct deterministic forecasting. Thanks to the recent achievements of ensemble methods, a novel ensemble Quantile Regression Neural Network (QRNN) based on Wavelet decomposition (WD) and least absolute shrinkage and selection operator (LASSO) for probabilistic short-term wind speed forecasting is developed here. The signal processing technology, feature extraction method and predicting model are ingeniously combined in the proposed ensemble QRNN. More specifically, the WD is utilized to extract the signal features into a collection of easy-to-analyze subseries. LASSO regression is combined with the QRNN to conduct the robust prediction. Finally, the kernel density estimation method is adopted to further enhance the forecasting precision. The forecasting performance between the proposed ensemble QRNN and several benchmark models are evaluated using a piece of field measured 10-min mean wind speed data. Results show that the proposed ensemble model can adequately enhance the performance of short-term wind speed forecasting, which can also quantify and reduce the uncertainty of the prediction results.

Integrated Multi-Head Self-Attention Transformer model for electricity demand prediction incorporating local climate variables

This paper develops a trustworthy deep learning model that considers electricity demand (G) and local climate conditions. The model utilises Multi-Head Self-Attention Transformer (TNET) to capture critical information from G, to attain reliable predictions with local climate (rainfall, radiation, humidity, evaporation, and maximum and minimum temperatures) data from Energex substations in Queensland, Australia. The TNET model is then evaluated with deep learning models (Long-Short Term Memory LSTM, Bidirectional LSTM BILSTM, Gated Recurrent Unit GRU, Convolutional Neural Networks CNN, and Deep Neural Network DNN) based on robust model assessment metrics. The Kernel Density Estimation method is used to generate the prediction interval (PI) of electricity demand forecasts and derive probability metrics and results to show the developed TNET model is accurate for all the substations. The study concludes that the proposed TNET model is a reliable electricity demand predictive tool that has high accuracy and low predictive errors and could be employed as a stratagem by demand modellers and energy policy-makers who wish to incorporate climatic factors into electricity demand patterns and develop national energy market insights and analysis systems.

Exploring the Construction of a Grey Relational Analysis-Rank Correlation-Based Indicator System for Common Prosperity: A Case Study of Zhejiang Province

Common prosperity is an essential requirement of socialism. This paper examines the discourse on the proportion of the middle-income group and the research of scholars on common prosperity both domestically and internationally. A method for estimating the middle-income group, incorporating the consumer price index, is proposed, and the proportion of the middle-income group in Zhejiang Province over the past decade is calculated using the kernel density estimation method and included in the indicator pool. Relevant indicators are selected through grey relational analysis and rank correlation analysis, and a measurement system for the degree of achieving common prosperity is constructed, consisting of five primary indicators and twenty-five secondary sub-indicators. Taking Zhejiang Province as an example, the degree of achieving common prosperity and the implementation status of the five dimensions over the past decade are calculated. The results show that the scores of the five dimensions have shown a spiral upward trend in the past decade, but due to the impact of the epidemic, the overall degree of achieving common prosperity has declined after 2020.

An interval water demand prediction method to reduce uncertainty: A case study of Sichuan Province, China

Effective prediction of water demand is a prerequisite for decision makers to achieve reliable management of water supply. Currently, the research on water demand prediction focuses on point prediction method. In this study, we constructed a GA-BP-KDE hybrid interval water demand prediction model by combining non-parametric estimation and point prediction. Multiple metaheuristic algorithms were used to optimize the Back-Propagation Neural Network (BP) and Kernel Extreme Learning Machine (KELM) network structures. The performance of the water demand point prediction models was compared by the Root Mean Squared Error (RMSE), Mean Absolute Percentage Error (MAPE), Kling-Gupta Efficiency (KGE), computation time, and fitness convergence curves. The kernel density estimation method (KDE) and the normal distribution method were used to fit the distribution of errors. The probability density function with the best fitting degree was selected based on the index G. The shortest confidence interval under 95% confidence was calculated according to the asymmetry of the error distribution. We predicted the impact indicator values for 2025 using the exponential smoothing method, and obtained water demand prediction intervals for various water use sectors. The results showed that the GA-BP model was the optimal model as it exhibited the highest computational efficiency, algorithmic stability, and prediction accuracy. The three prediction intervals estimated after adjusting the KDE bandwidth parameter covered most of the sample points in the test set. The prediction intervals of the four water use sectors were evaluated as F values of 1.6845, 1.3294, 1.6237, and 1.3600, which indicates high accuracy and quality of the prediction intervals. The mixed water demand interval prediction based on GA-BP-KDE reduces the uncertainty of the point prediction results and can provide a basis for water resource management by decision makers.

Kernel-based learning framework for discovering the governing equations of stochastic jump-diffusion processes directly from data.

Discovering the underlying mathematical-physical equationsof complex systems directly from observational data has been a challenging inversion problem. We propose a data-driven framework for identifying dynamical information in stochastic diffusion or stochastic jump-diffusion systems. The probability density function is utilized to relate the Kramers-Moyal expansion to the governing equations, and the kernel density estimation method, improved by the Fourier transform idea, is used to extract the Kramers-Moyal coefficients from the time series of the state variables of the system. These coefficients provide the data expression of the governing equationsof the system. Then a data-driven sparse identification algorithm is used to reconstruct the underlying dynamic equations. The proposed framework does not rely on prior assumptions, and all results are obtained directly from the data. In addition, we demonstrate its validity and accuracy using illustrative one- and two-dimensional examples.

Measuring the Construction Efficiency of Zero-Waste City Clusters Based on an Undesirable Super-Efficiency Model and Kernel Density Estimation Method

The global total amount of generated solid waste is currently on a rapid growth trend. China, as the largest developing country, promulgated its Pilot Work Plan for the Construction of Zero-Waste Cities led by the new development concept in 2018 after recognizing the inadequacy and urgency of solid waste management, and the lack of valuable experience and benchmark cities for the construction of zero-waste cities. This study uses the undesirable super-efficiency model and kernel density estimation method to measure the efficiency of zero-waste city construction in 16 prefecture-level cities in Shandong Province and analyze their spatial and temporal differences. Three major problems were found, namely, low regional coordination, the rigid policies of some local governments, and the unbalanced development of scale efficiency and pure technical efficiency. Results show that the zero-waste city construction efficiency as a whole shows a declining and then fluctuating growth trend, and that low-scale efficiency is the main reason behind the decrease in construction efficiency. Suggestions are then provided considering three aspects: improving regional synergy; improving government quality and capacity, and strengthening government supervision and revitalizing the market; and introducing social capital for environmental pollution treatment. These suggestions ultimately help improve the level of zero-waste city construction.

Spatial patterns and characteristics of global piracy analyzed using a geographic information system

Pirate attacks are among the most important factors affecting maritime safety in recent years. In this study, big data were analyzed to extract the patterns and characteristics of piracy incidents and to reveal risk control options and recommendations for anti-piracy measures. Global and regional spatial patterns and characteristics were identified with the support of a geographic information system. In total, 3675 maritime piracy incidents from 2010 to 2022 were collected from the Piracy and Armed Robbery module of the Global Integrated Shipping Information System to profile the characteristics of global piracy. To visualize and analyze the features of maritime piracy, we used three geospatial techniques: kernel density estimation (KDE), k-means clustering, and buffer analysis. These geospatial techniques were used to create a KDE map for identifying piracy-prone areas. We subdivided the incidents into several classes and analyzed the features within each class to calculate the incidents that occurred in coastal areas. The following results were obtained from the geospatial analysis. First, the results of the KDE method revealed specific regions that were particularly prone to piracy, namely the Gulf of Guinea in West Africa; the seas around East Africa and the Arabian Sea; the Malacca Strait and parts of Southeast Asia and the Bay of Bengal; and the seas around South America. Second, the distributions of maritime piracy incidents by different temporal criteria, location, and ship type were compared within different classes. In particular, we found that 79.97% of minor incidents, 43.4% of less serious incidents, 50% of serious incidents, and 30.9% of very serious incidents occurred within 40 km of the coastline. The results obtained from the study contributed to an understanding of the spatial patterns of maritime piracy and provided information useful to maritime safety organizations for enhancing shipping safety.

The forensic information identification based on machine learning algorithms

Investigating crimes in selected areas, studying their occurrence and appropriate graphical visualization may be an important supportive information for police units. Nowadays, the available IT tools can improve the work of law enforcement agencies. For this purpose, in this work, we propose an exploration approach which allows for analyzing crime events that are recorded in the city of Baltimore, Maryland, USA. Based on the collected data, seven types of offenses are recorded. First, they are analyzed in terms of time verifying whether any type of event depends on the day of the week or a period of the day. Then the distribution of the crimes is examined by spatial clusterization and kernel density estimation methods. As a result of the analysis, it is shown when and where the citizens of the considered city are subject to the highest crime rate.

Compilation of load spectrum of CNC machine tools reliability test program based on Weibull kernel function

The load spectrum is the foundational data for reliability tests that simulate actual working conditions. Determining typical working conditions and accurate load extrapolation are the key to the load spectrum. This paper proposes a method for compiling the load spectrum of a reliability test program of CNC machine tools based on Weibull kernel function. The aforementioned method aims to address the issues commonly encountered in the load spectrum, such as complex factors that affect typical working conditions, heterogeneous load data of working conditions, and reliance on assumption distribution during load extrapolation. The method involves a determination process for typical working conditions using the Weibull kernel function and a non-parametric load extrapolation method based on kernel function. Firstly, this paper proposes a kernel density estimation method based on Weibull kernel function to address the issues of probability density contribution value deviation caused by the inconsistency between the conventional kernel function symmetry and the off-peak characteristic of load. The approach is based on the physical meaning and generalization of the Weibull distribution parameters and is used to determine the typical working conditions of CNC machine tools. Secondly, this paper proposes a nonparametric rainflow extrapolation method for cutting loads of CNC machine tools based on two-dimensional kernel density estimation. The approach takes advantage of the nonparametric rainflow extrapolation method and considers the characteristics of the cutting load. And the load spectrum of the three-dimensional cutting force of the CNC machine tool is constructed using the mean-range probability density distribution of the cutting load. Finally, the reliability test program loading spectrum of CNC machine tools is determined using the Conover ratio coefficient. Through case analysis, it can be known that the nuclear density estimation method proposed in this paper can improve the compilation accuracy of the load spectrum and has practical application significance.

Extraction and Joint Method of PV–Load Typical Scenes Considering Temporal and Spatial Distribution Characteristics

Regarding the generation and integration of typical scenes of PV and loads in urban photovoltaic distribution networks, as well as the insufficient consideration of the spatiotemporal correlation between PV and loads, this paper proposes a typical scene extraction method based on local linear embedding, kernel density estimation, and a joint PV–load typical scene extraction method based on the FP-growth algorithm. Firstly, the daily operation matrices of PV and load are constructed by using the historical operation data of PV and load. Then, the typical scenes are extracted by the dimensionality reduction of local linear embedding and the kernel density estimation method. Finally, the strong association rules of PV–meteorological conditions and load–meteorological conditions are mined based on the FP-growth algorithm, respectively. The association of PV–load typical daily operation scenarios is completed using meteorological conditions as a link. This experiment involved one year of operation data of a distribution network containing PV in Qingyuan, Guangdong Province. The typical scene extraction joint method, Latin hypercube sampling method, and k-means clustering-based scene generation method proposed in this paper are used for comparison, respectively. The results show that compared to the other two scenario generation methods, the error between the typical scenario obtained by this method and the actual operating scenario of the distribution network is smaller. The extracted typical PV and load scenarios can better fit the actual PV and load operation scenarios, which have more reference value for the operation planning of actual distribution networks containing PV.

Evaluation of sustainable development efficiency in Chinese provinces- based on closed-loop feedback three-stage dynamic network slack-based measure model

Coordination of economic, environmental, and social development is essential for sustainable development in China. A closed-loop feedback three-stage dynamic network slack-based measurement model was proposed to measure the sustainable development efficiency of 30 provinces in China during 2005–2020. The spatiotemporal evolution characteristics and coordination of sustainable development efficiency were explored using the Dagum–Gini coefficient decomposition method, Malmquist index model, and kernel density estimation method. As indicated, the overall sustainable development efficiency of China has increased with an average of 0.7140. The efficiency level of regional sustainable development displayed a "stepped-like" spatial distribution pattern, exhibiting a successive "east-central-west" decrease. The sustainable development efficiency levels of the respective stages differed notably, and the efficiency values of stages 2 and 3 were considerably lower than those of stage 1. The contribution rate of the between-region difference to the overall degree of variation was the highest, followed by the contribution rate within the region. Notably, the contribution rate of transvariation intensity reached a minimum value. During the study period, the distribution centre of sustainable development efficiency in China moved continuously to the right, the peak height increased, and the width contracted. This study provides a valuable policy reference for China’s sustainable development and ideas regarding its global response to energy and environmental issues.

The application of big data technology in rural tourism landscape planning under the background of the intelligent era

Abstract In the background of the intelligent era, combining big data technology to improve rural tourism landscape planning and scale management is an important means to promote rural transformation and development and farmers’ employment and income. Firstly, a clustering algorithm is proposed to be applied to rural tourism landscape planning based on big data, and the clustering algorithm mainly consists of heat measurement, spatial analysis method, kernel density estimation and hot spot identification method. Then, based on the current situation of rural tourism landscape development in China, the rural tourism network structure evaluation index system is constructed, and the evaluation index system consists of network density, central potential, average path, and clustering coefficient. Finally, to verify the accurate prediction performance of the method in this paper, rural tourism in Guizhou province is selected as the research object, and the experiment consists of 100 statistical iterations of the accurate prediction performance of the two methods. The results show that the method of this paper: with the increase of the number of iterations, the prediction accuracy increases from the initial 78.62 to 99.3%, the average prediction accuracy is 93.56%, and the accuracy of rural tourism passenger flow demand prediction by the method of this paper is higher. This study guides the efficient flow of rural tourism and promotes the high-quality development of rural tourism, which is of great significance to the regional cooperation and coordinated development of rural tourism, spatial optimization and traffic diversion, planning and construction and marketing.

Reliability of Ensemble Climatological Forecasts

AbstractEnsemble climatological forecasts play a critical part in benchmarking the predictive performance of hydroclimatic forecasts. Accounting for the skewness and censoring characteristics of hydroclimatic variables, ensemble climatological forecasts can be generated by the log, Box‐Cox and log‐sinh transformations, by the combinations of the Bernoulli distribution with the Gaussian, Gamma, log‐normal, generalized extreme value, generalized logistic and Pearson type III distributions and by the non‐parametric resampling, empirical cumulative distribution function and kernel density estimation methods. This paper is concentrated on the reliability of the 12 types of ensemble climatological forecasts. Specifically, mathematical formulations are presented and large‐sample tests are devised to verify the forecast reliability for the Multi‐Source Weighted‐Ensemble Precipitation version 2 across the globe. Climatological forecasts of monthly precipitation over 18,425 grid cells are generated for 30 years under leave‐one‐year‐out cross validation, leading to 6,633,000 (12 × 18425 × 30) sets of ensemble climatological forecasts. The results point out that the reliability of climatological forecasts considerably varies across the 12 methods, particularly in regions with high hydroclimatic variability. One observation is that climatological forecasts tend to deviate from the distributions of observations when there is inadequate flexibility to fit precipitation data. Another observation is that ensemble spreads can be overly wide when there exist overfits of sample‐specific noises in cross validation. Through the tests of global precipitation, the robustness of the log‐sinh transformation and the Bernoulli‐Gamma distribution is highlighted. Overall, the investigations can serve as a guidance on the uses of transformations, distributions and non‐parametric methods in generating climatological forecasts.

A new probabilistic assessment process for human health risk (HHR) in groundwater with extensive fluoride and nitrate optimized by non parametric estimation method.

Excessive amounts of fluoride (F-) and nitrate (NO3-) in groundwater pose a significant threat to human health. However, a quantitative approach to assessing the human health risks caused by these harmful substances is lacking. To optimize the probabilistic assessment process for human health risk (HHR), this study introduced kernel density estimation (KDE) into the stochastic simulation of F- and NO3- content in groundwater samples. The potential HHRs caused by F- and NO3- in Songyuan City were summarized by combining the probabilistic and deterministic assessments. This study found that the concentrations of F- and NO3- did not follow common probability density functions (PDFs), but the KDE method passed the Kolmogorov-Smirnov test with the critical value of 0.067 and 0.062, showing high fitting accuracy. Monte Carlo simulation indicated that the probability of NO3- for children and adult exceeding the standard is 21.95% and 15.14%, respectively, which is comparable with the results of the deterministic assessment, but the probabilistic assessment emphasized lower probability of HHRs in children caused by excess F-(4.14%). Global sensitivity analysis revealed that excessive NO3- in groundwater has the highest sensitivity of the HHR (>0.1), followed by other factors representing water use habits (>0.01). This study presents a refined probabilistic assessment method for HHR and provides a scientific reference for understanding the state of groundwater environments.

Spatial differences, dynamic evolution, and convergence of carbon productivity in China.

China is currently developing a green economy, and improving carbon productivity (CAP) is an important part of this process. The current study applied a minimum distance to strong efficient frontier (MinDS) model to measure China's CAP. The Dagum Gini coefficient and kernel density estimation methods were further used to reveal its spatial differences and dynamic evolution, while the coefficient of variation and spatial convergence models were employed to examine its convergence characteristics. The results showed significant spatial differences in China's CAP, with primarily high and low spatial distribution characteristics in the east and west, respectively. Between-regional differences were the main sources of the overall differences. Moreover, the differences between overall, eastern, central, and western regions of China all exhibited a widening trend. Although none showed σ convergence, all had significant absolute β spatial convergence and conditional β spatial convergence characteristics. Collectively, the findings of this study objectively reflect the real level, distribution characteristics, and spatial convergence characteristics of CAP in China as a whole and in each region, while also providing a reference basis for achieving peak carbon neutrality.

Measuring dense false positive regions from segmentation result for whole slide tissue histology image

Evaluating a segmentation model is critical for constructing computer-aided diagnosis (CAD) systems, in which the segmented regions will be used for downstream analysis. However, existing segmentation evaluation metrics may not reflect every aspect of a trained segmentation model performance in the context of the whole slide tissue histology images (WSIs). Specifically, existing segmentation metrics generally ignore the impact of densely packed false positive pixels (DFP) in the WSI segmentation result. This study presents a new and efficient metric, named MAFaR, accounting for DFP regions in digital WSI segmentation. The proposed metric consists of two modules: 1) Estimation of DFP regions; 2) Calculation of MAFaR score. In module 1, a Gaussian Kernel Density Estimation method was used to estimate the density of the false positive (FP) regions in segmentation result (SR). Then a two-step Mean-shift clustering algorithm was applied to the high-density FP regions to estimate the DFP regions. In module 2, the ratio of DFP regions area to the positive regions area were used for MAFaR calculation. We conducted two experiments to evaluate the effectiveness of the MAFaR score. In the first experiment, we compared MAFaR with existing metrics related to FP regions, the proposed MAFaR score can reflect the impact of DFP regions. In the second experiment, MAFaR scores were compared with the manual evaluation scores given by three experienced engineers and found high correlation (Spearman’s rank correlation coefficients greater than 0.7) and high agreement (Kendall coefficient = 0.839). Therefore, the MAFaR can be used with other segmentation metrics for evaluating WSI segmentation.

Temporal–Spatial Variations and Convergence Analysis of Land Use Eco-Efficiency in the Urban Agglomerations of the Yellow River Basin in China

Achieving synergistic development of efficient urban land use and the natural environment is crucial in promoting green urbanization. The assessment of land use eco-efficiency (LUEE) and its temporal–spatial changes provides an effective means of quantifying the relationship between the urban ecological environment and land use. Targeting 55 selected cities in the Yellow River Basin (YRB), in this study, we utilize the Super-EBM method to gauge the LUEE. We explore the temporal patterns and the spatial convergence of LUEE utilizing kernel density estimation and spatial econometric methods. Considering the resource and environmental costs of land use, we assumed the industrial pollutant emissions generated during urban land use as the undesired outputs and designed a framework for measuring the level of LUEE under double constraints, which theoretically revealed the formation process and spatial convergence mechanism of LUEE. The results show the following: (1) Throughout the sample period, the LUEE of the YRB urban agglomeration decreased from 0.158 in 2009 to 0.094 in 2020, indicating a decreasing spatial disparity in LUEE over time. Notably, the Lanxi urban cluster exhibited the largest gap in LUEE, whereas the Guanzhong Plain urban agglomeration displayed the smallest gap. The hyper-variable density exceeded the inter-group gap as the main factor leading to the difference in LUEE. (2) Although the LUEE of urban agglomerations has increased, there still exists a noticeable polarization phenomenon. (3) The LUEE of YRB demonstrates a pattern of conditional convergence and exerts a significant spatial spillover effect. Over time, the LUEE of YRB will tend towards an individual steady state. The findings have implications for strengthening linkage and synergy among cities in YRB, promoting factor integration across administrative regions, and formulating heterogeneous policies.