Multivariate Kernel Research Articles

Laser ablation inductively coupled plasma mass spectrometry analysis of potash and m-Na-Al glasses in China- using Kernel methods for trace element analysis

Monochrome drawn beads were widely circulated in South and Southeast Asia as early as the second century BC. This article aims to identify the glass beads unearthed from different sites in China and discuss their possible sources. Twenty-seven mineral soda alumina (m-Na-Al) glass and eighty-seven potash glass beads unearthed in different provinces in China were analysed by Laser Ablation Inductively Coupled Plasma Mass Spectrometry. The trace element analysis through Multivariate Kernel Density Estimation and Maximum Mean Discrepancy indicates the silica sources of m-Na-Al glass and most of the potash glass unearthed from Guangxi are identical. They were presumably produced somewhere in northeastern India or Southeast Asia and exported through the Maritime Silk Road. The silica sources of m-Na-Al glass in Henan and the rest of the potash glasses are geologically close. They were likely produced in southern India or Sri Lanka and exported through the North and Southwest Silk Roads. Future research on isotopic analysis will reveal more information about primary/secondary glass production in China, South and Southeast Asia.

Multivariate, region-based genetic analyses of facets of reproductive aging in White and Black women.

BackgroundAge at final menstrual period (FMP) and the accompanying hormone trajectories across the menopause transition do not occur in isolation, but likely share molecular pathways. Understanding the genetics underlying the endocrinology of the menopause transition may be enhanced by jointly analyzing multiple interrelated traits.MethodsIn a sample of 347 White and 164 Black women from the Study of Women's Health Across the Nation (SWAN), we investigated pleiotropic effects of 54 candidate genetic regions of interest (ROI) on 5 menopausal traits (age at FMP and premenopausal and postmenopausal levels of follicle stimulation hormone and estradiol) using multivariate kernel regression (Multi‐SKAT). A backward elimination procedure was used to identify which subset of traits were most strongly associated with a specific ROI.ResultsIn White women, the 20 kb ROI around rs10734411 was significantly associated with the multivariate distribution of age at FMP, premenopausal estradiol, and postmenopausal estradiol (omnibus p‐value = .00004). This association did not replicate in the smaller sample of Black women.ConclusionThis study using a region‐based, multiple‐trait approach suggests a shared genetic basis among multiple facets of reproductive aging.

The Gauss hypergeometric covariance kernel for modeling second-order stationary random fields in Euclidean spaces: its compact support, properties and spectral representation

This paper presents a parametric family of compactly-supported positive semidefinite kernels aimed to model the covariance structure of second-order stationary isotropic random fields defined in the d-dimensional Euclidean space. Both the covariance and its spectral density have an analytic expression involving the hypergeometric functions $${}_2F_1$$ and $${}_1F_2$$ , respectively, and four real-valued parameters related to the correlation range, smoothness and shape of the covariance. The presented hypergeometric kernel family contains, as special cases, the spherical, cubic, penta, Askey, generalized Wendland and truncated power covariances and, as asymptotic cases, the Matérn, Laguerre, Tricomi, incomplete gamma and Gaussian covariances, among others. The parameter space of the univariate hypergeometric kernel is identified and its functional properties—continuity, smoothness, transitive upscaling (montée) and downscaling (descente)—are examined. Several sets of sufficient conditions are also derived to obtain valid stationary bivariate and multivariate covariance kernels, characterized by four matrix-valued parameters. Such kernels turn out to be versatile, insofar as the direct and cross-covariances do not necessarily have the same shapes, correlation ranges or behaviors at short scale, thus associated with vector random fields whose components are cross-correlated but have different spatial structures.

Bayesian nonparametric change point detection for multivariate time series with missing observations

A time series is a commonly observed type of data, and it is analyzed in several ways in real applications. Within the possible analysis, change point detection is one of the crucial inferential targets for studying the behavior of a time series. We consider a multiple change point detection model for a multivariate time series. Among the possible approaches to perform multiple change point detection, we propose an extension to the multivariate case of one of the main state-of-the-art approaches, working in a Bayesian nonparametric framework. We combine a combinatorial prior distribution, which relies on a model-based clustering approach to detect the change points, with a multivariate kernel for time-dependent realizations in a general fashion. We further extend the model to the case of missing observations and derive opportune quantities to perform data imputation. Thereafter, we investigate the properties of the multivariate model with an extensive simulation study, and we apply the model to perform change point detection in two real data applications.

Potential Trade Vulnerability of Bangladesh: An Exploratory Analysis

Bangladesh's integration in the global economy has hitherto proven to be an important force behind its economic growth. However, exclusively trade dependent growth is also trade vulnerable growth. This paper explores the factors that may potentially affect the trade vulnerability of Bangladesh. Results of the bivariate non-parametric local linear kernel regression estimation reveal that the minimum wage of readymade garment workers, manufacturing cost, utilities cost, crude oil prices, and climate change are positively related to trade volatility, while improved political stability is negatively related to trade volatility. Multivariate kernel regressions with composite indicators show that macroeconomic factors, such as exchange rate, foreign exchange reserves and budget balance, have a statistically significant impact on the trade volatility of Bangladesh. In view of these preliminary results, a number of policy recommendations are suggested to deal with the short run and long run trade vulnerability of Bangladesh.

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.

Interval Prediction of Photovoltaic Power Using Improved NARX Network and Density Peak Clustering Based on Kernel Mahalanobis Distance

Photovoltaic (PV) power forecasting can provide strong support for the safe operation of the power system. Existing forecasting methods are ineffective for grid scheduling decisions or risk analysis. The novel multicluster interval prediction method is proposed to consider the volatility and randomness of PV power output. First, this method utilizes the sparse autoencoder (SAE) and Bayesian regularized NARX network (BRNARX) for point forecasting of PV power. Second, density peak clustering improved by kernel Mahalanobis distance (KMDDPC) is applied to classify the dataset into multiple clusters, including forecasting error and meteorological factors. Finally, the joint probability density is established by multivariate kernel density estimation (MKDE) to accomplish the PV power interval prediction. The proposed hybrid method is applied for the interval prediction of PV power at Yulara, Australia. Comparative research of point forecasting is implemented to evaluate the machine learning and deep learning methods, with the proposed SAE‐BRNARX under four different periods. Results shows that the average values of nRMSE, MRE, nMAE, and R2 for the four periods are 4.45%, 0.90%, −0.15%, 3.39%, and 95.93%, respectively. Moreover, the results of interval prediction obtained by the other interval prediction approaches are compared with the proposed KMDDPC‐MKDE. It shows that the average values of PICP, PINAW, ACE, and nMPICD for four periods are 93.93%, 9.50%, 3.93%, and 7.10% at 90% confidence level, respectively. Outcomes demonstrate that the proposed method can obtain more accuracy, a higher coverage rate, narrower average bandwidth, and a closer distance between the middle of interval and actual value than other methods.

Probabilistic Revenue Analysis of Microgrid Considering Source-Load and Forecast Uncertainties

Due to the randomness of load and renewable energy generation (REG), microgrids face multiple uncertainties. These uncertainties lead to the uncertainty of microgrid operation and bring more challenges to the economic evaluation of microgrids. In this paper, an economic evaluation method for determining microgrid revenue distribution is proposed. Considering the dual uncertainties of source-load and forecast, and temporal autocorrelation of time series, the probabilistic model of uncertainties is established by multivariate kernel density estimation (KDE). Then the random scenarios including forecasting values are generated and used in optimal dispatch calculation for the detailed production simulation. The probabilistic revenue is derived with a method based on Monte Carlo method. Finally, a case study is carried out based on the real data of an industrial park. The results demonstrate the necessity and effectiveness of the probabilistic revenue analysis proposed in this paper. This method can reveal the actual values of each component of a microgrid (e.g., device or algorithm) in specific scenes and provides more insights into investment decisions.

Supervised Multivariate Kernel Density Estimation for Enhanced Plasma Etching Endpoint Detection

The advancement of semiconductor technology nodes requires precise control of their manufacturing process, including plasma etching, which is highly important in terms of the yield, cost, and device performance. Endpoint detection (EPD) is an imperative technique for controlling this process. Here, we propose a novel EPD scheme based on multivariate kernel density estimation (MKDE). The proposed approach is developed by extending the conventional unsupervised learning MKDE method to supervised learning. The performance of the proposed scheme is validated on randomly selected optical emission spectroscopy data collected from an industrial semiconductor manufacturing process. Because the proposed approach uses target values (labeling) of data, it demonstrates enhanced EPD performance compared to the conventional MKDE method, even without threshold presetting.

Laser ablation inductively coupled plasma mass spectrometry analysis of Chinese lead-barium glass: combining multivariate kernel density estimation and maximum mean discrepancy to reinterpret the raw glass used for producing lead-barium glass

Laser ablation inductively coupled plasma mass spectrometry analysis of Chinese lead-barium glass: combining multivariate kernel density estimation and maximum mean discrepancy to reinterpret the raw glass used for producing lead-barium glass

Matrix valued positive definite kernels related to the generalized Aitken's integral for Gaussians

We introduce a method to construct general multivariate positive definite kernels on a nonempty set XX that employs a prescribed bounded completely monotone function and special multivariate functions on XX. The method is consistent with a generalized version of Aitken's integral formula for Gaussians. In the case in which XX is a cartesian product, the method produces nonseparable positive definite kernels that may be useful in multivariate interpolation. In addition, it can be interpreted as an abstract multivariate version of the well-established Gneiting's model for constructing space-time covariances commonly highly cited in the literature. Many parametric models discussed in statistics can be interpreted as particular cases of the method.

Strong consistency of the mode of multivariate recursive kernel density estimator under strong mixing hypothesis

In this research paper, we define a kernel estimator of the mode based on the recursive kernel density estimator developed by [23]. In addition, we establish its almost sure convergence under strong mixing hypothesis. Finally, we corroborate these theoretical results through numerical simulations.

An Efficient Radio Map Learning Scheme Based on Kernel Density Function

Training an accurate and up-to-date radio map has always been a primary concern for implementing a WiFi fingerprint-based localization system. This paper presents a novel radio map learning scheme for online learning a set of kernel density functions, which function like a traditional radio map in WiFi fingerprint-based localization systems. To be specific, each kernel density function corresponds to one specific access point (AP) and predicts the probability of having a received signal strength (RSS) measurement from this AP at any position. In the offline phase, a set of coarse-grained kernel density functions are initially established by the Multivariate Kernel Density Estimation (MKDE) through a fast site survey. In the online phase, these kernel density functions are recursively refined through Incremental-MKDE (IMKDE) using freshly crowdsourced fingerprints, which essentially fuses the historical features in the previous kernel density functions and up-to-date features in the current fingerprints. A compression technique is applied to improve the computation and storage efficiency. In addition, pedestrian dead reckoning (PDR) is leveraged to calibrate the location labels of crowdsourced fingerprints. Extensive experiments are carried out in a real scenario of nearly 1000 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$m^2$</tex-math></inline-formula> for five months, and a comparison made between the IMKDE based method and several existing popular solutions confirms the superiority of the proposed IMKDE in terms of both computational complexity and localization accuracy.

On the Use of a Modified Intersection of Confidence Intervals (MICIH) Kernel Density Estimation Approach

Density estimation is an important aspect of statistics. Statistical inference often requires the knowledge of observed data density. A common method of density estimation is the kernel density estimation (KDE). It is a nonparametric estimation approach which requires a kernel function and a window size (smoothing parameter H). It aids density estimation and pattern recognition. So, this work focuses on the use of a modified intersection of confidence intervals (MICIH) approach in estimating density. The Nigerian crime rate data reported to the Police as reported by the National Bureau of Statistics was used to demonstrate this new approach. This approach in the multivariate kernel density estimation is based on the data. The main way to improve density estimation is to obtain a reduced mean squared error (MSE), the errors for this approach was evaluated. Some improvements were seen. The aim is to achieve adaptive kernel density estimation. This was achieved under a sufficiently smoothing technique. This adaptive approach was based on the bandwidths selection. The quality of the estimates obtained of the MICIH approach when applied, showed some improvements over the existing methods. The MICIH approach has reduced mean squared error and relative faster rate of convergence compared to some other approaches. The approach of MICIH has reduced points of discontinuities in the graphical densities the datasets. This will help to correct points of discontinuities and display adaptive density. Keywords: approach, bandwidth, estimate, error, kernel density

Data-Driven Nonparametric Joint Chance Constraints for Economic Dispatch with Renewable Generation

This article presents data-driven nonparametric joint chance constraints (JCCs) for ramp-constrained economic dispatch. Power generated by renewable sources, such as solar farms, is modeled as an uncertain parameter that may not belong to any parametric class of probability functions. Thus, transmission line flow limitation, which time-independent constraints, are formulated as nonparametric JCCs joint over unknown cumulative distribution functions of renewable generation sources. In addition, thermal units' time-dependent spinning reserve constraints are modeled as nonparametric JCCs joint over scheduling time periods. An approach is presented based on a multivariate kernel density estimator to convert economic dispatch with data-driven nonparametric JCCs into an optimization model solvable by standard solvers. A reduced, more conservative risk level is calculated to ensure JCCs' satisfaction, given the distance between true unknown and estimated cumulative distribution functions by kernel density estimator. An initiation strategy is applied to speed up the optimization solution time. Numerical results show that using data-driven nonparametric JCCs enhances system reliability significantly as compared to using individual chance constraints and parametric JCCs.

Gaussian process analysis of electron energy loss spectroscopy data: multivariate reconstruction and kernel control

Advances in hyperspectral imaging including electron energy loss spectroscopy bring forth the challenges of exploratory and physics-based analysis of multidimensional data sets. The multivariate linear unmixing methods generally explore similarities in the energy dimension, but ignore correlations in the spatial domain. At the same time, Gaussian process (GP) explicitly incorporate spatial correlations in the form of kernel functions but is computationally intensive. Here, we implement a GP method operating on the full spatial domain and reduced representations in the energy domain. In this multivariate GP, the information between the components is shared via a common spatial kernel structure, while allowing for variability in the relative noise magnitude or image morphology. We explore the role of kernel constraints on the quality of the reconstruction, and suggest an approach for estimating them from the experimental data. We further show that spatial information contained in higher-order components can be reconstructed and spatially localized.

Spatial Analysis of the 2018 Logistics Performance Index Using Multivariate Kernel Function to Improve Geographically Weighted Regression Models

This paper analyzes the 2018 Logistics Performance Index (LPI) from the World Bank to determine the spatial effects of countries’ logistics performance. Although the standardized ordinary least square (OLS) models show good results, the spatial lags and Moran’s I of LPI suggest the OLS assumptions are violated. Consequently, an improved geographically weighted regression (IGWR) model using multivariate kernel functions (MKF) is implemented. Through the analysis of the Moran scatter plot, the authors identified the countries that have different logistics performance development trends in the four quadrants representing the relationship between the spatial lags and the LPI. Using trade activity (i.e., import/export) in the MKF, the authors compared different MKF types and bandwidths to ensure the model’s predictability and accuracy and found that the adaptive Gaussian MKF is suitable. Finally, the IGWR model indicates both positive and negative influencing factors on LPI overall score. Specifically, the improvements of LPI are more associated to economic variables in mid- and low-income countries around the world, and are more related to import of construction equipment in the Middle East. Also, business environment is more important in Latin America and the Pacific. European countries are more sensitive to customs efficiency, whereas Pacific-Asian countries are more sensitive to quality of infrastructure and have higher coefficients than African and American countries. This spatial heterogeneity is related to the specific factors that promote the development of their logistics performance.

Twenty-two families of multivariate covariance kernels on spheres, with their spectral representations and sufficient validity conditions

Twenty-two families of multivariate covariance kernels on spheres, with their spectral representations and sufficient validity conditions

Processing outcrop point clouds to 3D rock structure using open source software

This study proposes a processing procedure to extract the 3D rock structure directly from point clouds using open source software. The basic processing involves: (1) estimating the Hough’s normal of each point; (2) converting the normal to dip direction and dip of the corresponding plane; (3) coloring each point in HSV color space according to its normal; (4) decoding the sets number using the multivariate kernel density estimators; (5) extracting and visualizing the set-based points; and (6) estimating the set-based geometric parameters and conducting stereographic projection. The result is an actual discrete fracture network aggregated with the set-based point clouds having HSV colors. From the initial point cloud to the completion of processing, we manage all data in one single file. The case studies show that the processing procedure can identify, extract, and quantify the fracture sets that have less exposed areas, which facilitates the evaluation of main risks.

Data-Driven Pareto-DE-Based Intelligent Optimal Operational Control for Stochastic Processes

In this article, the optimal operational control problem is considered for complex industrial processes with stochastic disturbances. The performance index is optimized by set points reselection on the operational control layer together with controllers design on the loop control layer. First, the operational indices are obtained through some optimization algorithms. Second, the controllers are designed in the ideal situation to ensure that the controlled variables can track desired set points. To minimize the performance deterioration caused by non-Gaussian stochastic noises or disturbances, a novel Pareto distribution estimation (Pareto DE)-based intelligent set-points reselection approach is proposed to optimize entropy and expectation simultaneously. In the proposed method, entropy is formulated in a recursive way basing on joint PDFs which are obtained through multivariate kernel density and bandwidth selection. Meanwhile, both the controller structure and controller parameters are fixed for whatever disturbances acting on the system. Finally, simulations are given to illustrate the effectiveness of the proposed strategy.