Kernel Function Research Articles

APPLIED MIXED KERNEL AND FOURIER SERIES MODELLING IN NONPARAMETRIC REGRESSION

There are three nonparametric regression approaches, namely, parametric, nonparametric and semi-parametric regression. Nonparametric regression allows the response variable to follow a different curve from one predictor variable to another. In paired data, the components of predictor variable and the response variable are assumed to follow unknown data patterns, so that they can be approximated by a kernel based regression model and Fourier series. The base components are approximated by kernel functions and Fourier series functions. Error is assumed to be normally distributed with zero mean and constant variance. The aim of this research is to make a kernel-based nonparametric regression model and Fourier series on poverty data in the Province of Bali. The research phase method begins with the introduction of the kernel based nonparametric regression model and the Fourier series. The next step is to study the estimation of the regression curve. The function estimation results are highly dependent on the bandwidth, smoothing and oscillation parameters. The resulting model gives a value of R2=0.6278, means that the used variables can explain the model by 62.78 percent. From the obtained modeling re-sults, the Open Unemployment Rate has a positive effect on the percentage of poor people in Bali. Keywords: Nonparametric Regression; Modeling; Kernel; Fourier Series.

Backstepping Control of a Class of Space-Time-Varying Linear Parabolic PDEs via Time Invariant Kernel Functions

Backstepping Control of a Class of Space-Time-Varying Linear Parabolic PDEs via Time Invariant Kernel Functions

Extending GPU-accelerated Gaussian integrals in the TeraChem software package to f type orbitals: Implementation and applications.

The increasing availability of graphics processing units (GPUs) for scientific computing has prompted interest in accelerating quantum chemical calculations through their use. However, the complexity of integral kernels for high angular momentum basis functions often limits the utility of GPU implementations with large basis sets or for metal containing systems. In this work, we report the implementation of f function support in the GPU-accelerated TeraChem software package through the development of efficient kernels for the evaluation of Hamiltonian integrals. The high efficiency of the resulting code is demonstrated through density functional theory (DFT) calculations on increasingly large organic molecules and transition metal complexes, as well as coupled cluster singles and doubles calculations on water clusters. Preliminary investigations into Ni(I) catalysis with DFT and the photochemistry of MnH(CH3) with complete active space self-consistent field are also carried out. Overall, our GPU-accelerated software appears to be well-suited for fast simulation of large transition metal containing systems, as well as organic molecules.

Key point trajectory prediction method of human stochastic posture falls

ABSTRACT The human body will show very complex and diversified posture changes in the process of falling, including body posture, limb position, angle and movement trajectory, etc. The coordinates of the key points of the model are mapped to the three-dimensional space to form a three-dimensional model and obtain the three-dimensional coordinates of the key points; The construction decomposition method is used to calculate the rotation matrix of each key point, and the rotation matrix is solved to obtain the angular displacement data of the key points on different degrees of freedom. The method of curve fitting combined with the weight distribution kernel function based on self-organizing mapping theory is used to obtain the motion trajectory prediction equation of the human body falling in different degrees of freedom at random positions in three-dimensional space, determine the key point trajectory of human random fall behaviour. The experimental results show that the mapped 3D model is consistent with the real human body structure. This method can accurately determine whether the human body falls or squats randomly, and the prediction results of the key points of the human fall are consistent with the actions of the human body after the fall.

Improved Bacterial Foraging Optimization Algorithm with Machine Learning-Driven Short-Term Electricity Load Forecasting: A Case Study in Peninsular Malaysia

Accurate electricity demand forecasting is crucial for ensuring the sustainability and reliability of power systems. Least square support vector machines (LSSVM) are well suited to handle complex non-linear power load series. However, the less optimal regularization parameter and the Gaussian kernel function in the LSSVM model have contributed to flawed forecasting accuracy and random generalization ability. Thus, these parameters of LSSVM need to be chosen appropriately using intelligent optimization algorithms. This study proposes a new hybrid model based on the LSSVM optimized by the improved bacterial foraging optimization algorithm (IBFOA) for forecasting the short-term daily electricity load in Peninsular Malaysia. The IBFOA based on the sine cosine equation addresses the limitations of fixed chemotaxis constants in the original bacterial foraging optimization algorithm (BFOA), enhancing its exploration and exploitation capabilities. Finally, the load forecasting model based on LSSVM-IBFOA is constructed using mean absolute percentage error (MAPE) as the objective function. The comparative analysis demonstrates the model, achieving the highest determination coefficient (R2) of 0.9880 and significantly reducing the average MAPE value by 28.36%, 27.72%, and 5.47% compared to the deep neural network (DNN), LSSVM, and LSSVM-BFOA, respectively. Additionally, IBFOA exhibits faster convergence times compared to BFOA, highlighting the practicality of LSSVM-IBFOA for short-term load forecasting.

DATA MODELING OF GOLD PRICES USING SUPPORT VECTOR REGRESSION WITH LINEAR, POLYNOMIAL, AND RADIAL BASIS FUNCTION KERNELS

Investment is a commitment of funds or other resources made with the goal of obtaining profits in the future. Gold is one of the commodities favored by investors because of its relatively stable value. Although relatively stable, gold prices experience fluctuations, which introduce risks associated with gold investments. The pattern of gold prices can be mathematically modeled using Support Vector Regression (SVR). SVR finds a function as a hyperplane (separating line) in the form of a regression function that fits all input data with an error and minimizes it as much as possible. SVR enables a balance between data fitting and overfitting through the use of kernel functions. The pattern of gold prices and SVR is the main focus of this research, aiming to model gold prices effectively. Furthermore, SVR seeks to obtain a hyperplane (regression function) that fits all input data by minimizing errors. The gold price modeling results using SVR indicated that the best model was obtained with a linear kernel, showing an error of 0.73% with parameters C = 10^(-4) and ? = 10^(-4). This implies the model's strong ability to follow data patterns accurately, resulting in highly reliable forecasting.

Development of Intrusion Detection & Prevention System (IDPS) Using SVM Model with New Kernel Function for Security Solutions

Development of Intrusion Detection & Prevention System (IDPS) Using SVM Model with New Kernel Function for Security Solutions

Using Key Predictors in an SVM Model for Differentiating Spinal Fractures and Herniated Intervertebral Discs in Preoperative Anesthesia Evaluation

Background/Objectives: Spinal conditions, such as fractures and herniated intervertebral discs (HIVDs), are often challenging to diagnose due to overlapping clinical symptoms and the difficulty in assessing their functional impact. Accurate differentiation between these conditions is crucial for effective treatment, particularly in the context of preoperative anesthesia evaluation, where understanding the underlying condition can influence anesthesia planning and pain management. Methods and Materials: This study presents a Support Vector Machine (SVM) model designed to distinguish between spinal fractures and HIVDs using key clinical predictors, including age, gender, preoperative Visual Analog Scale (VAS) pain scores, and the number of spinal fractures. A retrospective analysis was conducted on a dataset of 199 patients diagnosed with these conditions. The SVM model, using a radial basis function (RBF) kernel, classified the conditions based on the selected predictors. Model performance was evaluated using precision, recall, accuracy, and the Kappa index, with Leave-One-Out (LOO) cross-validation applied to ensure robust results. Results: The SVM model achieved a precision of 92.1% for fracture cases and 91.2% for HIVDs, with recall rates of 98.1% for fractures and 70.5% for HIVDs. The overall accuracy was 92%, and the Kappa index was 0.76, indicating substantial agreement. The analysis revealed that age and VAS pain scores were the most critical predictors for accurately diagnosing these conditions. Conclusions: These results highlight the potential of the SVM model with an RBF kernel to reliably differentiate between spinal fractures and HIVDs using routine clinical data. Future work could enhance model performance by incorporating additional clinical parameters relevant to preoperative anesthesia evaluation.

Load forecasting based on multi-core learning Support Vector Machine (SVM)

Abstract The development of smart grids requires enhanced data integration, robust risk assessment, and dynamic response optimization. In this paper, a multi-core learning Support Vector Machine (SVM) model is presented to improve the accuracy and efficiency of load and photovoltaic output forecasting. The model leverages kernel function optimization and parallel computing frameworks to handle large-scale data efficiently. Additionally, a comprehensive risk assessment system is developed to quantify risks such as overvoltage, undervoltage, line overload, and load loss in distribution networks. An adaptive genetic algorithm-based risk control model is also proposed, optimized in two stages—day-ahead and intra-day—to achieve minimal comprehensive risk through real-time adjustments in distributed power output and electric vehicle charging strategies. Furthermore, an integrated virtual synchronous control online verification method for source-network-load-storage is introduced, enhancing system response speed and control accuracy. These innovations collectively provide a solid theoretical foundation and technical support for the efficient and safe operation of smart grids, addressing the increasing demands of modern energy systems.

Parameter-adaptive variational autoencoder for linear/nonlinear blind source separation

AbstractBlind source separation (BSS) serves as an important technique in the field of structural health monitoring (SHM), particularly for solving modal decomposition tasks. This study proposes a novel approach to both linear and nonlinear BSS problems in the Variational Autoencoder (VAE) framework, where the encoding and decoding processes of VAE are interpreted as procedures for inferring sources from observations and remixing these sources, respectively. In this way, the distribution of latent variables inferred by VAE is equivalent to the distribution of sources. We make improvements to the vanilla VAE to augment its effectiveness for BSS. First, we substitute standard normal distributions with trainable Gaussian processes (GP) as priors for latent variables and implement an exponential function as the activation function for adaptive parameters in the GP kernel functions. While the form of the priors is set as GP, the parameters of their kernel functions are not fixed but automatically converge to suitable values during the model training process. Additionally, a hyperparameter is introduced to balance the terms in the loss function. The proposed method is referred to as parameter-adaptive VAE (PAVAE). Then, upon different assumptions of the variances of sources, the proposed PAVAE is branched into two types: homoscedastic PAVAE (Ho-PAVAE) and heteroscedastic PAVAE (He-PAVAE). Through numerical and laboratory experiments, we demonstrate the effectiveness of the proposed method in solving BSS problems and their potential to underpin future research in SHM.

Investigating the Mechanical Characteristics and Fracture Morphologies of Basalt Fiber Concrete: Insights from Uniaxial Compression Tests and Meshless Numerical Simulations

To explore the mechanical properties and fracture modes of basalt fiber-reinforced concrete, single-doped and hybrid-doped basalt fiber-reinforced concrete was prepared, and uniaxial failure tests under different basalt fiber-reinforced concrete contents were carried out. At the same time, the smooth kernel function in the traditional SPH method was improved, and the basalt fiber random generation algorithm was embedded in the SPH program to realize the simulation of the progressive failure of basalt fiber-reinforced concrete. The results show that under the circumstance with no basalt fiber, the specimen final failure mode is damage on the upper and lower surface, as well as the side edge, while the interior of the specimen center is basically intact, indicating that there is an obvious stress concentration phenomenon on the upper and lower surface when the specimen is compressed. Under the circumstance with basalt fiber, longitudinal cracks begin to appear inside the specimen. With the increase in the content, the crack location gradually develops from the edge to the middle, and the crack number gradually increases. This indicates that appropriately increasing the fiber content in concrete may improve the stress state of concrete, change the eccentric compression to axial compression, and indirectly increase the compressive strength of concrete. The numerical simulation results are consistent with the test results, verifying the rationality of the numerical simulation algorithm. For the concrete model without the basalt fiber, shear cracks are generated around the model. For the concrete model with basalt fiber, in addition to shear cracks, the tensile cracks generated at the basalt fiber inside the model eventually lead to the splitting failure of the model. The strength of concrete samples with basalt content of 0.1%, 0.2%, and 0.3% is increased by 1.69%, 5.10%, and 4.31%, respectively, compared to the concrete sample without basalt fiber. It can be seen that with the increase in the content of single-doped basalt fiber, the concrete strength is improved to a certain extent, but the improvement degree is not high; For hybrid-doped basalt fiber-reinforced concrete, the strength of concrete samples with basalt content of 0.1%, 0.2%, and 0.3% is increased by 14.51%, 15.02%, and 30.31%, respectively, compared to the concrete sample without basalt fiber. Therefore, compared with the single-doped basalt fiber process, hybrid doping is easier to improve the strength of concrete.

Analyzing and forecasting air pollution concentration in the capital and Southern Thailand using a lag-dependent Gaussian process model.

The air pollution problem has now amassed worldwide attention due to its multifaceted harm to human health. Exploring the concentration of air pollution and improving forecast have important consideration worldwide. In this research, we analyze the air pollution concentration of Southern Thailand and compare it with the central region. Also, we proposed a methodology based on the lag-dependent Gaussian process (LDGP), a Bayesian non-parametric machine learning model, with a stable optimization approach, which is a cluster-based multi-starter technique based on the Nelder-Mead optimizer. This model also provides the confidence band for forecasted values. We also used autoregressive deep neural network (AR-DNN), autoregressive random forest (AR-RF), gradient boosting (GB), and K-nearest neighbors (KNN) models. A comparison of the proposed methodology was performed on the daily air pollution data collected from the southern provinces and also from the capital of Thailand from 1 January 2018 to 31 December 2022. We used well-established performance evaluation measures to compare the performance of the models. To evaluate the bias due to overfit, we performed a tenfold cross-validation for all the pollutants in each region and compared the models to choose the best one. Moreover, we explored the concentration of air pollution in these regions. Results of descriptive analysis revealed that Bangkok had a much higher concentration of air pollution as compared to the southern region. However, the southern region had higher exposure to PM air pollutants as per WHO recommendations and also had higher exposure to O3 and CO levels. The proposed LDGP model outperformed the other machine learning models for forecasting all air pollutants. Hence, it is recommended to be used by experts for further research and studies with different kernel functions. This research is also expected to contribute to local government planning and prevention and worldwide use of the same methodology for the sustainability of public health.

Predicting shear strength of corroded RC columns: A probabilistic model with enhanced Gaussian Process Regression

This study proposes a new probabilistic model for predicting the shear strength of corroded reinforced concrete (RC) columns. The probabilistic model addresses limitations of traditional methods by combining mechanical understanding with enhanced Gaussian Process Regression (GPR). A novel mean function for enhanced GPR is developed first based on the shear resistance mechanism of corroded RC columns. Then the hyper-parameters of both the mean function and kernel function for the enhanced GPR are optimized using the maximum likelihood estimation method. This leads to the establishment of the probabilistic model that is based on the enhanced GPR. Finally, the accuracy and effectiveness of the enhanced GPR probabilistic model are validated by comparing it with both traditional mechanical models and machine learning models. The results indicate that the proposed probabilistic model can not only describes the probabilistic characteristics for shear strength of corroded RC columns based on probability density functions, but also provides an efficient calibration method for traditional prediction models based on confidence intervals.

Android Malware Detection Using Support Vector Regression for Dynamic Feature Analysis

Mobile devices face significant security challenges due to the increasing proliferation of Android malware. This study introduces an innovative approach to Android malware detection, combining Support Vector Regression (SVR) and dynamic feature analysis to address escalating mobile security challenges. Our research aimed to develop a more accurate and reliable malware detection system capable of identifying both known and novel malware variants. We implemented a comprehensive methodology encompassing dynamic feature extraction from Android applications, feature preprocessing and normalization, and the application of SVR with a Radial Basis Function (RBF) kernel for malware classification. Our results demonstrate the SVR-based model’s superior performance, achieving 95.74% accuracy, 94.76% precision, 98.06% recall, and a 96.38% F1-score, outperforming benchmark algorithms including SVM, Random Forest, and CNN. The model exhibited excellent discriminative ability with an Area Under the Curve (AUC) of 0.98 in ROC analysis. The proposed model’s capacity to capture complex, non-linear relationships in the feature space significantly enhanced its effectiveness in distinguishing between benign and malicious applications. This research provides a robust foundation for advancing Android malware detection systems, offering valuable insights for researchers and security practitioners in addressing evolving malware challenges.

Using Machine Learning Techniques to Predict Significant Wave Height Compared with Parametric Methods

Prediction of Sea Wave parameters is an important issue as it is the main design factor for maritime structures. Previously, researchers have used many parametric and numerical approaches, which may be complex in application, take a long time in preparation and sometimes require a bathymetric survey. Recently, soft computing techniques such as Fuzzy Inference Systems, Genetic Algorithm, Machine Learning, etc. have been used to predict sea wave parameters in many marine areas around the world. The ease of application, high accuracy and low computational time of these techniques make them a very good choice in many engineering applications. This study focuses on prediction of significant wave height (Hs) by applying one of the most advanced Machine Learning techniques known as Support Vector Machine (SVM). SVM models are built on the basis of different Kernel functions (Linear, Sigmoid, Radial Basis Function, and Polynomial) which transform the input data into an n-dimensional space where a hyperplane can be generated to partition the data. The results of SVM models are analyzed, evaluated and then compared with the results of commonly used parametric models (P-M, SPM, and CEM). This study shows that the P-M model has reliable and satisfactory results among all parametric models, as its statistical errors are close to those of SVM models (RBF and Polynomial), while all of them are identical in their correlation factors (0.999). Moreover, the parametric models (SPM and CEM) are more accurate in their results than the SVM models (Linear and Sigmoid). Also, this study confirms that the SVM models (RBF and polynomial) are the most accurate models overall, as they have the best generalization error among all models. Finally, it can be concluded that SVM models (RBF and Polynomial) are a promising technique in the sea wave height prediction and can be used as an economic and accurate alternative solution to other prediction models.

Local maximum synchrosqueezing adaptive transformation for cross-instantaneous frequencies analysis

Abstract To overcome the shortcomings of existing time-frequency (TF) analysis (TFA) methods in analyzing signals containing cross-instantaneous frequencies (IFs), this paper proposes an adaptive TFA technique combined with image processing methods based on local maximum synchrosqueezing transform. The core idea of the proposed algorithm is to localize the filtering of signals containing several different IF components using kernel functions containing several different directions, respectively, to achieve energy separation at the crossing frequencies. In turn, the local maximum synchrosqueezing transform is used to rearrange the TF energy to the true IF ridges of the signal to improve the TF energy concentration. Simulation data demonstrates that the proposed algorithm has higher energy aggregation and better noise immunity, especially for signals with cross-IFs. Applying the proposed method to animal acoustic and radar wave signals of pedestrians can accurately describe the differences in the frequency change patterns and the temporal distribution of energy in the signals, thereby providing a judgment basis for effectively identifying and classifying the signals.

Application of machine learning algorithms for predicting the life-long physiological effects of zinc oxide Micro/Nano particles on Carum copticum

Nanoparticles impose multidimensional effects on living cells that significantly vary among different studies. Machine learning (ML) methods are recommended to elucidate more consistence and predictable relations among the affected parameters. In this study, nine ML algorithms [Support-Vector Regression (SVR), Linear, Bagging, Stochastic Gradient Descent (SGD), Gaussian Process, Random Sample Consensus (RANSAC), Partial Least Squares (PLS), Kernel Ridge, and Random Forest] were applied to evaluate their efficiency in predicting the effects of zinc oxide nanoparticles (ZnO NPs: 0.5, 1, 5, 25, and 125 µM) and microparticles (ZnO MPs: 1, 5, 25, and 125 µM) on Carum copticum. The plant root/shoot biomass; number of leaves, branches, umbellates, and flowers; protein content; reducing sugars; phenolic compounds; chlorophylls (a, b, Total); carotenoids; anthocyanins; H2O2; proline; malondialdehyde (MDA); tissue zinc content; superoxide dismutase (SOD) activity; and media ΔpH were measured and considered input variables. All levels of ZnO MPs treatments increased growth parameters compared to the control (ZnSO4). The highest shoot/root fresh and dry mass were recorded at 5 µM ZnO MPs compared with the control. The root fresh/dry mass under ZnO NPs treatments was more sensitive than shoot parameters. The number of flowers increased by 134 and 79% in MPs and NPs treatments compared to the control, respectively. ZnO NPs reduced protein content by up to 81% in 125 µM NPs compared to ZnSO4. Reducing sugar content increased to 25, 40 and 36% in 5, 25, 125 µM MPs and 67, 68, 26, 26 and 21% in 0.5, 1, 5, 25 and 125 µM NPs treatments, respectively. The pH alteration was more significant under NPs and affected zinc uptake. All levels of ZnO NPs treatments increased growth parameters compared to the control. All ML algorithms showed varied efficiencies in predicting the nonlinear relationships among parameters, with higher efficiency in predicting the behavior of root and shoot dry mass, root fresh weight and number of flowers according to R2 index. The model obtained from SVR with the radial basis function (RBF) kernel was selected as a comprehensive model for predicting and determining the efficacy of the results.

Rapid Classification of Milk Using a Cost-Effective Near Infrared Spectroscopy Device and Variable Cluster-Support Vector Machine (VC-SVM) Hybrid Models.

Removing fat from whole milk and adding water to milk to increase its volume are among the most common food fraud practices that alter the characteristics of milk. Usually, deviations from the expected fat content can indicate adulteration. Infrared spectroscopy is a commonly used technique for distinguishing pure milk from adulterated milk, even when it comes from different animal species. More recently, portable spectrometers have enabled in situ analysis with analytical performance comparable to that of benchtop instruments. Partial Least Square (PLS) analysis is the most popular tool for developing calibration models, although the increasing availability of portable near infrared spectroscopy (NIRS) has led to the use of alternative supervised techniques, including support vector machine (SVM). The aim of this study was to develop and implement a method based on the combination of a compact and low-cost Fourier Transform near infrared (FT-NIR) spectrometer and variable cluster-support vector machine (VC-SVM) hybrid model for the rapid classification of milk in accordance with EU Regulation EC No. 1308/2013 without any pre-treatment. The results obtained from the external validation of the VC-SVM hybrid model showed a perfect classification capacity (100% sensitivity, 100% specificity, MCC = 1) for the radial basis function (RBF) kernel when used to classify whole vs. not-whole and skimmed vs. not-skimmed milk samples. A strong classification capacity (94.4% sensitivity, 100% specificity, MCC = 0.95) was also achieved in discriminating semi-skimmed vs. not-semi-skimmed milk samples. This approach provides the dairy industry with a practical, simple and efficient solution to quickly identify skimmed, semi-skimmed and whole milk and detect potential fraud.

A Feature-Weighted Support Vector Regression Machine Based on Hilbert–Schmidt Independence Criterion Least Absolute Shrinkage and Selection Operator

Support vector regression (SVR) is a powerful kernel-based regression prediction algorithm that performs excellently in various application scenarios. However, for real-world data, the general SVR often fails to achieve good predictive performance due to its inability to assess feature contribution accurately. Feature weighting is a suitable solution to address this issue, applying correlation measurement methods to obtain reasonable weights for features based on their contributions to the output. In this paper, based on the idea of a Hilbert–Schmidt independence criterion least absolute shrinkage and selection operator (HSIC LASSO) for selecting features with minimal redundancy and maximum relevance, we propose a novel feature-weighted SVR that considers the importance of features to the output and the redundancy between features. In this approach, the HSIC is utilized to effectively measure the correlation between features as well as that between features and the output. The feature weights are obtained by solving a LASSO regression problem. Compared to other feature weighting methods, our method takes much more comprehensive consideration of weight calculation, and the obtained weighted kernel function can lead to more precise predictions for unknown data. Comprehensive experiments on real datasets from the University of California Irvine (UCI) machine learning repository demonstrate the effectiveness of the proposed method.

Research on Stock Price Prediction Model Based on Sentiment Factor and Multi-Core Bagging Algorithm

Stock price prediction model is one of the key research points in the quantitative financial field. With the rapid development of data acquisition and storage technology, the data of emotional factors based on nonlinear structure is increasing. How to combine this part of information with common European technology factors to increase the ability of the model is a problem that needs to be solved. Based on this, this paper proposes a method of uncertainty quantification that combines European-and non-European data. Specifically, on the one hand, the Gaussian process regression model is used to capture the unknown relationship between predictive variables and price; on the other hand, the multi-kernel learning technology based on European and non- European kernel functions is used to combine the effective information of European and non- European predictive variables. Moreover, the proposed method can weigh the bias of the prediction model against the variance by using the Bagging algorithm. The simulated data analysis shows that the proposed method not only improves the prediction performance of the European Gaussian process, but also works in the presence of irrelevant predictive variables. Finally, the actual data analysis shows that the proposed method has achieved good prediction results in the task of predicting the rise and fall of stock prices.