Selection Of Kernel Function Research Articles

Tool condition monitoring using I-kaz enhanced kernel extreme learning machine

Abstract In order to improve the accuracy of tool condition monitoring (TCM) in milling, an I-kaz enhanced Kernel Extreme learning Machine (I-kaz_KELM) method is proposed by combining the KELM and I-kaz statistical algorithm. It uses the I-kaz angle function to replace the conventional kernel function to avoid the selection of kernel function and the pre-set of its parameters. A two-layer network model of the I-kaz_KELM is constructed to improve the KELM in feature learning of complex non-linear high-dimensional. Research and analysis of two milling TCM public benchmark datasets (PHM 2010 TCM dataset and NASA TCM dataset) confirmed that the monitoring accuracy of the proposed method is better than SVM and KELM under limited samples. The RESM of the proposed method is reduced by at least 10% compared to the other two methods, and the RESM fluctuation amplitudes of the proposed method with model parameters is reduced by 35%–95% than that of the two other methods. It can be demonstrated that the proposed method can significantly improve learning performance without significantly affecting the learning speed, and has stronger robustness due to reduced sensitivity to the model parameter to be optimized.

Hyper‐Parameter Optimization of Kernel Functions on Multi‐Class Text Categorization: A Comparative Evaluation

ABSTRACTIn recent years, machine learning (ML) has witnessed a paradigm shift in kernel function selection, which is pivotal in optimizing various ML models. Despite multiple studies about its significance, a comprehensive understanding of kernel function selection, particularly about model performance, still needs to be explored. Challenges remain in selecting and optimizing kernel functions to improve model performance and efficiency. The study investigates how gamma parameter and cost parameter influence performance metrics in multi‐class classification tasks using various kernel‐based algorithms. Through sensitivity analysis, the impact of these parameters on classification performance and computational efficiency is assessed. The experimental setup involves deploying ML models using four kernel‐based algorithms: Support Vector Machine, Radial Basis Function, Polynomial Kernel, and Sigmoid Kernel. Data preparation includes text processing, categorization, and feature extraction using TfidfVectorizer, followed by model training and validation. Results indicate that Support Vector Machine with default settings and Radial Basis Function kernel consistently outperforms polynomial and sigmoid kernels. Adjusting gamma improves model accuracy and precision, highlighting its role in capturing complex relationships. Regularization cost parameters, however, show minimal impact on performance. The study also reveals that configurations with moderate gamma values achieve better balance between performance and computational time compared to higher gamma values or no gamma adjustment. The findings underscore the delicate balance between model performance and computational efficiency by highlighting the trade‐offs between model complexity and efficiency.

PMWFCM: A Possibility based MultiKernel Weighted Fuzzy Clustering Algorithm for classification of driving behaviors

Fuzzy clustering algorithms are widely applied in the field of traffic driving, aiding in the classification of driving behaviors from massive traffic data and enhancing traffic safety levels. However, classical Fuzzy C-Means (FCM) algorithms are sensitive to noise during the clustering process, leading to suboptimal performance when dealing with traffic datasets with lower accuracy. Moreover, single-kernel clustering algorithms are greatly influenced by kernel function selection. To address these issues, this paper proposes a Possibility Weighted Multi-Kernel Fuzzy Clustering Algorithm (PMWFCM). By integrating possibility-based fuzzy clustering with FCM and introducing a multi-kernel weighting mechanism, PMWFCM effectively reduces FCM’s sensitivity to outliers while resolving issues of clustering consistency in Possibilistic C-Means (PCM) algorithms, overcoming the challenges associated with kernel function selection. Validation on three different types of datasets demonstrates that the PMWFCM algorithm performs exceptionally well in terms of average accuracy, normalized information, average time, robustness, and convergence. When applied to the evaluation of driving behaviors in traffic datasets. Therefore, the improved FCM algorithm proposed in this paper can accurately and comprehensively reflect changes in traffic data, providing a solid theoretical foundation for identifying and assessing major risk types among passenger drivers.

Kernel Function Selection for FISVDD Applied to Outliers Detection Application for Energy Time Series Datasets

Forecasting energy consumption is crucial for maintaining stability in the energy supply-demand balance. This process requires accurate data, necessitating deep preprocessing steps, with outlier detection being a pivotal task. While most existing methods are tailored for batch learning, smart grid data collection operates continuously, demanding online algorithms for effective data cleaning. This paper proposes an analytical study emphasizing the significance of selecting an appropriate kernel function for data description methods and its impact on forecasting efficiency. The Fast Incremental Support Vector Data Description (FISVDD) algorithm is chosen as a kernel-based approach for outlier detection in time series datasets. The evaluation involves different kernel functions on two datasets: Electrical Grid Stability Simulated Data and Individual Household Electric Power Consumption Dataset. Criteria such as the objective function and data distribution are considered to determine the most suitable kernel function. FISVDD's performance with the right kernel function is compared with other outlier detection methods, and the results are fed into a Gated Recurrent Unit model to visualize the impact on forecasting. Mean Squared Error evaluation reveals that FISVDD with the appropriate kernel function yields the best results, underscoring the strength of data description methods with the appropriate kernel function.

Analysis of dissolved oxygen influencing factors and concentration prediction using input variable selection technique: A hybrid machine learning approach

Accurate quantification of dissolved oxygen (DO) is critically important for the protection and management of aquatic ecosystems. Successful applications have utilized mechanistic and data-driven models to simulate DO content in aquatic ecosystems. However, mechanistic models present challenges due to their complex and difficult-to-solve conditions, making them less portable. Additionally, data-driven model predictions are hindered by the challenge of numerous input variables, impacting both the running speed and prediction performance of the model. To address these challenges, water quality data and meteorological data of the Tanjiang River were obtained. The maximum information coefficient (MIC) input variable selection technique was employed to identify primary environmental factors influencing DO changes. Furthermore, coupled with support vector regression (SVR), two models (SVR and MIC-SVR) were employed to estimate the DO concentration of the Tanjiang River, and the optimal model was established. The results indicated a shift in the primary pollution factor from ammonia nitrogen to total phosphorus after recent treatment in the Tanjiang River. In comparison with the SVR model, the root mean square error (RMSE) of the MIC-SVR model was reduced by 4.46%, and the Nash-efficiency coefficient (NSE) was improved by 45.85%. In addition, study of kernel function selection revealed that considering as many kernel functions as possible is necessary for improving the performance of the SVR model. Conclusively, the proposed MIC-SVR model serves as an effective tool to analyze the relationship between DO and environmental factors, identifying the primary causes of low DO, and accurately predict the DO concentration in the Tanjiang River (especially in its middle and lower reaches), thus providing a reference for governmental decision-making on water environmental protection and water resource management.

Feature Extraction of a Planetary Gearbox Based on the KPCA Dual-Kernel Function Optimized by the Swarm Intelligent Fusion Algorithm

The feature extraction problem of coupled vibration signals with multiple fault modes of planetary gears has not been solved effectively. At present, kernel principal component analysis (KPCA) is usually used to solve nonlinear feature extraction problems, but the kernel function selection and its blind parameter setting greatly affect the performance of the algorithm. For the optimization of the kernel parameters, it is very urgent to study the theoretical modeling to improve the performance of kernel principal component analysis. Aiming at the deficiency of kernel principal component analysis using the single-kernel function for the nonlinear mapping of feature extraction, a dual-kernel function based on the flexible linear combination of a radial basis kernel function and polynomial kernel function is proposed. In order to increase the scientificity of setting the kernel parameters and the flexible weight coefficient, a mathematical model for dual-kernel parameter optimization was constructed based on a Fisher criterion discriminant analysis. In addition, this paper puts forward a swarm intelligent fusion algorithm to increase this method’s advantages for optimization problems, involving the shuffled frog leaping algorithm combined with particle swarm optimization (SFLA-PSO). The new fusion algorithm was applied to optimize the kernel parameters to improve the performance of KPCA nonlinear mapping. The optimized dual-kernel function KPCA (DKKPCA) was applied to the feature extraction of planetary gear wear damage, and had a good identification effect on the fuzzy damage boundary of the planetary gearbox. The conclusion is that the DKKPCA optimized by the SFLA-PSO swarm intelligent fusion algorithm not only effectively improves the performance of feature extraction, but also enables the adaptive selection of parameters for the dual-kernel function and the adjustment of weights for the basic kernel function through a certain degree of optimization; so, this method has great potential for practical use.

Analisis Data Time Series Menggunakan Model Kernel: Pemodelan Data Harga Saham MDKA

<p>Classic time series data analysis techniques, such as autoregressive, model stationary data in which the values of prior observations influence the current observations through a process known as linear regression. There are several requirements for error assumptions in autoregressive, including independence, normal distribution with a zero mean and constant variance. It is frequently discovered that these assumptions are challenging to verify when modelling real data. Kernel time series regression is an alternative model that does not require error assumptions. Non-stationary time series data can be effectively modelled using the kernel time series method. Time series data that isn't yet stationary is made stationary first, then the data is modified by forming the current stationary time series data as the response variable and the previous period data as the predictor variable. Next, regression kernel modelling is carried out while applying kernel weight function and determining the optimal bandwidth. For development of science, the optimal bandwidth can be achieved by minimizing the MSE, CV, GCV, or UBR values. It is possible to use R<sup>2</sup> or MAPE as the kernel time series regression model's goodness metric. A strong model is generated while modelling MDKA stock price data using kernel regression utilizing the Gaussian kernel function and optimal bandwidth selection using GCV since R<sup>2</sup> is 0.9828372 more than 0.67 and MAPE is 1.985681% under 10%.</p><p><strong>Keywords</strong><strong>: </strong>3 time series; kernel regression; GCV; MDKA stock price.</p>

Bias correction based on AR model in spurious regression

<abstract><p>The regression of mutually independent time series, whether stationary or non-stationary, will result in autocorrelation in the random error term. This leads to the over-rejection of the null hypothesis in the conventional t-test, causing spurious regression. We propose a new method to reduce spurious regression by applying the Cochrane-Orutt feasible generalized least squares method based on a bias-corrected method for a first-order autoregressive model in finite samples. This method eliminates the requirements for a kernel function and bandwidth selection, making it simpler to implement than the traditional heteroskedasticity and autocorrelation consistent method. A series of Monte Carlo simulations indicate that our method can decrease the probability of spurious regression among stationary, non-stationary, or trend-stationary series within a sample size of 10–50. We applied this proposed method to the actual data studied by Yule in 1926, and found that it can significantly minimize spurious regression. Thus, we deduce that there is no significant regressive relationship between the proportion of marriages in the Church of England and the mortality rate in England and Wales.</p></abstract>

Wheat Quantity Monitoring Methods Based on Inventory Measurement and SVR Prediction Model

Due to the influences of the storage environment, water content change, particle settlement, natural loss, and other factors, the distribution density of wheat and the volume of grain pile in the storage process are gradually changed so that the single weight calculation method cannot objectively evaluate the storage quantity of wheat and also causes difficulties to the regular inspection of the quantity of wheat stock. To meet the practical needs of wheat inventory monitoring, a wheat inventory monitoring method based on inventory measurement and the support vector machine regression (SVR) prediction model is proposed. By collecting the working papers for the physical inspection of wheat in grain warehouses in Shanxi province, Hebei province, Henan province, Jiangsu province, and other places, the storage time, storage weight, storage moisture content, measured moisture content, measured volume weight, measured net volume, and measured weight for inspection were selected as training samples for the SVR prediction model, and kernel function selection and parameter optimization were carried out. We developed an optimal prediction model for the amount of wheat in the grain depots. In the actual grain store measurement process, the net volume of wheat in the current grain store was obtained by a laser volumetric measuring apparatus, the actual bulk density of wheat was sampled, and the actual moisture content of wheat was measured by sampling. The three samples, their storage time, their storage moisture content, and their storage weight were fed into the trained SVR prediction model as new samples, and the predicted weight of the wheat in the current grain store was obtained from the output. The error rate calculation procedure was introduced to achieve an anomalous judgment error rate for grain depots. The experimental results showed that the SVR prediction model based on the linear kernel function had a very low mean squared error and high determination coefficient, and the average prediction accuracy of the grain stock error rate reached 93.2 percent, which can meet the requirements of wheat quantity monitoring in grain warehouses.

Memory-dependent derivative grey Bernoulli model and its application in electricity generation forecast

PurposeThis paper aims to develop a novel grey Bernoulli model with memory characteristics, which is designed to dynamically choose the optimal memory kernel function and the length of memory dependence period, ultimately enhancing the model's predictive accuracy.Design/methodology/approachThis paper enhances the traditional grey Bernoulli model by introducing memory-dependent derivatives, resulting in a novel memory-dependent derivative grey model. Additionally, fractional-order accumulation is employed for preprocessing the original data. The length of the memory dependence period for memory-dependent derivatives is determined through grey correlation analysis. Furthermore, the whale optimization algorithm is utilized to optimize the cumulative order, power index and memory kernel function index of the model, enabling adaptability to diverse scenarios.FindingsThe selection of appropriate memory kernel functions and memory dependency lengths will improve model prediction performance. The model can adaptively select the memory kernel function and memory dependence length, and the performance of the model is better than other comparison models.Research limitations/implicationsThe model presented in this article has some limitations. The grey model is itself suitable for small sample data, and memory-dependent derivatives mainly consider the memory effect on a fixed length. Therefore, this model is mainly applicable to data prediction with short-term memory effect and has certain limitations on time series of long-term memory.Practical implicationsIn practical systems, memory effects typically exhibit a decaying pattern, which is effectively characterized by the memory kernel function. The model in this study skillfully determines the appropriate kernel functions and memory dependency lengths to capture these memory effects, enhancing its alignment with real-world scenarios.Originality/valueBased on the memory-dependent derivative method, a memory-dependent derivative grey Bernoulli model that more accurately reflects the actual memory effect is constructed and applied to power generation forecasting in China, South Korea and India.

Bayesian structural identification using Gaussian Process discrepancy models

Bayesian model updating based on Gaussian Process (GP) models has received attention in recent years, which incorporates kernel-based GPs to provide enhanced fidelity response predictions. Although most kernel functions provide high fitting accuracy in the training data set, their out-of-sample predictions can be highly inaccurate. This paper investigates this problem by reformulating the problem on a consistent probabilistic foundation, reviewing common choices of kernel covariance functions, and proposing a new Bayesian model selection for kernel function selection, aiming to create a balance between fitting accuracy, generalizability, and model parsimony. Computational aspects are addressed via Laplace approximation and sampling techniques, providing detailed algorithms and strategies. Numerical and experimental examples are included to demonstrate the accuracy and robustness of the proposed framework. As a result, an exponential-trigonometric covariance function is characterized and justified based on the Bayesian model selection approach and observations of the sample autocorrelation function of the response discrepancies.

Boundary-adaptive kernel density estimation: the case of (near) uniform density

We consider nonparametric kernel estimation of density functions in the bounded-support setting having known support [ a , b ] using a boundary-adaptive kernel function and data-driven bandwidth selection, where a and b are finite and known prior to estimation. We observe, theoretically and in finite sample settings, that when bounds are known a priori this kernel approach is capable of outperforming even correctly specified parametric models, in the case of the uniform distribution. We demonstrate that this result has implications for modelling a range of densities other than the uniform case. Furthermore, when bounds [ a , b ] are unknown and the empirical support (i.e. [ min ( x i ) , max ( x i ) ] ) is used in their place, similar behaviour surfaces.

Side-Channel Power Analysis Based on SA-SVM

Support vector machines (SVMs) have been widely used in side-channel power analysis. The selection of the penalty factor and kernel parameter heavily influences how well support vector machines work. Setting reasonable SVM hyperparameters is a key issue in side-channel power analysis. The novel side-channel power analysis method SA-SVM, which combines simulated annealing (SA) and support vector machines (SVMs) to analyze the power traces and crack the key, is proposed in this paper as a solution to this issue. This method differs from other approaches in that it integrates SA and SVMs, enabling us to more effectively explore the search space and produce superior results. In this paper, we conducted experiments on SA-SVM and SVM models from three different aspects: the selection of kernel functions, the number of parameters, and the number of eigenvalues. To compare our results with previous research, we performed experimental evaluations on open datasets. The results indicate that, compared with the SVM model, the SA-SVM model improved the accuracy by 0.25% to 3.25% and reduced the required time by 39.96% to 98.02% when the point of interest was 53, recovering the key using only three power traces. The SA-SVM model outperforms existing methods in terms of accuracy and computation time.

Phonetic Feature Extraction and Recognition Model in Korean Pronunciation Practice Based on AdaBoost

This paper proposes a phonetic feature extraction and recognition model in Korean pronunciation exercises based on AdaBoot moments. Feature extraction algorithms have a great influence on speech emotion recognition algorithms, among which Mel-frequency Cepstral Coefficients (MFCC) is the most commonly used feature in speech emotion recognition. The feature extraction method and the influence of SVM kernel function and parameter selection on the recognition result are studied, and the existing speech feature extraction algorithms and their respective advantages and disadvantages are analyzed, as well as the influence of different kernel functions, kernel parameters and penalty parameters on the recognition performance. An improved grid optimization method is used to further improve the recognition time of voice information.

A Time Series Data Regression Model Based on Multi-kernel KPCA Dimension Reduction and Bagging Algorithms

Regression models for high-dimensional data have always been a hot topic in the field of statistical learning. Considering the case that the predictor variable is a high-frequency time series and the response variable is a continuous scalar, this paper proposes a regression method based on a multi-kernel KPCA Dimension reduction method and the Bagging algorithms. The proposed method adaptively solves the problem of kernel function selection and unsupervised ness in KPCA Dimension reduction by splicing the projection data under various kernel functions and using the Bagging algorithms to mine the relationship between projection data and the response variable. In the real data analysis, this paper selects the multiple regression model, the LASSO regression based on model selection, the multiple regression model based on PCA Dimension reduction and single-kernel KPCA Dimension reduction as comparison methods. The results show that the proposed method has better performance than other comparison methods. Since the basic regressor in the Bagging framework is model-free, some prediction models can be used to improve the prediction accuracy for more complex data situations.

Inversion in an uncertain ocean using Gaussian processes.

Gaussian processes (GPs) can capture correlation of the acoustic field at different depths in the ocean. This feature is exploited in this work for pre-processing acoustic data before these are employed for source localization and environmental inversion using matched field inversion (MFI) in an underwater waveguide. Via the application of GPs, the data are denoised and interpolated, generating densely populated acoustic fields at virtual arrays, which are then used as data in MFI. Replicas are also computed at the virtual receivers at which field predictions are made. The correlations among field measurements at distinct spatial points are manifested through the selection of kernel functions. These rely on hyperparameters, that are estimated through a maximum likelihood process for optimal denoising and interpolation. The approach, employing Gaussian and Matérn kernels, is tested on synthetic and real data with both an exhaustive search and genetic algorithms and is found to be superior to conventional beamformer MFI. It is also shown that the Matérn kernel, providing more degrees of freedom because of an increased number of hyperparameters, is preferable over the frequently used Gaussian kernel.

Coal Gangue Recognition during Coal Preparation Using an Adaptive Boosting Algorithm

The recognition of coal and gangue is the premise and foundation of coal gangue intelligent sorting. Adaptive boosting (AdaBoost) algorithm-based coal gangue identification has not been studied in depth. This paper proposed a coal gangue image recognition algorithm and a strong classifier based on the AdaBoost algorithm with a genetic algorithm (GA)-optimized support vector machine (SVM). One thousand coal gangue images were collected on-site and expanded to five thousand via rotation and exposure adjustment. The 12 gray-level gradient co-occurrence matrix texture features of the images were extracted to construct a feature vector, establishing the training dataset and test dataset. Selection of the SVM kernel function, the GA optimization parameter setting, and the base classifier number was discussed. The coal gangue image recognition effects of the AdaB-GA-SVM classifier and the other strong classifiers with different base SVM classifiers were investigated. The results indicated that the recognition accuracy of GA-SVM was the best when the kernel function of SVM was RBF and the population number, crossover probability, and mutation probability were 80, 0.9, and 0.005, respectively. The AdaB-GA-SVM classifier has excellent identification and effective classification performance with the highest accuracy of 95%, a precision rate of 92.8%, recall rate of 97.3%, and KS values of 0.79.

Bayesian optimization of ball milling conditions to obtain highly crystal-oriented Sm-Fe-N powder

The intrinsic magnetic properties of Sm2Fe17N3 are comparable or superior to those of Nd2Fe14B alloys. However, these properties have not been successfully demonstrated to date. Ball milling is commonly used to process Sm2Fe17N3 alloys because it can refine the particle size to increase their coercivity. Surfactant-assisted ball milling (SABM) produces crystal-oriented flake-like particles. Increasing the milling time and speed reduces the particle size, whereas increasing the oleic acid content changes the particle morphology from spherical to flaky. However, ball milling decomposes the Sm2Fe17N3 phase into the magnetically soft α-Fe phase, which is detrimental to remanence. Therefore, we applied the Bayesian optimization method to optimize the process conditions. Experimental process systems in laboratories are not fully established; therefore, experimental data sometime include outliers, which makes acquiring models from learning datasets difficult. In the case of a small experimental dataset, identifying an outlier is difficult. We proposed a Bayesian optimization with kernel function selection and a data screening method for a learning dataset that includes unexpected outliers. We examined the proposed system for the optimization of the SABM of Sm2Fe17N3 using actual experimental results, including outliers. The combination of kernel function selection and data screening was effective in allowing outliers to be identified in small datasets. Knowledge of the process was incorporated during data screening to optimize the process conditions, allowing the formation of a highly crystal-oriented powder.

Application of Support Vector Machines for Breast Calcification Cluster Detection and Mass Classification

Breast cancer has become “the most common cancer worldwide”, and it is an urgent problem in the medical field to improve the detection rate of breast cancer through early diagnosis and treatment. Based on the current research on medical image processing, our work selects breast images from the MIAS database for pre-processing, segmentation, texture feature extraction and classification, and conducts an in-depth investigation and experimental validation on the theoretical basis of support vector machine algorithm, kernel function selection, and key parameter optimization. The results show the effectiveness of support vector machines in detecting abnormal areas and classifying masses in breast images and provide research ideas for breast cancer diagnosis.

Unified whale optimization algorithm based multi-kernel SVR ensemble learning for wind speed forecasting

Support vector regression (SVR) is widely used in the field of wind speed forecasting because of its excellent nonlinear learning ability. However, the drawback of SVR is the model selection problem, which has the high complexity O(K×m3) including kernel function selection and parameter selection. To solve this problem, this paper proposes a multi-kernel SVR ensemble (MKSVRE) model based on unified optimization and whale optimization algorithm (WOA), where the MKSVRE model is used to solve the kernel function selection problem, and the unified optimization and the WOA are used to solve the parameter selection problem. The proposed model provides an alternative without the need to specifically select a kernel function and thus enhances the adaptability of SVR to diverse data. In addition, the unified optimization takes into account the interactions between models and achieves a global parameter selection. The proposed model is tested by simulations on wind speed data from Shandong Province, China. By comparing the prediction results of the proposed model, the single kernel SVR models, the models before and after optimization, and six other models, the effectiveness of the proposed model is confirmed.