Kernel Function Research Articles

Double-transfer learning-based least squares wavelet support vector machine for water quality classification

In the context of intelligent wastewater interception systems, the enhancement of decision control capability heavily relies on precise water quality classification outcomes. Nonetheless, conventional classification techniques encounter challenges in attaining satisfactory accuracy because of the intricate interplay between feature parameters of water quality and the imbalanced distribution of samples across different classes. In this paper, a least squares wavelet support vector machine (LSWSVM) is proposed with a double-transfer learning (DTL) strategy and an enhanced adaptive differential evolution (EADE) algorithm, referred to as DTL-EADE-LSWSVM. Firstly, the radial basis function is replaced by a wavelet function with multiresolution analysis to enhance the generalization ability of the LSWSVM. Secondly, three adaptive adjustment strategies for mutation factor, crossover probability and population size are designed in the EADE algorithm. Then, the EADE algorithm is adopted to obtain the optimal penalty factor and the parameter of the wavelet kernel function of the LSWSVM. Thirdly, the DTL strategy is developed to transfer the classification labels and model knowledge of the LSWSVM as well as the optimal population and optimal parameters of the EADE in the source domain to the target domain to improve the optimization efficiency and classification performance of the model in the target domain. Finally, the classification accuracy of the class imbalance samples is improved by reshaping the objective function. The experimental results indicate that the accuracy of the proposed DTL-EADE-LSWSVM classification model on balanced and imbalanced datasets is 92.5 % and 92.4 %, respectively, which is better than that of neural networks, stochastic deep forests and classical SVMs. In addition, the proposed DTL strategy has a stronger knowledge transfer capability than the single transfer learning strategy. The proposed DTL-EADE-LSWSVM is fully capable of classifying water quality in wastewater intercepting systems.

Mixture Gaussian process model with Gaussian mixture distribution for big data

In the era of chemical big data, the high complexity and strong interdependencies present in the datasets pose considerable challenges when constructing accurate parametric models. The Gaussian process model, owing to its non-parametric nature, demonstrates better adaptability when confronted with complex and interdependent data. However, the standard Gaussian process has two significant limitations. Firstly, the time complexity of inverting its kernel matrix during the inference process is O(n)3. Secondly, all data share a common kernel function parameter, which mixes different data types and reduces the model accuracy in mixing-category data identification problems. In light of this, this paper proposes a mixture Gaussian process model that addresses these limitations. This model reduces time complexity and distinguishes data based on different data features. It incorporates a Gaussian mixture distribution for the inducing variables to approximate the original data distribution. Stochastic Variational Inference is utilized to reduce the computational time required for parameter inference. The inducing variables have distinct parameters for the kernel function based on the data category, leading to improved analytical accuracy and reduced time complexity of the Gaussian process model. Numerical experiments are conducted to analyze and compare the performance of the proposed model on different-sized datasets and various data category cases.

Neural operators for robust output regulation of hyperbolic PDEs

The recently introduced neural operator (NO) has been employed as a gain approximator in the backstepping stabilization control of first-order hyperbolic and parabolic partial differential equation (PDE) systems. Due to the global approximation ability of the DeepONet, the NO provides approximate spatial gain function with arbitrary accuracy. The closed-loop system stability can be ensured by the backstepping controller involving the approximate gain with sufficiently small error. In this paper, the NO theory is leveraged to solve the robust output regulation problem for a class of uncertain hyperbolic PDE systems under the design framework of backstepping-based regulator. The NO is trained offline on a dataset containing a sufficient number of system parameters and corresponding prior solutions of the kernel equation, so as to generate feedback gain for the robust regulator. Once the NO is trained, the kernel equation does not need to be solved ever again, for any new system parameters that do not exceed the range of the training set. Based on the internal model principle, the regulator is inherently robust to a degree of parameter uncertainty and error in approximate gain. Therefore, the tracking error can still converge to 0 if the extended regulator equations are solvable and the parameter uncertainty leads to an asymptotically stable origin. We provide a series of theory proofs and a numerical test under the approximate control and observation gains to demonstrate the robust regulation problem. It is shown that the NO is almost three orders of magnitude faster than PDE solver in generating kernel function, and the loss remains on the order of 10−4 in the test. This provides an opportunity to use the NO methodology for accelerated gain scheduling regulation for PDEs with time-varying system parameters.

Classification and Novelty Detection of Tampered ICs Using ResCav

This paper investigates the capabilities of the resonant cavity system (ResCav) for detecting tampered integrated circuits (ICs) within supply chains. Prior research showcased ResCav’s ability to discern minor circuit variations, this study focuses on enhancing supervised classification results and introduces a one-class support vector machine (SVM) approach with a modified radial basis function kernel for novelty detection. Through finer hyperparameter tuning, the system achieves improved classification accuracy, demonstrating its potential to identify nuanced alterations with even higher precision and recall rates. Additionally, the application of a one-class SVM enables the detection of tampered ICs without reliance on labeled datasets, expanding utility in scenarios where access is limited to golden ICs. These advancements in ResCav’s capabilities signify progress in failure prevention methodologies, offering an efficient and non-destructive solution crucial for safeguarding against counterfeit and non-conforming components infiltrating critical supply chains.

On the Dirichlet problem for fractional Laplace equation on a general domain

In this paper, we study the weak strong uniqueness of the Dirichlet type problems of fractional Laplace (Poisson) equations. We construct the Green’s function and the Poisson kernel. We then provide a somewhat sharp condition for the solution to be unique. We also show that the solution under such condition exists and must be given by our Green’s function and Poisson kernel. In doing these, we establish several basic and useful properties of the Green’s function and Poisson kernel. Based on these, we obtain some further a priori estimates of the solutions. Surprisingly those estimates are quite different from the ones for the local type elliptic equations such as Laplace equations. These are basic properties to the fractional Laplace equations and can be useful in the study of related problems.

Thermal Casimir effect for a Dirac field on flat space with a nontrivial circular boundary condition

This work investigates the thermal Casimir effect associated with a massive spinor field defined on a four-dimensional flat space with a circularly compactified spatial dimension whose periodicity is oriented along a vector in the xy plane. We employ the generalized zeta function method to establish a finite definition for the vacuum free energy density. This definition conveniently separates into the zero-temperature Casimir energy density and additional terms accounting for temperature corrections. The structure of existing divergences is analyzed from the asymptotic behavior of the spinor heat kernel function and removed in the renormalization by subtracting scheme. The only non-null heat coefficient is the one associated with the Euclidean divergence. We also address the need for a finite renormalization to treat the ambiguity in the zeta function regularization prescription associated with this Euclidean heat kernel coefficient and ensure that the renormalization procedure is unique. The high- and low-temperature asymptotic limits are also explored. In particular, we explicitly show that free energy density lacks a classical limit at high temperatures, and the entropy density agrees with the Nernst heat theorem at low temperatures. Published by the American Physical Society 2024

Implementation of laser-light backscattering imaging for authentication of the geographic origin of Indonesia region citrus

Citrus fruit (Citrus nobilis Lour.) from the Indonesian region is reported to have high economic value due to attractive nutritional, nutraceutical, and sensory attributes. However, authenticating the geographic origins is challenging because of adulteration and similarity in visual appearance. Therefore, this study aimed to develop an effective method based on laser-light backscattering imaging (LLBI) for authentication of the geographic origin of the region citrus. A total of 200 citrus samples were collected from Medan, Malang, Jember, and Banyuwangi regions, which were the four main citrus-producing areas in Indonesia. Approximately three different laser wavelengths, namely 450, 532, and 648 nm were beamed to produce the backscattering image. Furthermore, a combination of the gray-level co-occurrence matrix (GLCM) method and support vector machine (SVM) algorithm was applied to extract texture features and build a classification model, respectively. In this context, three kernel functions, such as linear, radial basis function, and polynomial, were compared in authenticating the geographic origin of citrus. The results showed that the proposed technique achieved 96.667 % accuracy and 3.333 % apparent error for authentication of the geographic origin. The proposed LLBI technique applied a laser wavelength of 450 nm and a polynomial kernel function as the best combination to produce reliable predictive power. This study held valuable implications for advancing sensing technology devices to authenticate geographic origin, specifically citrus fruit.

Non‐linear phylogenetic regression using regularised kernels

Abstract Phylogenetic regression is a type of generalised least squares (GLS) method that incorporates a modelled covariance matrix based on the evolutionary relationships between species (i.e. phylogenetic relationships). While this method has found widespread use in hypothesis testing via phylogenetic comparative methods, such as phylogenetic ANOVA, its ability to account for non‐linear relationships has received little attention. To address this, here we implement a phylogenetic Kernel Ridge Regression (phyloKRR) method that utilises GLS in a high‐dimensional feature space, employing linear combinations of phylogenetically weighted data to account for non‐linearity. We analysed two biological datasets using the Radial Basis Function and linear kernel function. The first dataset contained morphometric data, while the second dataset comprised discrete trait data and diversification rates as response variable. Hyperparameter tuning of the model was achieved through cross‐validation rounds in the training set. In the tested biological datasets, phyloKRR reduced the error rate (as measured by RMSE) by around 20% compared to linear‐based regression when data did not exhibit linear relationships. In simulated datasets, the error rate decreased almost exponentially with the level of non‐linearity. These results show that introducing kernels into phylogenetic regression analysis presents a novel and promising tool for complementing phylogenetic comparative methods. We have integrated this method into Python package named phyloKRR, which is freely available at: https://github.com/ulises‐rosas/phylokrr.

Deep Learning-Based Defects Detection in Keyhole TIG Welding with Enhanced Vision.

Keyhole tungsten inert gas (keyhole TIG) welding is renowned for its advanced efficiency, necessitating a real-time defect detection method that integrates deep learning and enhanced vision techniques. This study employs a multi-layer deep neural network trained on an extensive welding image dataset. Neural networks can capture complex nonlinear relationships through multi-layer transformations without manual feature selection. Conversely, the nonlinear modeling ability of support vector machines (SVM) is limited by manually selected kernel functions and parameters, resulting in poor performance for recognizing burn-through and good welds images. SVMs handle only lower-level features such as porosity and excel only in detecting simple edges and shapes. However, neural networks excel in processing deep feature maps of "molten pools" and can encode deep defects that are often confused in keyhole TIG. Applying a four-class classification task to weld pool images, the neural network adeptly distinguishes various weld states, including good welds, burn-through, partial penetration, and undercut. Experimental results demonstrate high accuracy and real-time performance. A comprehensive dataset, prepared through meticulous preprocessing and augmentation, ensures reliable results. This method provides an effective solution for quality control and defect prevention in keyhole TIG welding process.

Enhanced multi-constraint dung beetle optimization-kernel extreme learning machine for lithium-ion battery state of health estimation with adaptive enhancement ability

Accurately estimating the state of health (SOH) of lithium batteries is a critical and challenging task in battery management systems. Data-driven models are widely used for SOH estimation but still suffer from the difficulty of balancing speed, accuracy, and adaptability. Therefore, this study constructs the dung beetle optimization algorithm to optimize the kernel extreme learning machine model. This paper addresses the issues of long iteration time and mismatches in kernel function mapping in data-driven models. To improve the model's generality, an adaptive learning kernel function is designed to complement the polynomial kernel function and form a joint function. This joint function is then introduced into a single implicit-layer extreme learning machine, which achieves fast speed and strong adaptive capability. To enhance the algorithmic parameter search capability, the optimal Latin hypercube idea, and the Osprey algorithm's global exploration strategy are introduced, which effectively improves the algorithm's global search capability. Additionally, it successfully regulated the positional update through the design of the logarithmic weighting factor, which improved the local search and convergence capabilities of the algorithm. The experiment validates the effectiveness and rationality of the proposed model for advancing battery management system applications.

Small data reliability analysis in concrete three-point bending tests: A Weibull mixture model approach based on Weibull fracture theory

Due to the high costs and time-consuming nature of experiments, data from concrete three-point bending tests are usually limited. Additionally, the performance of concrete is influenced by various factors such as mix composition and sample preparation methods, leading to significant variability in test results. This poses a major challenge for the reliability analysis of small data from repeated tests. In reliability analysis, statistical models are particularly important as they allow for the prediction of performance and failure probabilities based on existing data. However, traditional statistical methods require a large number of similar samples for data processing and may need specific adjustments due to the diversity of practical applications. To address these issues, this study proposes a mixture model that combines domain knowledge of concrete with Weibull fracture theory and uses the Clustering-Circular Block Bootstrap method for sample augmentation. By analyzing real data obtained from concrete three-point bending tests, we accurately estimated the failure probability of concrete. Additionally, the study uses Gaussian process regression with a spectral mixture kernel function to fit the threshold fracture strength of concrete and estimate failure probabilities. The results show that the proposed method can accurately fit small datasets, with a RMSE of 0.320 and a MAPE of 0.100. The nominal bending strength range at a 5% failure probability is 2.0 MPa to 6.5 MPa, depending on the sample height and pre-crack length. Statistical learning demonstrates that the proposed method excels in fitting small datasets, providing a solid framework for predicting concrete strength and reliability.

CHINESE YUAN EXCHANGE RATE AGAINST THE INDONESIAN RUPIAH PREDICTION USING SUPPORT VECTOR REGRESSION

This study aims to forecast the exchange rate between the Chinese Yuan (CNY) and the Indonesian Rupiah (IDR) using Support Vector Regression (SVR), a machine-learning technique that can handle nonlinear and complex data. The authors utilize the monthly selling exchange rate of CNY against IDR from January 2012 to October 2023 sourced from the “investing” platform. The optimal SVR model is obtained by splitting the data into 113 training samples and 28 testing samples and using the Radial Basis Function (RBF) kernel. The model achieves high accuracy, with a Mean Absolute Percentage Error (MAPE) of 1.738%, a Root Mean Squared Error (RMSE) of 50.661 for the training data and a MAPE of 2.516%, and an RMSE of 64.735 for the testing data. The results of this paper can provide valuable insights for policymakers, investors, and traders who are interested in the CNY/IDR exchange rate dynamics and the economic implications of the Belt and Road Initiative (BRI). The study aligns with the Sustainable Development Goals (SDGs), specifically SDG 8, aiming to promote sustained, inclusive, and sustainable economic growth.

Selective multiple kernel fuzzy clustering with locality preserved ensemble

Multiple kernel fuzzy clustering (MKFC) has demonstrated promising performance in capturing the non-linear relationships within data. However, its effectiveness relies heavily on the appropriate selection of the fuzzification coefficient and kernel functions. To address this challenge, this paper proposes a novel clustering ensemble approach for improving the robustness and accuracy of the MKFC algorithm. The proposed method employs a multi-objective evolutionary optimization approach to heuristically select the optimal fuzzification and kernel coefficients. By employing the selected coefficients, the MKFC algorithm generates a diverse set of accurate candidate clustering results. Subsequently, a locality preserved ensemble mechanism is introduced to derive the final partition matrix, ensuring that all candidate clusterings within the Pareto non-dominated set contribute to the final consensus matrix. Moreover, this mechanism incorporates the knowledge about the locality of the dataset via a graph regularization term, thereby further enhancing the clustering performance. Comprehensive experiments conducted on widely adopted benchmark datasets demonstrate the superiority of the proposed method over the state-of-the-art approaches.

Typicality-Aware Adaptive Similarity Matrix for Unsupervised Learning.

Graph-based clustering approaches, especially the family of spectral clustering, have been widely used in machine learning areas. The alternatives usually engage a similarity matrix that is constructed in advance or learned from a probabilistic perspective. However, unreasonable similarity matrix construction inevitably leads to performance degradation, and the sum-to-one probability constraints may make the approaches sensitive to noisy scenarios. To address these issues, the notion of typicality-aware adaptive similarity matrix learning is presented in this study. The typicality (possibility) rather than the probability of each sample being a neighbor of other samples is measured and adaptively learned. By introducing a robust balance term, the similarity between any pairs of samples is only related to the distance between them, yet it is not affected by other samples. Therefore, the impact caused by the noisy data or outliers can be alleviated, and meanwhile, the neighborhood structures can be well captured according to the joint distance between samples and their spectral embeddings. Moreover, the generated similarity matrix has block diagonal properties that are beneficial to correct clustering. Interestingly, the results optimized by the typicality-aware adaptive similarity matrix learning share the common essence with the Gaussian kernel function, and the latter can be directly derived from the former. Extensive experiments on synthetic and well-known benchmark datasets demonstrate the superiority of the proposed idea when comparing with some state-of-the-art methods.

Image restoration model for microscopic defocused images based on blurring kernel guidance

Defocus blurring imaging seriously affects the observation accuracy and application range of optical microscopes, and the blurring kernel function is a key parameter for high-resolution image restoration. However, its solving process is complicated and high in computational cost. Image restoration based on most neural networks has high requirements on data sets and the image resolution after restoration is limited because of the lack of quantitative estimation of blurring kernels. In this study, an image restoration method guided by blurring kernel estimation for microscopic defocused images is proposed. First, to reduce the blurring kernel estimation error caused by the positive and negative difference in microscopic defocused imaging, a defocused image classification network is designed to classify the input defocused images with different defocus distances and directions, and its output images are input into the blurring kernel extraction network composed of the feature extraction, correlation, and blurring kernel reconstruction layers. Second, a non-blind defocused image restoration model to restore the high-resolution images is proposed by introducing the blurring kernel extraction module into the restoration network based on U-Net, and the blurring kernel estimation and image restoration losses are jointly trained to realize image restoration guided by blurring kernel estimation. Finally, the experimental results of our proposed method demonstrate significant improvements in both the peak signal-to-noise ratio and structural similarity index measure when compared to other methods.

Power quality disturbance signal classification in microgrid based on kernel extreme learning machine

AbstractThis paper presents a kernel extreme learning machine (KELM) integrated with the improved whale optimization algorithm (IWOA) to address the power quality disturbance (PQD) issue in microgrids. First, an adaptive variational mode decomposition method is employed to extract PQD signals in microgrids. Then, the IWOA is utilized to optimize the penalty factor and kernel function parameters for the KELM classifier model, thereby enhancing the performance of the classifier. Furthermore, the test results indicate that the proposed IWOA–KELM achieves high classification accuracy and rapid convergence for complex PQD signals.

Flood Prediction Using Support Vector Regression (Case Study of Floodgates in Jakarta)

Flood can be interpreted as an event that occurs suddenly and quickly enough where the water discharge in the drainage channel cannot be accommodated, so that the blocked area causes the water discharge in the drainage channel in several surrounding areas to overflow and is one of the natural disasters that occurs at an unexpected time and cannot be prevented, because of this, a prediction must be made to detect floods for the next day. Flood prediction is a crucial aspect of disaster management and mitigation, particularly in flood-prone areas such as Jakarta, Indonesia. This study aims to leverage Support Vector Regression (SVR) to predict flood events by analyzing various environmental and hydrological factors that influence flooding. The primary data sources include historical wheater data, river water levels, floodgate positions in Jakarta. The data preprocessing involved cleaning, handling missing values, and normalizing the datasets to ensure compatibility with the SVR model. Feature selection was conducted to identify the most relevant predictors of flooding, such as wheater data, and river water levels. The dataset was then split into training and testing sets, maintaining an 80-20 ratio to ensure robust model validation. An SVR model with a radial basis function (RBF) kernel was trained on the standardized training data. The model's performance was evaluated using Root Mean Squared Error (RMSE) as the primary metric. The RMSE produced in this study was 0.112 with an R Square accuracy of 0.977. The results indicated that the SVR model could effectively predict flood events with a reasonable degree of accuracy, demonstrating its potential as a valuable tool in flood forecasting.

Predicting borrower default risk using support vector machine AI models

Precise prediction on the likelihood of borrower default is pivotal for credit institution and decision makers to mitigate the loss of capital and rationalize decision process. This article reviewed the Effects of Support Vector Machine (SVM) models with radial basis function (RBF) kernel in predicting the mortality rate of borrowers. By integrating with a dataset of approximately 100,000 borrowers profile harvested through historical loan performance, we set up the SVM model, and employed a feature-distribution method utilizing grid search and cross-validation technique to fine-tune the predictive model of SVM. Results indicated that the model accomplished an excellent performance with accuracy of 92%, precision of 89%, the recall and F1-score of 85% and 87%, respectively, alongside an Area Under the Curve -Receiver Operating Characteristic (AUC-ROC value of 0.95). It was evinced that the model performed substantially better than traditional logistic regression and decision trees in discriminating defaulter from non-defaulter. The outcome informs that an in-depth process should be implemented on data preprocessing, featureselection, and parameter tuning to achieve a robust predictive model for credit risk assessment. The article concludes the potentials of AI based on the resort to artificial technology in revolutionising the risk assessment scheme within the financial industry.

COMPARISION OF RICE PRICE PREDICTION RESULTS IN EAST JAVA USING FOURIER SERIES ESTIMATOR AND GAUSSIAN KERNEL ESTIMATOR SIMULTANEOUSLY

Extreme weather changes and the El Nino phenomenon in 2023 will cause drought, resulting in a decrease in rice production and an increase in rice prices. It has significantly impacted East Java Province as it is the most extensive rice supplier in Indonesia. This study aims to predict the price of rice with six different qualities using the Fourier series estimator and Gaussian kernel function simultaneously. The results show that the Gaussian kernel method, with a bandwidth value of 1, produces a better model with a MAPE value of 0.228259% than the sine function Fourier series method in predicting rice prices based on six different qualities. The prediction results using the Gaussian kernel function method are categorized as highly accurate because they are less than 10%. This research accelerates the realization of SDG 2 related to "Zero Hunger" through government policies to control the high price of rice in Indonesia. Recommendations that can be given through the research results include cooperation with the government, which can help access information and resources needed to manage price risks.

RTSMFFDE-HKRR: A fault diagnosis method for train bearing in noise environment

The bearings have been exposed to a noisy environment for an extended period, making it challenging to identify fault characteristics accurately and resulting in low accuracy. In this study, we proposed a technique for diagnosing train-bearing faults in noisy environments using refined time-shift multiscale fractional order fuzzy dispersion entropy and hybrid kernel ridge regression (RTSMFFDE-HKRR) to enhance the precision of fault detection. Firstly, RTSMFFDE is proposed based on multiscale fuzzy dispersion entropy by combining the theories of refinement, time-shifting, and fractional order. Revising the refinement process helps to stabilize the entropy value when dealing with a large scale factor. Implementing time-shifting techniques can help preserve the original signal features more effectively. The theory of fractional order strengthens the noise-resistant performance of the algorithm, and the proposed RTSMFFDE has a superior feature extraction capability. Subsequently, a hybrid kernel function is formulated through the combination of the radial basis kernel function (RBF) and the linear kernel function, aiming to improve the nonlinear mapping ability and anti-noise ability of ridge regression classification algorithm. Finally, two sets of experimental cases were used to verify the proposed RTSMFFDE-HKRR. The results show that the fault feature information extracted by RTSMFFDE in noisy environment is more comprehensive, and the classification effect of HKRR is more significant. In the fault diagnosis of two bearing simulation test beds, the accuracy rate of RTSMFFDE-HKRR is up to 100%. In the noisy environment, the accuracy rate is 98.84% and 97.32%, which is much higher than other diagnostic models. RTSMFFDE-HKRR is suitable for train bearing fault diagnosis in noisy environment.