Traditional Kernel Function Research Articles

Hydraulic fracturing modelling of glutenite formations using an improved form of SPH method

Due to the low permeability and high heterogeneity properties of glutenite formations, the hydraulic fracture morphologies are extremely distorted during hydraulic fracturing operations, which is difficult to predict by traditional numerical method. Based on the existing limitations (i.e., the mesh re-division problems in FEM, complex parameter calibrations in DEM), an improved Smoothed Particle Hydrodynamics (SPH) method for modelling the hydraulic fracturing of glutenite formations was proposed. The interaction modes between the liquid and solid particles were first defined and the transformation algorithms of liquid, particles and damaged particles were also proposed. Then, the fracture mark ξ was introduced and the traditional kernel function in SPH was improved to simulate the hydraulic fracturing process. The “random gravel generation” algorithm combined with the “searching radius method” were proposed to well reproduce the meso-structures of glutenite. After that, the SPH model of glutenite was established, based on which, the influence of factors such as gravel size, content, strength as well as confining pressure were investigated. Results show that the crack patterns mainly include: 1) Propagating through the gravel; 2) Propagating around the gravel; 3) Stopping inside the gravel; 4) Crack bifurcation. The research results can provide some references for the comprehensive understandings of the internal mechanisms of glutenite hydraulic fracturing processes as well as the applications of SPH method into the simulations of glutenite hydraulic fracturing.

Simulating the chemical-mechanical-damage coupling problems of cement-based materials using an improved smoothed particle hydrodynamics method

The applications of Smoothed Particle Hydrodynamics (SPH) into the chemical - mechanical - damage coupling problems of cement - based materials have been rarely investigated. Based on this background, the diffusion equations of chemical ion concentration in SPH form are derived. Traditional kernel function in SPH is improved by introducing the ion concentration damage coefficient Dc. Firstly, the chemical corrosion processes of a semicircular corrosion pit are simulated, and the rationality is verified by comparing with previous experimental results. Then the effects of different bedding direction, random aggregates and their anisotropy degrees on the chemical corrosion processes are discussed. Finally, a chemical-stress-damage coupling model is established to simulate the crack propagation processes. The research results can provide some references for the comprehensive understandings of the chemical-stress-damage coupling laws, as well as the applications of SPH method into the chemical-stress-damage coupling simulations of cement-based materials.

Numerical investigation and experimental study on fracture processes of central flawed sandstone Brazilian discs

The propagations and connections of rock mass fissures are direct factors that lead to failure of rock engineering structures. Based on this, the traditional kernel function in the smoothed particle hydrodynamics (SPH) method was improved, which could simulate the progressive propagation processes of rock fissures. Brazilian disc samples of red sandstone with different fissure angles were prepared, and experiments on the crack propagations of Brazilian discs under uniaxial compression were carried out combined with digital image correlation technology. The results show that when the inclination angle of the prefabricated fissure is 0°, cracks initiate from the middle of the fissure and propagate along the loading direction; “Wing cracks” occur at prefabricated fissure inclination angles of 30°∼60°; when the inclination angle is 90°, cracks propagate along the direction of the prefabricated fissure. The peak load of the samples first decreases and then increases with increasing inclination angle, and was minimum when the angle was 60°. An improved SPH algorithm was used to simulate the crack growth of Brazilian discs with different fissure angles, and the simulation results are consistent with the experimental results, which verifies the rationality of the proposed method. However, most rock engineering problems are three-dimensional, so future research directions should focus on the development of 3D SPH parallel programs.

An improved meshless method for modeling the mesoscale cracking processes of concrete containing random aggregates and initial defects

Traditional kernel functions in SPH has been improved to realize the simulations of progressive cracking processes; The generation method of meso properties in concrete has been proposed, and the “region searching” algorithm has been developed. Uniaxial tension numerical simulations of concrete specimens with different initial defects and aggregate percentages are carried out, results show that the initial defects and aggregate percentages have great impacts on concrete failure modes. The rationality of the improved method is verified by comparing with previous experimental and numerical results, and future research directions should focus on the developments of multi-field coupling 3D parallel MSC-IKSPH programs.

An improved Smoothed Particle Hydrodynamics (SPH) method for modelling the cracking processes of teeth and its applications

The present work aims to propose a meshless method to establish the tooth meso-structures and model the tooth fracturing processes as well as investigate the influencing factors that affect the dental mechanical properties. To this end, the traditional kernel function in the SPH method has been improved by introducing a fracture mark ξ to realize the progressive failure processes of teeth; The “Particle Searching Method” has been proposed, which can realize the establishments of microstructures of teeth such as enamel, dentine, pulp, PDL and alvedar bones. The Weibull function is introduced to represent the heterogeneity of teeth, which can realize the random distribution characteristics of dental mechanical parameters. The simulation results of homogeneous and heterogeneous teeth show that the failure mode changes from tensile splitting (homogeneous) to shear failure (heterogeneous). Meanwhile, the fracture networks become more complex, and the failure stress decreases sharply. The cuspal angles also have a great impact on the teeth fracture characteristics. The failure modes changes from tensile splitting of the enamel tip to the cracking from the contact points between the enamel and the rigid ball; Different fssural morphologies have little influences on the teeth failure characteristics. The research results can provide some references for the applications of SPH method into biomechanical simulations such as teeth failure. Meanwhile, it can also provide some guidance for the understandings of the internal mechanisms of teeth fracture processes, the diagnosis and treatments of clinical diseased teeth as well as the design of bionic teeth materials.

Multiple kernel learning for label relation and class imbalance in multi-label learning

There are two common challenges in multi-label learning (MLL), complex label relation and imbalanced class. Few studies have focused on addressing both problems at the same time. In this paper, we propose a multiple kernel learning (MKL) approach to tackle two challenges, named as Multi-Kernel Multi-Label (MKML) method. MKML contains three kernel modules. The first kernel module adopts the traditional kernel function which contains the global information, and the other two kernel modules are designed for the two problems respectively. The second kernel module learns the inter-label relation by adding supervised information. The third kernel module adjusts the imbalanced decision boundary through multi-layer fusion strategy, which is proved to improve the representation ability of kernels in this paper. Finally, the proposed joint optimization method in this MKL framework achieves good generalization ability. We conduct several related experiments using real-world datasets to evaluate the effectiveness of our method. The results demonstrate that MKML outperforms other state-of-the art methods in MLL task.

Random Fourier Approximation of the Kernel Function in Programmable Networks

Abstract Random Fourier features represent one of the most influential and wide-spread techniques in machine learning to scale up kernel algorithms. As the methods based on random Fourier approximation of the kernel function can overcome the shortcomings of machine learning methods that require a large number of labeled sample, it is effective to be applied to the practical areas where samples are difficult to obtain. Network traffic forwarding policy making is one such practical application, and it is widely concerned in the programmable networks. With the advantages of kernel techniques and random Fourier features, this paper proposes an application of network traffic forwarding policy making method based on random Fourier approximation of kernel function in programmable networks to realize traffic forwarding policy making to improve the security of networks. The core of the method is to map traffic forwarding features to Hilbert high-dimensional space through random Fourier transform, and then uses the principle of maximum interval to detect adversarial samples. Compared with the traditional kernel function method, it improves the algorithm efficiency from square efficiency to linear efficiency. The AUC on the data set from real-world network reached 0.9984, showing that the method proposed can realize traffic forwarding policy making effectively to improve the security of programmable networks.

Combined Economic-Emission Dispatch of External Optimization Integrating Renewable Energy Resources Stochastic Wind and Solar

Economic dispatch in the standard power system network frequently prioritizes instant economic gains while overlooking the detrimental environmental effects of gas discharges from thermal power stations. Economic emission dispatch (EED) has received a lot of consideration in current years as a way to alleviate this shortage. The unpredictability and intermittence of renewable energy sources like wind and solar power are raising the difficulty of electric grid planning as renewable production penetration rises. This research proposes a modified MMOCE to improve dispatch efficiency with considerable renewable energy consumption. A congestion calculation method and a new external storage process are added to the traditional kernel function method to address multi-objective optimization issues. The energy and transportation sectors are two of the most significant producers of GHG emissions. Improved vehicle productivity is a partial answer, but to limit the rate of GHG emissions, it is important to use RESs in the network. It is, however, critical to evaluate the efficacy of each approach. In this research, the environmental and economic aspects of employing RESs will be examined using a mixture of generating cost and GHG emissions from the two businesses stated. To overcome the ELD problem, an enhanced PSO is employed. However, solutions for reducing time consumption for the high-dimensional ELD issue are not considered in this study.

Weighted p-norm distance t kernel SVM classification algorithm based on improved polarization

The kernel function in SVM enables linear segmentation in a feature space for a large number of linear inseparable data. The kernel function that is selected directly affects the classification performance of SVM. To improve the applicability and classification prediction effect of SVM in different areas, in this paper, we propose a weighted p-norm distance t kernel SVM classification algorithm based on improved polarization. A t-class kernel function is constructed according to the t distribution probability density function, and its theoretical proof is presented. To find a suitable mapping space, the t-class kernel function is extended to the p-norm distance kernel. The training samples are obtained by stratified sampling, and the affinity matrix is redefined. The improved local kernel polarization is established to obtain the optimal kernel weights and kernel parameters so that different kernel functions are weighted combinations. The cumulative optimal performance rate is constructed to evaluate the overall classification performance of different kernel SVM algorithms, and the significant effects of different p-norms on the classification performance of SVM are verified by 10 times fivefold cross-validation statistical comparison tests. In most cases, the results using 6 real datasets show that compared with the traditional kernel function, the proposed weighted p-norm distance t kernel can improve the classification prediction performance of SVM.

Random Fourier feature-based fuzzy clustering with [formula omitted]-Laplacian regularization

Random feature is one successful technique to approximate traditional kernel functions, and the random feature-based fuzzy clustering has been proved to be effective and efficient for handling non-linear data. However, the existing random feature-based fuzzy clustering methods fail to consider the locality information hidden in original input data. From some perspective, the membership obtained by fuzzy clustering can be seen as the encoding results of data. Thus, constraining the relationships between membership degrees to be consistent with that of data is beneficial to improve clustering performance. To this end, we propose a novel random Fourier feature-based fuzzy clustering method (pLRFCM) in this paper. The random Fourier feature is used to approximate Gaussian kernels in this method, and the fuzzy clustering is performed in the feature space. More importantly, the p-Laplacian regularization is conducted on the membership matrix to preserve the local structures of original data into the clustering results, to guarantee good partition of data. The maximum-entropy technique is also utilized to fine-tune the weights of features automatically during the process of clustering, so as to further promote the performance of clustering. In the experiments on four synthetic non-linear datasets and eight real-world datasets, pLRFCM outperforms several classical and state-of-the-art fuzzy clustering methods.

Self-learning regression interpolation based on Ricker kernel function for seismic data

Seismic data interpolation techniques are extremely economical for removing negative effects resulting from insufficient spatial sampling. In recent years, self-learning mechanism-based methods (relatively intelligent methods), such as machine learning (ML) and deep learning, have increasingly attracted the attention of many scholars. Support vector regression machine (SVR), a kind of ML method, can obtain good reconstructed performance for seismic data interpolation. However, the performance is influenced directly by the kernel function, which controls the map from the input space to the feature space. In other words, a good and suitable kernel function can contribute to the extraction of good features and improve the self-learning ability. In this paper, Ricker kernel function suitable for seismic data, rather than the traditional Gaussian kernel function, will be introduced and applied in the new SVR-based interpolation method. In detail, the Ricker wavelet is widely used to simulate seismic data. And the Ricker kernel function can be used specially for the seismic data process. Under the guarantee of the special kernel function, the input time-space vector series are trained as a better model for future prediction of missing seismic data. Numerical experiments on synthetic and real field data show better reconstruction ability than that of SVR based on the traditional kernel function. Furthermore, we discuss the difference between the relatively shallow ML method (SVR) and the deep learning neural networks method. Except for the computer hardware, deep neural learning methods will impose stringent requirements on the training data, not only with respect to quantity but also including data quality. From this perspective, SVR shows more flexibility in the self-learning process.

Intrinsic Quasi-Periodicity in Hong Kong Housing Price and Its Prediction

Housing price time series is worth studying as it is closely related to the well-being of society. In the Hong Kong housing market from 1992 to 2010, signs of quasi-periodicity in housing price and transaction volume can be observed. We find that there is an overall periodicity of approximately 30 months in housing price changes and a strong lead–lag relationship between housing price and transaction volume. Analysis of the cross-covariance of the housing price, transaction volume and prime lending rate reveals that this quasi-periodicity is potentially driven by prime lending rates. Incorporation of quasi-periodicity into the kernel of Gaussian processes further enables us to construct a predictive model of the Hong Kong housing price trends that outperforms other traditional kernel functions.

Single-Image Super-Resolution based on Steering Kernel and Gaussian Process Regression

Single-image super-resolution (SR) imaging is a fundamental problem in image processing; it is important in entertainment, video surveillance, remote sensing, medicine, and other fields. Gaussian process regression (GPR) is a kernel method whereby nonlinear mapping relationships in data can be learned. However, the traditional Gaussian kernel function used in GPR is isotropic and fails to capture complex image structures. Accordingly, the structure information of image patches, termed steering kernel coefficients (SKCs), is extracted by a steering kernel function. After patches with similar structure are clustered according to their SKCs, an anisotropic automatic-relevance-determination (ARD) kernel function is used to learn the model for each cluster. Aiming at learning a structure-sensitive GPR model, we integrate the SKCs and ARD to achieve improved performance for GPR-based SR. Experiments demonstrate that the proposed method can effectively capture the structural relevance of image patches and yield promising results.

Software defect prediction model based on distance metric learning

Software defect prediction (SDP) is a very important way for analyzing software quality and reducing development costs. The data during software lifecycle can be used to predict software defect. Currently, many SDP models have been proposed; however, their performance was not always ideal. In many existing prediction models based on machine learning, the distance metric between samples has significant impact on the performance of the SDP model. In addition, most samples are usually class imbalanced. To solve these issues, in this paper, a novel distance metric learning based on cost-sensitive learning (CSL) is proposed for reducing the impact of class imbalance of samples, which is then applied to the large margin distribution machine (LDM) to substitute the traditional kernel function. Further, the improvement and optimization of LDM based on CSL are also studied, and the improved LDM is used as the SDP model, called as CS-ILDM. Subsequently, the proposed CS-ILDM is applied to five publicly available data sets from the NASA Metrics Data Program repository and its performance is compared to other existing SDP models. The experimental results confirm that the proposed CS-ILDM not only has good prediction performance, but also can reduce the misprediction cost and avoid the impact of class imbalance of samples.

DUKMSVM: A Framework of Deep Uniform Kernel Mapping Support Vector Machine for Short Text Classification

This paper mainly deals with the problem of short text classification. There are two main contributions. Firstly, we introduce a framework of deep uniform kernel mapping support vector machine (DUKMSVM). The significant merit of this framework is that by expressing the kernel mapping function explicitly with a deep neural network, it is in essence an explicit kernel mapping instead of the traditional kernel function, and it allows better flexibility in dealing with various applications by applying different neural network structures. Secondly, to validate the effectiveness of this framework and to improve the performance of short text classification, we explicitly express the kernel mapping using bidirectional recurrent neural network (BRNN), and propose a deep bidirectional recurrent kernel mapping support vector machine (DRKMSVM) for short text classification. Experimental results on five public short text classification datasets indicate that in terms of classification accuracy, precision, recall rate and F1-score, the DRKMSVM achieves the best performance with the average values of accuracy, precision, recall rate, and F1-score of 87.23%, 86.99%, 86.13% and 86.51% respectively compared to traditional SVM, convolutional neural network (CNN), Naive Bayes (NB), and Deep Neural Mapping Support Vector Machine (DNMSVM) which applies multi-layer perceptron for kernel mapping.

A smoothed particle hydrodynamics-phase field method with radial basis functions and moving least squares for meshfree simulation of dendritic solidification

We present a robust and efficient approach to meshfree phase-field (PF) simulation of dendritic solidification on arbitrary domain geometries using smoothed particle hydrodynamics (SPH). We use radial basis functions (RBFs) and moving least squares (MLS) as alternative approaches for constructing kernel approximation functions exhibiting a higher order of consistency than traditional kernel functions used in SPH. In the proposed smoothed particle hydrodynamics-phase field method (SPH–PFM), proper discretization of the PF order parameter at the diffuse interface region can be easily accomplished independently from the particle spacing resolution used for computing the thermal field distribution. We use an implicit geometry construction approach to automatically generate virtual boundary particles to impose Neumann-type boundary conditions at the domain boundaries. We solve the Allen–Cahn equation locally at particles constructed at a narrow band around the interface region. Additionally, only first-order derivatives of the meshfree approximation functions are needed in our implementation to solve the governing equations. Mathematical formulation and detailed analysis will be presented and discussed where we investigate the effect of the meshfree approximation scheme on the final morphology of the grown dendrite.

Application of a new hybrid particle swarm optimization-mixed kernels function-based support vector machine model for reservoir porosity prediction: A case study in Jacksonburg-Stringtown oil field, West Virginia, USA

Porosity is a fundamental property that characterizes the storage capability of fluid and gas-bearing formations in a reservoir. An accurate porosity value can be measured from core samples in the laboratory; however, core analysis is expensive and time consuming. Well-log data can be used to calculate porosity, but the availability of log suites is often limited in mature fields. Therefore, robust porosity prediction requires integration of core-measured porosity with available well-log suites to control for changes in lithology and fluid content. A support vector machine (SVM) model with mixed kernel function (MKF) is used to construct the relationship between limited conventional well-log suites and sparse core data. Porosity is the desired output, and two conventional well-log responses (gamma ray [GR] and bulk density) and three well-log-derived parameters (the slope of GR, the slope of density, and [Formula: see text]) are input parameters. A global stochastic searching algorithm, particle swarm optimization (PSO), is applied to improve the efficiency of locating the appropriate values of five control parameters in MKF-SVM model. The results of SVM with different traditional kernel functions were compared, and the MKF-SVM model provided an improvement over the traditional SVM model. To confirm the advantage of the hybrid PSO-MKF-SVM model, the results from three models: (1) radial basis function (RBF)-based least-squares SVM, (2) multilayer perceptron artificial neural network (ANN), and (3) RBF ANN, are compared with the result of the hybrid PSO-MKF-SVM model. The results indicate that the hybrid PSO-MKF-SVM model improves porosity prediction with the highest correlation coefficient ([Formula: see text] of 0.9560), the highest coefficient of determination ([Formula: see text] of 0.9140), the lowest root-mean-square error (1.6505), average absolute error value (1.4050), and maximum absolute error (2.717).

Content-based image retrieval model based on cost sensitive learning

How to retrieve the desired images quickly and accurately from the large scale image database has become a hot topic in the field of multimedia research. Many content-based image retrieval (CBIR) technologies already exist, but they are not always satisfactory. In many applications, the CBIR model based on machine learning relies heavily on the distance metric between samples. Although the traditional distance metric methods are simple and convenient, it is not always appropriate for CBIR tasks. In this paper, a novel distance metric learning (DML) method based on cost sensitive learning (CSL) is studied, and then it is used in a large margin distribution learning machine (LDM) to replace the traditional kernel functions. The improved LDM also takes into account CSL, and which is called CS-DLDM. Finally, CS-DLDM model is applied to CBIR tasks for implementation classification. We compare the proposed CS-DLDM model with other classifiers based on CSL. The experimental results show that the proposed CS-DLDM model not only has satisfactory classification performance but also the lowest misclassification cost, can effectively avoid the class imbalance of sample.

Sparse representation for kernel function selection of support vector machine

Support vector machine (SVM) is a kind of learning method based on the kernel, and it is well known that different kernel functions have significant different influences on the performance of SVM. Thus, how to obtain an effective method for the kernel functions election becomes an important issue in the researching field of SVM. Since different kernel functions contain different geometric measurement characteristics, selecting an appropriate kernel function can results in satisfying generalisation ability of SVM. However, the traditional method for the SVM kernel function choice is manually designated, which contains great limitations and blindness, obviously. Based on sparse representation theory, this paper presents a kernel function selection method, which can take the measurement features of different kernel functions into account and make a reasonable choice of the kernel function of SVM according to specific problems. Finally, simulation experiments are given to show that the method in this paper can overcome the shortcomings of the traditional kernel function selection in SVM model, and achieve the optimal performance.

Modeling the resonant frequency of compact microstrip antenna by the PSO‐based SVM with the hybrid kernel function

SummaryA methodology based on the support vector machine (SVM) combined with a hybrid kernel function (HKF) for accurately modeling the resonant frequencies of the compact microstrip antenna (MSA) is presented and dedicated to reduce the number of samples and simplify the structure when predicting the resonant frequency of the compact MSA by artificial neural network. The parameters of the SVMs and weight coefficients of the HKF are optimized by means of particle swarm optimization algorithm. In addition, two different kernel functions (KFs), namely polynomial KF (a kind of global KF) and Cauchy KF (a kind of local KF), are employed to overcome the disadvantages of traditional KF. The proposed method is validated by the UCI database. The evaluation results show that the HKF can improve the learning ability and generalization ability of the SVM. Furthermore, the resonant frequencies of a planar inverted F‐shaped antenna and an L‐shaped MSA are modeled by the proposed method. Predictive results with high accuracy demonstrate that the particle swarm optimization‐based SVM with the HKF can improve the prediction accuracy for a small dataset. Copyright © 2016 John Wiley & Sons, Ltd.