Owing to the constraints of time and space complexity, network intrusion detection systems (NIDSs) based on support vector machines (SVMs) face the “curse of dimensionality” in a large-scale, high-dimensional feature space. This study pro...
The direct strong-form collocation method with reproducing kernel approximation is introduced to efficiently and effectively solve the natural convection problem within a parallelogrammic enclosure. As the convection behavior in the fluid-saturated p...
We study the multivariate
This paper is concerned with the more general nonlinear stochastic Volterra integral equations with doubly singular kernels, whose singular points include both
Solomonoff induction mixes all computable explanations with description-length weights, but it is incomputable. This theory-and-position paper argues that practical approximation must be category-native: one should first declare the mathematical cate...
Bayesian statistical inference under unknown or hard to asses likelihood functions is a very challenging task. Currently, approximate Bayesian computation (ABC) techniques have emerged as a widely used set of likelihood-free methods. A vast number of...
The regularization parameter plays an important role in regularization-based electrical tomography (ET) algorithms, but the existing methods generally cannot determine the parameter. Moreover, these methods are not real-time since a thorough search m...
In this study, we develop a class of multivariate HHC-type operators generated by adjustable half-hyperbolic tangent activation functions and a symmetrized kernel structure. The analysis is carried out within the classical framework of positive linea...
We address the challenging application of 3D pore scale reactive flow under varying geometry parameters. The task is to predict time-dependent integral quantities, i.e., breakthrough curves, from the given geometries. As the 3D reactive flow simulati...
A meshless, quasi-convex reproducing kernel particle framework for three-dimensional steady-state thermomechanical coupling problems is presented in this paper. A meshfree, second-order, quasi-convex reproducing kernel scheme is employed to approxima...
We apply the reproducing kernel method and group preserving scheme for investigating the Lane–Emden equation. The reproducing kernel method is implemented by the useful reproducing kernel functions and the numerical approximations are given. These ap...
This paper develops a Banach space-valued approximation framework based on symmetrized neural network (SNN) operators generated by a deformation-dependent sigmoidal activation function. Symmetry is introduced directly at the activation level through...
In this article, a novel hybrid method of multilevel kernel degeneration and adaptive cross approximation (MLKD-ACA) algorithm with integral kernel truncations is proposed to accelerate solving integral equations using method of moments (MoM), and to...
We study a Durrmeyer–Beta-type positive linear operator on the half-line, constructed from rising-factorial weights and a normalized beta-prime kernel. Exact raw moments through degree four and the corresponding central moments are derived unde...
The weighted reproducing kernel collocation method exhibits high accuracy and efficiency in solving inverse problems as compared with traditional mesh-based methods. Nevertheless, it is known that computing higher order reproducing kernel (RK) shape...
It is desirable to combine the expressive power of deep learning with Gaussian Process (GP) in one expressive Bayesian learning model. Deep kernel learning showed success as a deep network used for feature extraction. Then, a GP was used as the funct...
The weighted gradient reproducing kernel collocation method is introduced to recover the heat source described by Poisson’s equation. As it is commonly known that there is no unique solution to the inverse heat source problem, the weak solution...
In this paper, we demonstrate the feasibility and efficiency of approximate computing techniques (ACTs) in the embedded Support Vector Machine (SVM) tensorial kernel circuit implementation in tactile sensing systems. Improving the performance of the...
This paper introduces a convolution model with non-singular rational kernels in which coefficients are considered complex. An interlacing property of the poles and zeros in these rational kernels permits the accurate approximation of the power law fu...
The geographic object-based image analysis (GEOBIA) framework has gained increasing interest for the last decade. One of its key advantages is the hierarchical representation of an image, where object topological features can be extracted and modeled...
A reproducing kernel Hilbert space (RKHS) approximation problem arising from learning theory is investigated. Some K-functionals and moduli of smoothness with respect to RKHSs are defined with Fourier–Bessel series and Fourier–Bessel tran...
Here we extended our earlier fractional monotone approximation theory to abstract fractional monotone approximation, with applications to Prabhakar fractional calculus and non-singular kernel fractional calculi. We cover both the left and right sides...
This paper considers two important problems for autonomous robot navigation in a dynamic environment, where the goal is to predict pedestrian motion and control a robot with the prediction for safe navigation. While there are several methods for pred...
Deep Gaussian Processes (DGPs) were proposed as an expressive Bayesian model capable of a mathematically grounded estimation of uncertainty. The expressivity of DPGs results from not only the compositional character but the distribution propagation w...
Many real-life processes are black-box problems, i.e., the internal workings are inaccessible or a closed-form mathematical expression of the likelihood function cannot be defined. For continuous random variables, likelihood-free inference problems c...
This paper integrates
In this paper, we introduce an integral transform with a kernel defined on the Wiener space. We first establish the existence of the integral transform and present several illustrative examples. As the main result, we derive an approximation theorem...
Electrical Tomography (ET) technology is widely used in multiphase flow detection due to its advantages of low cost, visualization, fast response, non-radiation, and non-invasiveness. However, ill-posed solutions lead to low image reconstruction reso...
We propose an incremental spectral clustering method for stream data clustering and apply it to stream image segmentation. The main idea in our work consists of generating the data points in the kernel space by Fastfood features and iteratively calcu...
Good data feature representation and high precision classifiers are the key steps for pattern recognition. However, when the data distributions between testing samples and training samples do not match, the traditional feature extraction methods and...
Modeling of impurity diffusion processes in a multiphase randomly inhomogeneous body is performed using the Feynman diagram technique. The impurity diffusion equations are formulated for each of the phases separately. Their random boundaries are subj...
Rolling bearings are key components of rotary machines. To ensure early effective fault diagnosis for bearings, a new rolling bearing fault diagnosis method based on variational mode decomposition (VMD) and an improved kernel extreme learning machine...
An approach to approximate the 2D Gaussian filter for all possible kernel sizes based on the binary optimization technique is introduced. The approximate filter coefficients are designed as negative powers of two, allowing hardware implementation wit...
Many dimensionality and model reduction techniques rely on estimating dominant eigenfunctions of associated dynamical operators from data. Important examples include the Koopman operator and its generator, but also the Schrödinger operator. We p...
This paper studies symmetrized neural network (SNN) operators generated by an adjustable half-hyperbolic tangent activation function. The construction is based on the paired density kernels
In this paper, a fast and accurate numerical Clenshaw-Curtis quadrature is proposed for the approximation of highly oscillatory integrals with Cauchy and logarithmic singularities,
In this paper, we consider a collocation method for solving a nonlinear Volterra integral equation involving the solution-dependent singular kernel
One of the main tasks in kernel methods is the selection of adequate mappings into higher dimension in order to improve class classification. However, this tends to be time consuming, and it may not finish with the best separation between classes. Th...
Representative points (rep-points) are a set of points that are optimally chosen for representing a big original data set or a target distribution in terms of a statistical criterion, such as mean square error and discrepancy. Most of the existing cr...
Gradient Learning (GL), aiming to estimate the gradient of target function, has attracted much attention in variable selection problems due to its mild structure requirements and wide applicability. Despite rapid progress, the majority of the existin...
During the period of rapid urbanization, the urban fringe area is the area where urban expansion occurs first, and land use change is the most active. Studying its evolution laws and characteristics is of great significance to urban planning and urba...
According to the principles of multiphysical, multiscale simulation of phenomena and processes which take place during the electric current treatment of liquid metals, the need to create an adjustable and concise geometrical platform for the big data...
In this paper, a reliability assessment and prediction method based on bearing vibration signals is proposed, which combines Adaptive Cyclostationary Blind Deconvolution (ACYCBD) and AdaBoost-Mixed Kernel Relevance Vector Machine. Firstly, CYCBD para...
The Euler difference approach has become a prevalent tool in the research of integral order differential equations. Nevertheless, a review of the literature reveals a dearth of studies examining fractional order models using the exponential Euler dif...
This paper introduces the fractional Fourier series on the fractional torus and proceeds to investigate several fundamental aspects. Our study includes topics such as fractional convolution, fractional approximation, fractional Fourier inversion, and...
Simple formulae for Lebesgue constants arising in the classical Fourier series approximation are obtained. Both even and odd cases are addressed, extending Fejér’s results. Asymptotic formulae are also obtained.
In this paper, we propose an efficient Nyström method with theoretical and empirical guarantees. In parallel computing environments and for sparse input kernel matrices, our algorithm can have computation efficiency comparable to the conventiona...
Deep-learning convolutional neural networks (CNNs) have proven to be successful in various cognitive applications with a multilayer structure. The high computational energy and time requirements hinder the practical application of CNNs; hence, the re...
This paper introduces a new class of King-type wavelet-assisted Kantorovich q-Baskakov operators, built to address the observation that classical operators of this type typically fail to reproduce the quadratic test function exactly. Moment formulas...
This paper develops asymptotic theory for kernel estimation of density-weighted conditional functionals and regression derivatives when responses are missing at random (MAR) and the observations form a strictly stationary ergodic process. Sequential...
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