Kernel methods are an extremely popular set of techniques used for many important machine learning and data analysis applications. In addition to having good practical performance, these methods are supported by a well-developed theory. Kernel methods use an implicit mapping of the input data into a high dimensional feature space defined by a kernel function, i.e., a function returning the inne...

We discuss the symmetric smoothed particle hydrodynamics (SSPH) method for generating basis functions for a meshless method. It admits a larger class of kernel functions than some other methods, including the smoothed particle hydrodynamics (SPH), the modified smoothed particle hydrodynamics (MSPH), the reproducing kernel particle method (RKPM), and the moving least squares (MLS) methods. For f...

This paper is concerned with a study of special integral equation. equation arises in many applied problems, including transmutation theory, inverse scattering the solution singular Sturm–Liouville and Shrödinger equations, representation solutions equations. A derived formulated using Riemann function hyperbolic In paper, existence unique to this proven by method successive approximations. The...

The object of this paper is to establish certain generalized fractional integration and differentiation involving generalized Mittag-Leffler function defined by Salim and Faraj [25]. The considered generalized fractional calculus operators contain the Appell's function $F_3$ [2, p.224] as kernel and are introduced by Saigo and Maeda [23]. The Marichev-Saigo-Maeda fractional calculus operators a...

Kernel-based methods like Support Vector Machines (SVM) have been established as powerful techniques in machine learning. The idea of SVM is to perform a mapping φ from the input space to a higher-dimensional feature space using a kernel function k, so that a linear learning algorithm can be employed. However, the burden of choosing the appropriate kernel function is usually left to the user. I...

OBJECTIVE Despite the rise of high-throughput technologies, clinical data such as age, gender and medical history guide clinical management for most diseases and examinations. To improve clinical management, available patient information should be fully exploited. This requires appropriate modeling of relevant parameters. METHODS When kernel methods are used, traditional kernel functions such...

this paper concentrates on a new procedure which experimentally recognises gears and bearings faults of a typical gearbox system using a least square support vector machine (lssvm). two wavelet selection criteria maximum energy to shannon entropy ratio and maximum relative wavelet energy are used and compared to select an appropriate wavelet for feature extraction. the fault diagnosis method co...