In this paper, some meshless methods based on the local Newton basis functions are used to solve some time dependent partial differential equations. For stability reasons, used variably scaled radial kernels for constructing Newton basis functions. In continuation, with considering presented basis functions as trial functions, approximated solution functions in the event of spatial variable wit...

Within kernel–based interpolation and its many applications, it is a well–documented but unsolved problem to handle the scaling or the shape parameter. We consider native spaces whose kernels allow us to change the kernel scale of a d–variate interpolation problem locally, depending on the requirements of the application. The trick is to define a scale function c on the domain Ω ⊂ Rd to transfo...

In kernel–based methods, how to handle the scaling or the choice of the shape parameter is a well– documented but still an open problem. The shape or scale parameter can be tuned by the user according to the applications, and it plays a crucial role both for the accuracy of the method and its stability. In [7], the Variably Scaled Kernels (VSKs) were introduced. The idea is to vary the scale in...

This paper presents a simple estimate to determine the width of Gaussian kernel with the adaptive scaling technique. The Gaussian kernel is widely employed in Radial Basis Function (RBF) network, Support Vector Machine (SVM), Least Squares Support Vector Machine (LS-SVM), Kriging, and so on. It is widely known that the width of the Gaussian kernel in these machine learning techniques plays an i...

As one of the supervised tensor learning methods, support machine (STM) for tensorial data classification is receiving increasing attention in and related applications, including remote sensing imaging, video processing, fault diagnosis, etc. Existing STM approaches lack consideration tensors terms reduction. To address this deficiency, we built a novel sparse model to control number binary dat...