Abstract In this paper, we will present a new method for a Volterra integral equation with weakly singular kernel in the reproducing kernel space. Firstly the equation is transformed into a new equivalent equation. Its exact solution is represented in the form of series in the reproducing kernel space. In the mean time, the n-term approximation un(t) to the exact solution u(t) is obtained. Some...

We consider the reproducing kernel Hilbert space Hμ induced by a kernel which is obtained using the Fourier-Stieltjes transform of a regular, positive, finite Borel measure μ on a locally compact abelian topological group Γ. Denote by G the dual of Γ. We determine Hμ as a certain subspace of the space C0(G) of all continuous function on G vanishing at infinity. Our main application is calculati...

The partition of unity is an essential ingredient for meshless methods named by GFEM, PUFEM (partition of unity FEM), XFEM(extended FEM), RKPM(reproducing kernel particle method), RPPM(reproducing polynomial particle method), the method of clouds in the literature. There are two popular choices for partition of unity: a piecewise linear FEM mesh and the Shepard-type partition of unity. However,...

We focus on three methods for finding a suitable subspace for regression in a reproducing kernel Hilbert space: kernel principal component analysis, kernel partial least squares and kernel canonical correlation analysis and we demonstrate how this fits within a more general context of subspace regression. For the kernel partial least squares case a least squares support vector machine style der...

This TR contains two brief reviews which will appear in the Proceedings of the 13th IFAC Symposium on System Identification (SYSID 2003), Rotterdam, August 2003. They are the basis for two talks in the invited session WeP02-Reproducing Kernels 1, and were prepared within the space limitations of the Proceedings. They are primarily based on work of the author and collaborators. There are many re...

Kernels between ensembles (or a collection of entities) have recently attracted growing interests in the literature on machine learning . In this paper, we focus on the ‘ensemble’ that is defined as a collection of vectors. One natural way to interpret such an ensemble is through the notion of matrix. We present two basic reproducing kernels between matrices: namely trace and determinant kernel...

Monitoring and controlling air quality parameters form an important subject of atmospheric and environmental research today due to the health impacts caused by the different pollutants present in the urban areas. The support vector machine (SVM), as a supervised learning analysis method, is considered an effective statistical tool for the prediction and analysis of air quality. The work present...

In this paper the accuracy of two machine learning algorithms including SVM and Bayesian Network are investigated as two important algorithms in diagnosis of Parkinson’s disease. We use Parkinson's disease data in the University of California, Irvine (UCI). In order to optimize the SVM algorithm, different kernel functions and C parameters have been used and our results show that SVM with C par...