Derivative reproducing properties for kernel methods in learning theory

Multiresolution Reproducing Kernel Particle Methods in Acoustics

In the analysis of complex phenomena of acoustic systems, the computational model-ing requires special attention for a realistic representation of the physics. As a powerful tool, the nite element method has been widely used in the study of complex systems. In order to capture the important physical phenomena, p-nite elements and/or hp-nite elements are employed. The reproducing kernel particle...

Online learning in Reproducing Kernel Hilbert Spaces

Bayesian Learning in Reproducing Kernel Hilbert Spaces

Support Vector Machines nd the hypothesis that corresponds to the centre of the largest hypersphere that can be placed inside version space, i.e. the space of all consistent hypotheses given a training set. The boundaries of version space touched by this hypersphere de ne the support vectors. An even more promising approach is to construct the hypothesis using the whole of version space. This i...

Kernel Methods for Unsupervised Learning Kernel Methods for Unsupervised Learning Title: Kernel Methods for Unsupervised Learning

Kernel Methods are algorithms that projects input data by a nonlinear mapping in a new space (Feature Space). In this thesis we have investigated Kernel Methods for Unsupervised learning, namely Kernel Methods that do not require targeted data. Two classical unsupervised learning problems using Kernel Methods have been tackled. The former is the Data Dimensionality Estimation, the latter is the...

Some Properties of Reproducing Kernel Banach and Hilbert Spaces

This paper is devoted to the study of reproducing kernel Hilbert spaces. We focus on multipliers of reproducing kernel Banach and Hilbert spaces. In particular, we try to extend this concept and prove some related theorems. Moreover, we focus on reproducing kernels in vector-valued reproducing kernel Hilbert spaces. In particular, we extend reproducing kernels to relative reproducing kernels an...