Reproducing kernel mesh-free collocation analysis of structural vibrations

Kernel Fisher’s Discriminant Analysis in Gaussian Reproducing Kernel Hilbert Space1

Kernel Fisher’s linear discriminant analysis (KFLDA) has been proposed for nonlinear binary classification (Mika, Rätsch, Weston, Schölkopf and Müller, 1999, Baudat and Anouar, 2000). It is a hybrid method of the classical Fisher’s linear discriminant analysis and a kernel machine. Experimental results (e.g., Schölkopf and Smola, 2002) have shown that the KFLDA performs slightly better in terms...

Analysis of Structural Vibrations due to Passage of Underground Trains

During the last decades, the railway traffic in densely populated areas has increased. At the same time, passenger trains have become faster and freight trains have become heavier. Consequently, trains are an increasing source of ground vibration, which may be a nuisance to people, buildings and sensitive equipment. In this research, a two-dimensional dynamic system, including underground train...

Method of Reproducing Kernel

Model-free Variable Selection in Reproducing Kernel Hilbert Space

Variable selection is popular in high-dimensional data analysis to identify the truly informative variables. Many variable selection methods have been developed under various model assumptions. Whereas success has been widely reported in literature, their performances largely depend on validity of the assumed models, such as the linear or additive models. This article introduces a model-free va...

A Meshless Collocation Method Based on the Differential Reproducing Kernel Approximation

A differential reproducing kernel (DRK) approximation-based collocation method is developed for solving ordinary and partial differential equations governing the oneand two-dimensional problems of elastic bodies, respectively. In the conventional reproducing kernel (RK) approximation, the shape functions for the derivatives of RK approximants are determined by directly differentiating the RK ap...