Krein reproducing kernel modules in Clifford analysis

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...

Method of Reproducing Kernel

Frame Analysis and Approximation in Reproducing Kernel Hilbert Spaces

We consider frames F in a given Hilbert space, and we show that every F may be obtained in a constructive way from a reproducing kernel and an orthonormal basis in an ambient Hilbert space. The construction is operator-theoretic, building on a geometric formula for the analysis operator defined from F . Our focus is on the infinite-dimensional case where a priori estimates play a central role, ...

Fisher’s Linear Discriminant Analysis for Weather Data by reproducing kernel Hilbert spaces framework

Recently with science and technology development, data with functional nature are easy to collect. Hence, statistical analysis of such data is of great importance. Similar to multivariate analysis, linear combinations of random variables have a key role in functional analysis. The role of Theory of Reproducing Kernel Hilbert Spaces is very important in this content. In this paper we study a gen...

Real reproducing kernel Hilbert spaces

P (α) = C(α, F (x, y)) = αF (x, x) + 2αF (x, y) + F (x, y)F (y, y), which is ≥ 0. In the case F (x, x) = 0, the fact that P ≥ 0 implies that F (x, y) = 0. In the case F (x, y) 6= 0, P (α) is a quadratic polynomial and because P ≥ 0 it follows that the discriminant of P is ≤ 0: 4F (x, y) − 4 · F (x, x) · F (x, y)F (y, y) ≤ 0. That is, F (x, y) ≤ F (x, y)F (x, x)F (y, y), and this implies that F ...