During the support period July 1, 2011 June 30, 2012, seven research papers were published. They consist of three types: • Research that directly addresses the kernel selection problem in machine learning [1, 2]. • Research that closely relates to the fundamental issues of the proposed research of this grant [3, 4, 5, 6]. • Research that is in the general context of computational mathematics [7...

An orthogonal decomposition method and implementation algorithm for speech signal processing are proposed in this paper. In the reproducing kernel function of Hilbert space ] , [ 1 2 b a W , a set of normalized orthogonal function system n j x 1 * )} ( {φ is generated, and speech signals can be orthogonally decomposed in ] , [ 1 2 b a W according to the basis n j x 1 * )} ( {φ , the orthogonal ...

In this paper, we prove convergence results for multiscale approximation using compactly supported radial basis functions restricted to the unit sphere, for target functions outside the reproducing kernel Hilbert space of the employed kernel.

Important information on the structure of complex systems can be obtained by measuring to what extent the individual components exchange information among each other. The linear Granger approach, to detect cause-effect relationships between time series, has emerged in recent years as a leading statistical technique to accomplish this task. Here we generalize Granger causality to the nonlinear c...

In this paper, we prove convergence results for multiscale approximation using compactly supported radial basis functions restricted to the unit sphere, for target functions outside the reproducing kernel Hilbert space of the employed kernel.

and Applied Analysis 3 2. Several Reproducing Kernel Spaces In this section, several reproducing kernels needed are constructed in order to solve 1.1 and 1.2 using RKHSmethod. Before the construction, we utilize the reproducing kernel concept. Throughout this paper C is the set of complex numbers, L2 a, b {u | ∫b a u2 x dx < ∞}, l2 {A | ∑∞i 1 Ai 2 < ∞}, and the superscript n in u n t denotes th...

In this paper we are concerned with reproducing kernel Hilbert spaces HK of functions from an input space into a Hilbert space Y , an environment appropriate for multi-task learning. The reproducing kernel K associated to HK has its values as operators on Y . Our primary goal here is to derive conditions which ensure that the kernel K is universal. This means that on every compact subset of the...