We construct genRBF kernel, which generalizes the classical Gaussian RBF kernel to the case of incomplete data. We model the uncertainty contained in missing attributes making use of data distribution and associate every point with a conditional probability density function. This allows to embed incomplete data into the function space and to define a kernel between two missing data points based...

In the study of smoothing spline estimators, some convolution-kernellike properties of the Green’s function for an appropriate boundary value problem, depending on the design density, are needed. For the uniform density, the Green’s function can be computed more or less explicitly. Then, integral equation methods are brought to bear to establish the kernel-like properties of said Green’s functi...

Microarray technique measures gene expression levels under various conditions, simultaneously. Microarray data are successfully analyzed by kernel methods for a variety of applications. A major drawback of microarray is technically error prone. To gain accurate analysis, we propose a method which produces a noise-tolerant kernel matrix. First of all, we devise a new distance function for microa...

Abstract This study employed soft computing techniques, namely, support vector machine (SVM) and Gaussian process regression (GPR) to predict the properties of a scour hole [depth (ds) length (Ls)] in diversion channel flow system. The considered different geometries channels (angles bed widths) hydraulic conditions. Four kernel function models for each technique (polynomial function, normalize...

In most kernel based machine learning algorithms and non-parametric statistics the key computational task is to compute a linear combination of local kernel functions centered on the training data, i.e., f(x) = ∑N i=1 qik(x, xi), which is the discrete Gauss transform for the Gaussian kernel. f is the regression/classification function in case of regularized least squares, Gaussian process regre...

We study the problem of finding an optimal kernel from a prescribed convex set of kernels K for learning a real-valued function by regularization. We establish for a wide variety of regularization functionals that this leads to a convex optimization problem and, for square loss regularization, we characterize the solution of this problem. We show that, although K may be an uncountable set, the ...

Recently, Y.Q. Bai, M. El Ghami and C. Roos [3] introduced a new class of so-called eligible kernel functions which are defined by some simple conditions. The authors designed primal-dual interiorpoint methods for linear optimization (LO) based on eligible kernel functions and simplified the analysis of these methods considerably. In this paper we consider the semidefinite optimization (SDO) pr...

Let X be a random variable taking values in a function space F, and let Y be a discrete random label with values 0 and 1. We investigate asymptotic properties of the moving window classification rule based on independent copies of the pair (X,Y ). Contrary to the finite dimensional case, it is shown that the moving window classifier is not universally consistent in the sense that its probabilit...

We propose one type of TOP (Tangent vector Of the Posterior log-odds) kernel and apply it to text categorization. In a number of categorization tasks including text categorization, negative examples are usually more common than positive examples and there may be several different types of negative examples. Therefore, we construct a TOP kernel, regarding the probabilistic model of negative exam...