There has been an increasing interest in kernel-based techniques, such as support vector techniques, regularization networks, and gaussian processes. There are inner relationships among those techniques, with the kernel function playing a central role. This article discusses a new class of kernel functions derived from the so-called frames in a function Hilbert space.

We introduce a general method to prove uniform in bandwidth consistency of kernel-type function estimators. Examples include the kernel density estimator, the Nadaraya–Watson regression estimator and the conditional empirical process. Our results may be useful to establish uniform consistency of data-driven bandwidth kernel-type function estimators.

We describe how to use Schoenberg’s theorem for a radial kernel combined with existing bounds on the approximation error functions for Gaussian kernels to obtain a bound on the approximation error function for the radial kernel. The result is applied to the exponential kernel and Student’s kernel. To establish these results we develop a general theory regarding mixtures of kernels. We analyze t...

Empirical success of kernel-based learning algorithms is very much dependent on the kernel function used. Instead of using a single fixed kernel function, multiple kernel learning (MKL) algorithms learn a combination of different kernel functions in order to obtain a similarity measure that better matches the underlying problem. We study multitask learning (MTL) problems and formulate a novel M...

In this paper we define a kernel function which is the primal space equivalent of infinitely large sparse threshold unit networks. We first explain how to couple a kernel function to an infinite recurrent neural network, and next we use this definition to apply the theory to sparse threshold unit networks. We validate this kernel function with a theoretical analysis and an illustrative signal p...

Recently, so-called self-regular barrier functions for primal-dual interior-point methods (IPMs) for linear optimization were introduced. Each such barrier function is determined by its (univariate) self-regular kernel function. We introduce a new class of kernel functions. The class is defined by some simple conditions on the kernel function and its derivatives. These properties enable us to d...

Kernel rootkits are a special category of malware that are deployed directly in the kernel and hence have unmitigated reign over the functionalities of the kernel itself. We seek to detect such rootkits that are deployed in the real world by first observing how the majority of kernel rootkits operate. To this end, comparable to how rootkits function in the real world, we write our own kernel ro...

This paper points out that many search relevance models in information retrieval, such as the Vector Space Model, BM25 and Language Models for Information Retrieval, can be viewed as a similarity function between pairs of objects of different types, referred to as an S-function. An S-function is specifically defined as the dot product between the images of two objects in a Hilbert space mapped ...

Abstract The Laplace transform method is applied in this article to study the semi-Hyers-Ulam-Rassias stability of a Volterra integro-differential equation order n, with convolution-type kernel. This kind extends original Hyers-Ulam whose originated 1940. A general integral formulated first, and then some particular cases (polynomial function exponential function) for from kernel are considered.

The prediction of lithology is necessary in all areas of petroleum engineering. This means that to design a project in any branch of petroleum engineering, the lithology must be well known. Support vector machines (SVM’s) use an analytical approach to classification based on statistical learning theory, the principles of structural risk minimization, and empirical risk minimization. In this res...