The choice of kernel is essential in kernel-based leaning methods. One way to choose a suitable kernel is cross-validation, but there is an alternative solution, that is, learning the kernel from data. In this project, two papers about learning the kernel matrix and kernel function from data are surveyed and compared. The method of learning the kernel matrix is implemented, and empirical result...

Based on a new parametric kernel function, this paper presents a primaldual large-update interior-point algorithm (IPM) for semi-definite optimization (SDO) problems. The new parametric function is neither self-regular function nor the usual logarithmic barrier function. It is strongly convex and possesses some novel analytic properties. We analyse this new parametric kernel function and show t...

In this paper, we introduce a new kernel function called polynomial radial basis function (PRBF) that could improve the classification accuracy of support vector machines (SVMs). The proposed kernel function combines both Gauss (RBF) and Polynomial (POLY) kernels and is stated in general form. It is shown that the proposed kernel converges faster than the Gauss and Polynomial kernels. The accur...

ll rights reserved. Recently the Chebyshev kernel has been proposed for SVM and it has been proven that it is a valid kernel for scalar valued inputs in [11]. However in pattern recognition, many applications require multidimensional vector inputs. Therefore there is a need to extend the previous work onto vector inputs. In [11], although it is not stated explicitly, the authors recommend evalu...

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...