In kernel-based learning algorithms the kernel function determines the scalar product and thereby the metric in the feature space in which the learning algorithm operates. The kernel is usually not adapted by the kernel method itself. Choosing the right kernel function is crucial for the training accuracy and generalization capabilities of the learning machine. It may also influence the runtime...

This paper presents approximate confidence intervals for each function of parameters in a Banach space based on a bootstrap algorithm. We apply kernel density approach to estimate the persistence landscape. In addition, we evaluate the quality distribution function estimator of random variables using integrated mean square error (IMSE). The results of simulation studies show a significant impro...

Support vector machines and other kernel methods have successfully been applied to various tasks in attribute-value learning. A kernel function is any function in input space that corresponds to an inner product in some feature space. In this discussion paper, we propose a kernel function on strongly typed first-order terms, and we show how this kernel corresponds to the linear inner product in...

Kernel methods implicitly map data points from the input space to some feature space where even relatively simple algorithms such as linear methods can deliver very impressive performance. Of crucial importance though is the choice of the kernel function, which determines the mapping between the input space and the feature space. The past few years have seen many efforts in learning either the ...

We aimed to derive a kernel function that accounts for the interaction among moving particles within the framework of particle method. To predict a computationally more accurate moving particle solution for the Navier-Stokes equations, kernel function is a key to success in the development of interaction model. Since the smoothed quantity of a scalar or a vector at a spatial location is mathema...

We develop a multi-kernel based regression method for graph signal processing where the target signal is assumed to be smooth over a graph. In multi-kernel regression, an effective kernel function is expressed as a linear combination of many basis kernel functions. We estimate the linear weights to learn the effective kernel function by appropriate regularization based on graph smoothness. We s...

Choosing an appropriate kernel is very important and critical when classifying a new problem with Support Vector Machine. So far, more attention has been paid on constructing new kernels and choosing suitable parameter values for a specific kernel function, but less on kernel selection. Furthermore, most of current kernel selection methods focus on seeking a best kernel with the highest classif...

This paper presents AutoDJ: a system for automatically generating music playlists based on one or more seed songs selected by a user. AutoDJ uses Gaussian Process Regression to learn a user preference function over songs. This function takes music metadata as inputs. This paper further introduces Kernel Meta-Training, which is a method of learning a Gaussian Process kernel from a distribution o...

the object of this paper is to establish certain generalized fractional integration and differentiation involving generalized mittag-leffler function defined by salim and faraj [25]. the considered generalized fractional calculus operators contain the appell's function $f_3$ [2, p.224] as kernel and are introduced by saigo and maeda [23]. the marichev-saigo-maeda fractional calculus operat...

Kernel methods are a powerful set of techniques for learning from data. One of the attractive properties of these techniques is that they rely only on a kernel function which provides the user-defined notion of similarity between two observations, to train the models. This report describes a strategy for evaluating kernel-based predictive models within a cross-validation framework when we also ...