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About 10,000 papers for “kernel functions”

Kernel functions.

Gregory R. Romanchek (8351193), Zheng Liu (28397), Shiva Abbaszadeh (5873699) · Figshare · 2020

<p>Examples of the Squared Exponential (a), periodic kernel (b), and locally periodic kernel (c).</p>

Cited by 0Open access

Reproducing Kernel Functions

Ali Akgül, Esra Karatas Akgül · Contact-less Assessment of In-vivo Body Signals Using Microwave Doppler Radar (InTech) · 2018

Cited by 0

Mathematical Background Kernel Functions and Feature Spaces Reproducing Kernel Hilbert Spaces Examples of Kernel Functions

Christian Igel, Christian Igel Kernels, Reproducing Kernel et al. · 2009

• complexity of learning problem depends on representation—e.g., how the data is represented/encoded • idea: make learning easier by changing the representation X: input space H: feature space Φ: X → H (feature map) and do the classification/regression in H • both increasing and reducing the dimensionality can be reasonable • example: data may be separable by a linear function in H Christian Igel: Kernels and Reproducing Kernel Hilbert Spaces 4 / 40Example I polynomial classifiers: suppose the n-dimensional x ∈ X = Rn are best represented by the dth order products (monomials) of the components xj of x, i.e., by the ·xj2 ·...·xjd, where ji,...,jd ∈ {1,...,n} xj1 for example by 2nd order monomials Φ2: R 2 → R 3 Φ2((x1,x2)) = (x 2 1,x 2 2, √ 2x1x2) (here the order of monomials is not considered and a weighting factor is used)

Cited by 0

New Reproducing Kernel Functions

Ali Akgül · Mathematical Problems in Engineering · 2015

Some new reproducing kernel functions on time scales are presented. Reproducing kernel functions have not been found on time scales till now. These functions are very important on time scales and they will be very useful for researchers. We need these functions to solve dynamic equations on time scales with the reproducing kernel method.

Cited by 37Open access

Convolution and kernel functions

Włodzimierz Greblicki, M. Pawlak · 2008

A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.

Cited by 0

Derivation of Aerodynamic Kernel Functions

Earl H. Dowell, C. S. Ventres · AIAA Journal · 1973

The method of Fourier transforms is used to determine the kernel function which relates the pressure on a lifting surface to the prescribed downwash within the framework of Dowell's (1971) shear flow model. This model is intended to improve upon the potential flow aerodynamic model by allowing for the aerodynamic boundary layer effects neglected in the potential flow model. For simplicity, incompressible, steady flow is considered. The proposed method is illustrated by deriving known results from potential flow theory.

Cited by 11

An Introduction to Kernel Functions

John Jenkins · 2013

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73There are a myriad number of data mining tasks that can be performed on sets of vectors with continuous vector components, i.e., whose values are real numbers. For wide vectors corresponding to high-dimensional spaces, it might be useful to filter out individual vector components that do not contribute to the data patterns being studied to make the problem easier to work with and to reduce noise (see Chapter 10 on dimension reduction). Perhaps the vectors are each assigned a discrete property, and we want to predict properties of new, unseen vectors (see Chapter 9 on classification).

Cited by 0

SVM kernel functions for classification

Ashish Patle, Deepak Singh Chouhan · 2013

A new generation learning system based on recent advances in statistical learning theory deliver state-of-the-art performance in real-world applications that is Support Vector Machines [2]. Applications such as text categorization, hand-written character recognition, image classification, bio-sequence analysis [9] etc for the classification and regression Most of the existing supervised classification methods are based on traditional statistics, which can provide ideal results when sample size is tending to infinity. However, only finite samples can be acquired in practice. In this paper, a novel learning method, Support Vector Machine (SVM), is applied on different data. This paper emphasizes the classification task with Support Vector Machine with different kernel function. It has several kernel functions including linear, polynomial and radial basis for performing classification [13].

Cited by 325

Loss reserving with kernel functions

Pérez Tiscareño, Reyna María · DSpace repository (University of Tartu) · 2017

Loss reserving is a fundamental concept of actuarial mathematics. A traditionally used method is the chain ladder method. While it is a simple and robust method and works well in many cases, it also has its limitations. The chain ladder method is applied to aggregated data triangle, in a way similar to constructing histograms. Thus, a natural way to improve the approach is to use kernel density estimation instead. This leads to an extension called the continuous chain ladder (CCL) method. In CCL, the main choices a researcher has to make is the choice of the kernel function and the choice of bandwidth, which introduces a suitable level of smoothing. The first choice is usually made for practical or theoretical reasons and it usually has a minor impact on the performance of the estimator. However, the choice of bandwidth can significantly affect the performance of the kernel estimator. There are several possible methods suggested in the literature to choose the bandwidth. To find the optimal bandwidth, the cross-validation procedure is used. A common method for find the optimal bandwidth is the cross-validation. As it is a very time-consuming procedure, some rules of thumb that allow to skip the cross-validation step, can significantly increase the performance of CCL. In this thesis, the main goal is to find the patterns how different input scenarios affect the optimal bandwidths of the CCL model.

Cited by 0Open access