In the context of difference image analysis (DIA), we present a new method for determining the convolution kernel matching a pair of images of the same field. Unlike the standard DIA technique which involves modelling the kernel as a linear combination of basis functions, we consider the kernel as a discrete pixel array and solve for the kernel pixel values directly using linear least-squares. ...

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...

The extended Airy kernel describes the space-time correlation functions for the Airy process, which is the limiting process for a polynuclear growth model. The Airy functions themselves are given by integrals in which the exponents have a cubic singularity, arising from the coalescence of two saddle points in an asymptotic analysis. Pearcey functions are given by integrals in which the exponent...

We provide novel methods for efficient dimensionality reduction in kernel spaces. That is, we provide efficient and explicit randomized maps from “data spaces” into “kernel spaces” of low dimension, which approximately preserve the original kernel values. The constructions are based on observing that such maps can be obtained from Locality-Sensitive Hash (LSH) functions, a primitive developed f...

Kernel models for classification and regression have emerged as widely applied tools in statistics and machine learning. We discuss a Bayesian framework and theory for kernel methods, providing a new rationalization of kernel regression based on nonparametric Bayesian models. Functional analytic results ensure that such a nonparametric prior specification induces a class of functions that span ...

In this paper, we prove convergence results for multiscale approximation using compactly supported radial basis functions restricted to the unit sphere, for target functions outside the reproducing kernel Hilbert space of the employed kernel.

In this paper, we prove convergence results for multiscale approximation using compactly supported radial basis functions restricted to the unit sphere, for target functions outside the reproducing kernel Hilbert space of the employed kernel.

1 SUMMARY Kernel models for classification and regression have emerged as widely applied tools in statistics and machine learning. We discuss a Bayesian framework and theory for kernel methods, providing a new rationalisation of kernel regression based on non-parametric Bayesian models. Functional analytic results ensure that such a non-parametric prior specification induces a class of function...

An overview of fuzzy c-means clustering algorithms is given where we focus on different objective functions: they use regularized dissimilarity, entropy-based function, and function for possibilistic clustering. Classification functions for the objective functions and their properties are studied. Fuzzy c-means algorithms using kernel functions is also discussed with kernelized cluster validity...

Modern monolithic OSes leverage the loadable kernel module paradigm to add functionality to the kernel and allow a system to communicate with an increasing number of I/O devices. This paradigm is convenient as OS designers can outsource extra functionality to third parties and keep the original kernel from growing too large. On the other hand, this paradigm represents an avenue for exploitation...