Performance of the linear models, widely used within the framework of adaptive line enhancement (ALE), deteriorates dramatically in the presence of non-Gaussian noises. On the other hand, adaptive implementation of nonlinear models, e.g. the Volterra filters, suffers from the severe problems of large number of parameters and slow convergence. Nonetheless, kernel methods are emerging solutions t...

The use of different kernel functions in SVM (Support Vector machines) has been reported in the literature. In this paper, the use of the q-Gaussian function as kernel function in SVM is investigated and q-Gaussian function is explored. While the q-Gaussian kernel SVM classifiers being built, cross validation methods are used to select the non-extensive entropic index q under varying feature si...

The equivalent kernel [1] is a way of understanding how Gaussian process regression works for large sample sizes based on a continuum limit. In this paper we show how to approximate the equivalent kernel of the widely-used squared exponential (or Gaussian) kernel and related kernels. This is easiest for uniform input densities, but we also discuss the generalization to the non-uniform case. We ...

Nowadays, Radar systems have many applications and radar imaging is one of the most important of these applications. Inverse Synthetic Aperture Radar (ISAR) is used to form an image from moving targets. Conventional methods use Fourier transform to retrieve Doppler information. However, because of maneuvering of the target, the Doppler spectrum becomes time-varying and the image is blurred. Joi...

This paper presents a simple estimate to determine the width of Gaussian kernel with the adaptive scaling technique. The Gaussian kernel is widely employed in Radial Basis Function (RBF) network, Support Vector Machine (SVM), Least Squares Support Vector Machine (LS-SVM), Kriging, and so on. It is widely known that the width of the Gaussian kernel in these machine learning techniques plays an i...

Gaussian kernel is a very popular kernel function used in many machine learning algorithms, especially in support vector machines (SVM). For nonlinear training instances in machine learning, it often outperforms polynomial kernels in model accuracy. The Gaussian kernel is heavily used in formulating nonlinear classical SVM. A very elegant quantum version of least square support vector machine w...

In this work, we evaluate the conditionally positive definite logarithmic kernel in kernel-based estimation of reflectance spectra. Reflectance spectra are estimated from responses of a 12-channel multispectral imaging system. We demonstrate the performance of the logarithmic kernel in comparison with the linear and Gaussian kernel using simulated and measured camera responses for the Pantone a...

Kernel Fisher discriminant analysis (KFDA) has been proposed for nonlinear binary classification. It is a hybrid method of the classical Fisher linear discriminant analysis and a kernel machine. Experimental results have shown that the KFDA performs slightly better in terms of prediction error than the popular support vector machines and is a strong competitor to the latter. However, there is v...