Related papers: Appropriate kernels for Divisive Normalization exp…

Divisive Normalization and the Wilson-Cowan equations are influential models of neural interaction and saturation [Carandini and Heeger Nat.Rev.Neurosci. 2012; Wilson and Cowan Kybernetik 1973]. However, they have not been analytically…

A fundamental step in many data-analysis techniques is the construction of an affinity matrix describing similarities between data points. When the data points reside in Euclidean space, a widespread approach is to from an affinity matrix…

Image acquisition and segmentation are likely to introduce noise. Further image processing such as image registration and parameterization can introduce additional noise. It is thus imperative to reduce noise measurements and boost signal.…

Kernel adaptive filters, a class of adaptive nonlinear time-series models, are known by their ability to learn expressive autoregressive patterns from sequential data. However, for trivial monotonic signals, they struggle to perform…

Fisher's linear discriminant analysis is a classical method for classification, yet it is limited to capturing linear features only. Kernel discriminant analysis as an extension is known to successfully alleviate the limitation through a…

Seismic noise cross correlations are used to image crustal structure and heterogeneity. Typically, seismic networks are only anisotropically illuminated by seismic noise, a consequence of the non-uniform distribution of sources. Here, we…

Complex-valued signals are used in the modeling of many systems in engineering and science, hence being of fundamental interest. Often, random complex-valued signals are considered to be proper. A proper complex random variable or process…

We present a Gaussian kernel loss function and training algorithm for convolutional neural networks that can be directly applied to both distance metric learning and image classification problems. Our method treats all training features…

A successful class of image denoising methods is based on Bayesian approaches working in wavelet representations. However, analytical estimates can be obtained only for particular combinations of analytical models of signal and noise, thus…

A very important property of a statistical distribution is to know whether it obeys Gaussian statistics or not. On the one hand, it is of paramount importance in the context of CMB anisotropy studies, since deviations from a Gaussian…

In this work we study the communication efficiency of a psychophysically-tuned cascade of Wilson-Cowan and Divisive Normalization layers that simulate the retina-V1 pathway. This is the first analysis of Wilson-Cowan networks in terms of…

Gaussian Process regression is a kernel method successfully adopted in many real-life applications. Recently, there is a growing interest on extending this method to non-Euclidean input spaces, like the one considered in this paper,…

The Gaussian kernel plays a central role in machine learning, uncertainty quantification and scattered data approximation, but has received relatively little attention from a numerical analysis standpoint. The basic problem of finding an…

We consider learning on graphs, guided by kernels that encode similarity between vertices. Our focus is on random walk kernels, the analogues of squared exponential kernels in Euclidean spaces. We show that on large, locally treelike,…

The present paper proposes generalized Gaussian kernel adaptive filtering, where the kernel parameters are adaptive and data-driven. The Gaussian kernel is parametrized by a center vector and a symmetric positive definite (SPD) precision…

We derive symmetric and antisymmetric kernels by symmetrizing and antisymmetrizing conventional kernels and analyze their properties. In particular, we compute the feature space dimensions of the resulting polynomial kernels, prove that the…

Supervised learning has recently garnered significant attention in the field of computational physics due to its ability to effectively extract complex patterns for tasks like solving partial differential equations, or predicting material…

It is a common assumption that the activation of different layers in neural networks follow Gaussian distribution. This distribution can be transformed using normalization techniques, such as batch-normalization, increasing convergence…

The normal distribution plays a central role in information theory - it is at the same time the best-case signal and worst-case noise distribution, has the greatest representational capacity of any distribution, and offers an equivalence…

This paper presents an analysis of properties of two hybrid discretization methods for Gaussian derivatives, based on convolutions with either the normalized sampled Gaussian kernel or the integrated Gaussian kernel followed by central…