Related papers: A Geometric Approach for Computing the Kernel of a…
Given an m x n rectangular mesh, its adjacency matrix A, having only integer entries, may be interpreted as a map between vector spaces over an arbitrary field K. We describe the kernel of A: it is a direct sum of two natural subspaces…
Ubiquitous geometric objects can be precisely and efficiently represented as polyhedra. The transformation of a polyhedron into a vector, known as polyhedra representation learning, is crucial for manipulating these shapes with mathematical…
This paper presents a novel approach for multi-kernel estimation by enhancing the KernelGAN algorithm, which traditionally estimates a single kernel for the entire image. We introduce Multi-KernelGAN, which extends KernelGAN's capabilities…
It is shown that the heat kernel operator for the Laplace operator on any covariantly constant curved background, i.e. in symmetric spaces, may be presented in form of an averaging over the Lie group of isometries with some nontrivial…
We present a general representation for solving problems in many-body perturbation theory. By projecting the single-particle Green's function to an auxiliary space we show how one can convert an arbitrary Feynman graph to a universal kernel…
Most state-of-the-art graph kernels only take local graph properties into account, i.e., the kernel is computed with regard to properties of the neighborhood of vertices or other small substructures. On the other hand, kernels that do take…
Low-rank approximation of kernels is a fundamental mathematical problem with widespread algorithmic applications. Often the kernel is restricted to an algebraic variety, e.g., in problems involving sparse or low-rank data. We show that…
In this paper, we propose to study a new geometric optimization problem called "geometric prototype" in Euclidean space. Given a set of patterns, where each pattern is represented by a (weighted or unweighted) point set, the geometric…
We introduce a theory of local kernels, which generalize the kernels used in the standard diffusion maps construction of nonparametric modeling. We prove that evaluating a local kernel on a data set gives a discrete representation of the…
Hermann Schwarz, while studying complex analysis, introduced the geometric interpretation for the Poisson kernel in 1890. We shall see here that the geometric interpretation can be useful to develop a new approach to some old classical…
This document reviews the definition of the kernel distance, providing a gentle introduction tailored to a reader with background in theoretical computer science, but limited exposure to technology more common to machine learning,…
We give two new global and algorithmic constructions of the reproducing kernel Hilbert space associated to a positive definite kernel. We further present ageneral positive definite kernel setting using bilinear forms, and we provide new…
We investigate a series of learning kernel problems with polynomial combinations of base kernels, which will help us solve regression and classification problems. We also perform some numerical experiments of polynomial kernels with…
Kernel methods are powerful tools in machine learning. They have to be computationally efficient. In this paper, we present a novel Geometric-based approach to compute efficiently the string subsequence kernel (SSK). Our main idea is that…
In this paper we revisit the kernel density estimation problem: given a kernel $K(x, y)$ and a dataset of $n$ points in high dimensional Euclidean space, prepare a data structure that can quickly output, given a query $q$, a…
Kernel density estimation is a convenient way to estimate the probability density of a distribution given the sample of data points. However, it has certain drawbacks: proper description of the density using narrow kernels needs large data…
Deep kernel learning refers to a Gaussian process that incorporates neural networks to improve the modelling of complex functions. We present a method that makes this approach feasible for problems where the data consists of line integral…
Quantum kernel methods are a promising method in quantum machine learning thanks to the guarantees connected to them. Their accessibility for analytic considerations also opens up the possibility of prescreening datasets based on their…
We introduce the loss kernel, an interpretability method for measuring similarity between data points according to a trained neural network. The kernel is the covariance matrix of per-sample losses computed under a distribution of…
Every polyhedral cone can be described either by its facets or by its extreme rays. Computation of one description from the other is a problem that can be very complex, i.e. one encounter the combinatorial explosion. We present here several…