Related papers: A Geometric Approach for Computing the Kernel of a…
Kernel methods are an incredibly popular technique for extending linear models to non-linear problems via a mapping to an implicit, high-dimensional feature space. While kernel methods are computationally cheaper than an explicit feature…
Polygon representation learning is essential for diverse applications, encompassing tasks such as shape coding, building pattern classification, and geographic question answering. While recent years have seen considerable advancements in…
This paper introduces an approach for detecting differences in the first-order structures of spatial point patterns. The proposed approach leverages the kernel mean embedding in a novel way by introducing its approximate version tailored to…
Understanding the spectral properties of kernels offers a principled perspective on generalization and representation quality. While deep models achieve state-of-the-art accuracy in molecular property prediction, kernel methods remain…
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…
The purpose of this article is to study operators whose kernel share some key features of Bergman kernels from complex analysis, and are approximate projectors. It turns out that they must be associated with a rich set of geometric data, on…
In this paper, we develop a quadrature framework for large-scale kernel machines via a numerical integration representation. Considering that the integration domain and measure of typical kernels, e.g., Gaussian kernels, arc-cosine kernels,…
Convolution is an important tool in the construction of positive definite kernels on a manifold. This contribution provides conditions on an $L^2$-positive definite and zonal kernel on the unit sphere of $\mathbb{C}^q$ in order that the…
We study the complexity of computing the mixed-integer hull $\operatorname{conv}(P\cap\mathbb{Z}^n\times\mathbb{R}^d)$ of a polyhedron $P$. Given an inequality description, with one integer variable, the mixed-integer hull can have…
Projective geometry provides the preferred framework for most implementations of Euclidean space in graphics applications. Translations and rotations are both linear transformations in projective geometry, which helps when it comes to…
In this work, we designed algorithms for the point in polygon problem based on the ray casting algorithm using equations from vector geometry. The algorithms were implemented using the python programming language. We tested the algorithm…
The geometric picture of the star-product based on its Fourier representation kernel is utilized in the evaluation of chains of star-products and the intuitive appreciation of their associativity and symmetries. Such constructions appear…
Spectrahedra are linear sections of the cone of positive semidefinite matrices that, as convex bodies, generalize the class of polyhedra. In this paper we investigate the problem of recognizing when a spectrahedron is polyhedral. We reprove…
We propose a new analytical approximation to the $\chi^2$ kernel that converges geometrically. The analytical approximation is derived with elementary methods and adapts to the input distribution for optimal convergence rate. Experiments…
We consider the problem of enumerating integer tetrahedra of fixed perimeter (sum of side-lengths) and/or diameter (maximum side-length), up to congruence. As we will see, this problem is considerably more difficult than the corresponding…
We consider the eigenvalue problem of certain kind of non-compact linear operators given as the sum of a multiplication and a kernel operator. A degenerate kernel method is used to approximate isolated eigenvalues. It is shown that entries…
A semilinear parabolic problem of second order with an unknown time-convolution kernel is considered. The missing kernel is recovered from an additional integral measurement. The existence, uniqueness and regularity of a weak solution is…
Geometric rounding of a mesh is the task of approximating its vertex coordinates by floating point numbers while preserving mesh structure. Geometric rounding allows algorithms of computational geometry to interface with numerical…
In this paper, we consider enumeration of geodesics on a polyhedron, where a geodesic means locally-shortest path between two points. Particularly, we consider the following preprocessing problem: given a point $s$ on a polyhedral surface…
The kernel matrix used in kernel methods encodes all the information required for solving complex nonlinear problems defined on data representations in the input space using simple, but implicitly defined, solutions. Spectral analysis on…