Related papers: Evaluating a distance function
We give an algorithm for approximating a given plane curve segment by a planar elastic curve. The method depends on an analytic representation of the space of elastic curve segments, together with a geometric method for obtaining a good…
The Simpson's formula is obtained by approximating the integral of a function on some interval by the integral of the quadratic polynomial determined by the function. However, a multidimensional analogue of the formula has not been given as…
Learning a distance function or metric on a given data manifold is of great importance in machine learning and pattern recognition. Many of the previous works first embed the manifold to Euclidean space and then learn the distance function.…
We discuss the problem of how to calculate the distance between two cosmological objects given their redshifts and angular separation on the sky. Although of a fundamental nature, this problem and its solution seem to lack a detailed…
A numerical method for an inverse problem for an elliptic equation with the running source at multiple positions is presented. This algorithm does not rely on a good first guess for the solution. The so-called "approximate global…
A function $f : \mathbb{F}_2^n \to \mathbb{R}$ is $s$-sparse if it has at most $s$ non-zero Fourier coefficients. Motivated by applications to fast sparse Fourier transforms over $\mathbb{F}_2^n$, we study efficient algorithms for the…
We give an overview of different approaches to measuring the similarity of, or the distance between, two graphs, highlighting connections between these approaches. We also discuss the complexity of computing the distances.
We obtain matching direct and inverse theorems for the degree of weighted $L_p$-approximation by polynomials with the Jacobi weights $(1-x)^\alpha (1+x)^\beta$. Combined, the estimates yield a constructive characterization of various…
We study the problem of approximating the level set of an unknown function by sequentially querying its values. We introduce a family of algorithms called Bisect and Approximate through which we reduce the level set approximation problem to…
The Hausdorff distance is a measure of (dis-)similarity between two sets which is widely used in various applications. Most of the applied literature is devoted to the computation for sets consisting of a finite number of points. This has…
Distance function is a main metrics of measuring the affinity between two data points in machine learning. Extant distance functions often provide unreachable distance values in real applications. This can lead to incorrect measure of the…
An $\epsilon$-approximate incidence between a point and some geometric object (line, circle, plane, sphere) occurs when the point and the object lie at distance at most $\epsilon$ from each other. Given a set of points and a set of objects,…
We consider the distributionally robust optimization and show that computing the distributional worst-case is equivalent to computing the projection onto the canonical simplex with additional linear inequality. We consider several distance…
Approximate Bayesian computation performs approximate inference for models where likelihood computations are expensive or impossible. Instead simulations from the model are performed for various parameter values and accepted if they are…
Singular and oscillatory functions feature in numerous applications. The high-accuracy approximation of such functions shall greatly help us develop high-order methods for solving applied mathematics problems. This paper demonstrates that…
In this paper, we study the Jacobi frame approximation with equispaced samples and derive an error estimation. We observe numerically that the approximation accuracy gradually decreases as the extended domain parameter $\gamma$ increases in…
Fractional calculus with respect to function $\psi$, also named as $\psi$-fractional calculus, generalizes the Hadamard and the Riemann-Liouville fractional calculi, which causes challenge in numerical treatment. In this paper we study…
In this short note, we show that the distance function to any finite set $X\subset \mathbb{R}^n$ is a topological Morse function, regardless of whether $X$ is in general position. We also precisely characterize its topological critical…
It is shown that the Rayleigh's dissipation function can be successfully applied in the solution of mechanical problems involving friction non-linear in the velocities. Through the study of surfaces at contact we arrive at a simple integral…
Given an arbitrary long but finite sequence of observations from a finite set, we construct a simple process that approximates the sequence, in the sense that with high probability the empirical frequency, as well as the empirical one-step…