相关论文: Uniformity of point samples in metric spaces using…

Data uniformity is a concept associated with several semantic data characteristics such as lack of features, correlation and sample bias. This article introduces a novel measure to assess data uniformity and detect uniform pointsets on…

WWe define the notion of a random metric space and prove that with probability one such a space is isometricto the Urysohn universal metric space. The main technique is the study of universal and random distance matrices; we relate the…

We extend the notion of the distance to a measure from Euclidean space to probability measures on general metric spaces as a way to do topological data analysis in a way that is robust to noise and outliers. We then give an efficient way to…

Uniform distribution of the points has been of interest to researchers for a long time and has applications in different areas of Mathematics and Computer Science. One of the well-known measures to evaluate the uniformity of a given…

In the uniformity testing task, an algorithm is provided with samples from an unknown probability distribution over a (known) finite domain, and must decide whether it is the uniform distribution, or, alternatively, if its total variation…

We say that a metric graph is uniformly bounded if the degrees of all vertices are uniformly bounded and the lengths of edges are pinched between two positive constants; a metric space is approximable by a uniform graph if there is one…

We survey a new area of parameter-free similarity distance measures useful in data-mining, pattern recognition, learning and automatic semantics extraction. Given a family of distances on a set of objects, a distance is universal up to a…

Author developed a uniform model for different spaces where distance and angle measure kinds are parameters. This model is calculus centric, but can also be used in theoretical research. It is useful in the following domains: deduction of…

The computational complexity of some depths that satisfy the projection property, such as the halfspace depth or the projection depth, is known to be high, especially for data of higher dimensionality. In such scenarios, the exact depth is…

We investigate lower asymptotic bounds of number variances for invariant locally square-integrable random measures on Euclidean and real hyperbolic spaces. In the Euclidean case we show that there are subsequences of radii for which the…

We introduce and investigate in this short report the new notion of uniform measure (distribution) on the arbitrary compact metric space. We consider also some possible applications of these measures in the theory of imbedding theorems and…

Discretization of the uniform norm of functions from a given finite dimensional subspace of continuous functions is studied. Previous known results show that for any $N$-dimensional subspace of the space of continuous functions it is…

Spectral analysis plays a crucial role in high-dimensional statistics, where determining the asymptotic distribution of various spectral statistics remains a challenging task. Due to the difficulties of deriving the analytic form, recent…

Many data analysis problems can be cast as distance geometry problems in \emph{space forms} -- Euclidean, spherical, or hyperbolic spaces. Often, absolute distance measurements are often unreliable or simply unavailable and only proxies to…

In this paper, we deal with uniform spaces whose diagonal uniformity admits a basis consisting of equivalence relations. Such non-Archimedean uniform spaces are particularly interesting for applications in commutative ring theory, because…

We propose an approach for capturing the signal variability in hyperspectral imagery using the framework of the Grassmann manifold. Labeled points from each class are sampled and used to form abstract points on the Grassmannian. The…

Given a probability measure with density, Fermat distances and density-driven metrics are conformal transformations of the Euclidean metric that shrink distances in high density areas and enlarge distances in low density areas. Although…

Distribution testing can be described as follows: $q$ samples are being drawn from some unknown distribution $P$ over a known domain $[n]$. After the sampling process, a decision must be made about whether $P$ holds some property, or is far…

How to distribute a set of points uniformly on a spherical surface is a very old problem that still lacks a definite answer. In this work, we introduce a physical measure of uniformity based on the distribution of distances between points,…

Randomly sampling points on surfaces is an essential operation in geometry processing. This sampling is computationally straightforward on explicit meshes, but it is much more difficult on other shape representations, such as widely-used…