Related papers: Nearest Neighbor and Contact Distance Distribution…
The closest pair of points problem or closest pair problem (CPP) is an important problem in computational geometry where we have to find a pair of points from a set of points in metric space with the smallest distance between them. This…
In the first part of a series of two papers, we present in considerable detail a collision-driven molecular dynamics algorithm for a system of nonspherical particles, within a parallelepiped simulation domain, under both periodic or…
Nearest neighbor is a popular class of classification methods with many desirable properties. For a large data set which cannot be loaded into the memory of a single machine due to computation, communication, privacy, or ownership…
Feature correspondence selection is pivotal to many feature-matching based tasks in computer vision. Searching for spatially k-nearest neighbors is a common strategy for extracting local information in many previous works. However, there is…
Incoherently illuminated or luminescent objects give rise to a low-contrast speckle-like pattern when observed through a thin diffusive medium, as such a medium effectively convolves their shape with a speckle-like point spread function…
A new formalism is presented for analytically obtaining the probability density function, \( P_{n}(s) \), for the distance between two random points in an \( n \)-dimensional sphere of radius \( R \). Our formalism allows \( P_{n}(s) \) to…
An accurate numerical consideration of 1D spinless fermion model with next-nearest neighbour (NNN) interactions is carried out for the electron concentrations 4/7. It is shown that depending on the parameters of the model it can be either…
The Reverse $k$-Nearest Neighbor (R$k$NN) query over moving objects on road networks seeks to find all moving objects that consider the specified query point as one of their $k$ nearest neighbors. In location based services, many users…
We use a geometric method to derive (two-dimensional) separation functions amongst pairs of objects within populations of specified position function $\mathrm{d} N/\mathrm{d} \vec{R}$. We present analytic solutions for separation functions…
The traditional k nearest neighbor (kNN) approach uses a distance formula within a spherical region to determine the k closest training observations to a test sample point. However, this approach may not work well when test point is located…
In this paper, we present a consensus-based decentralized multi-robot approach to reconstruct a discrete distribution of features, modeled as an occupancy grid map, that represent information contained in a bounded planar 2D environment,…
Proximity maps and regions are defined based on the relative allocation of points from two or more classes in an area of interest and are used to construct random graphs called proximity catch digraphs (PCDs) which have applications in…
Identifying nearest neighbors accurately is essential in particle-based simulations, from analyzing local structure to detecting phase transitions. While parameter-free methods such as Voronoi tessellation and the solid-angle…
Approximating distributions from their samples is a canonical statistical-learning problem. One of its most powerful and successful modalities approximates every distribution to an $\ell_1$ distance essentially at most a constant times…
K-Nearest Neighbours (k-NN) is a popular classification and regression algorithm, yet one of its main limitations is the difficulty in choosing the number of neighbours. We present a Bayesian algorithm to compute the posterior probability…
Nanoparticles (NPs) have proven their applicability in biosensing, drug delivery, and photo-thermal therapy, but their performance depends critically on the distribution and number of functional groups on their surface. When studying…
Starting with a similarity function between objects, it is possible to define a distance metric on pairs of objects, and more generally on probability distributions over them. These distance metrics have a deep basis in functional analysis,…
This report presents a new, algorithmic approach to the distributions of the distance between two points distributed uniformly at random in various polygons, based on the extended Kinematic Measure (KM) from integral geometry. We first…
The problem of nearest-neighbor (NN) condensation aims to reduce the size of a training set of a nearest-neighbor classifier while maintaining its classification accuracy. Although many condensation techniques have been proposed, few bounds…
In applications such as wireless communication, it is important to study the statistical properties of $L_{2}$, the minimal arc distance between a random point (e.g., a cellphone user) uniformly distributed on a sphere to a set of…