Given n data points in d-dimensional space, nearest neighbor searching involves determining the nearest of these data points to a given query point. Most average-case analyses of nearest neighbor searching algorithms are made under the simplifying assumption that d is xed and that n is so large relative to d that boundary eeects can be ignored. This means that for any query point the statistica...

We suggest a simple modification to the Kd-tree search algorithm for nearest neighbor search resulting in an improved performance. The Kd-tree data structure seems to work well in finding nearest neighbors in low dimensions but its performance degrades even if the number of dimensions increases to more than two. Since the exact nearest neighbor search problem suffers from the curse of dimension...

kernel density estimators are the basic tools for density estimation in non-parametric statistics.  the k-nearest neighbor kernel estimators represent a special form of kernel density estimators, in  which  the  bandwidth  is varied depending on the location of the sample points. in this paper‎, we  initially introduce the k-nearest neighbor kernel density estimator in the random left-truncatio...

We consider clusters formed by points randomly distributed in space, each point being connected to its nearest neighbor or to its nearest and next nearest neighbors. The size distribution of such clusters in n-dimensional space is presented.

Given a closed set C in a Banach space (X, ‖ · ‖), a point x ∈ X is said to have a nearest point in C if there exists z ∈ C such that dC(x) = ‖x − z‖, where dC is the distance of x from C. We shortly survey the problem of studying the size of the set of points in X which have nearest points in C. We then turn to the topic of delta-convex functions and indicate how it is related to finding neare...

In the Nearest Neighbor problem (NN), the objects in the database that are nearer to a given query object than any other objects in the database have to be found. In the conceptually inverse problem, Reverse Nearest Neighbor problem (RNN), objects that have the query object as their nearest neighbor have to be found. Reverse Nearest Neighbors queries have emerged as an important class of querie...

We examine a variant of the clasic nearest neighbor problem, where given a set of k points, we preprocess the points so that we can quickly answer the distance to the nearest neighbor to a query point. We specifically focus on the case where all points—both the k original points as well all query points—are confined to an n×n integer grid in the plane. Furthermore, we only require the distance ...

The “nearest neighbor” relation, or more generally the “k nearest neighbors” relation, defined for a set of points in a metric space, has found many uses in computational geometry and clustering analysis, yet surprisingly little is known about some of its basic properties. In this paper, we consider some natural questions that are motivated by geometric embedding problems. We derive bounds on t...