Consider a set  of  points that are independently and uniformly distributed in the -dimensional unit cube. Let  ∈  . There exists almost-surely  ∈  such that  6=  and | − |  | − | for all  ∈  ,  6= ,  6= . The point  is called the nearest neighbor of  and we write  ≺ . Note that  ≺  does not imply  ≺ . Draw an edge connecting  and  if and only if  ≺ ; the resulti...

Motivated by applications in computer vision and databases, we introduce and study the Simultaneous Nearest Neighbor Search (SNN) problem. Given a set of data points, the goal of SNN is to design a data structure that, given a collection of queries, finds a collection of close points that are “compatible” with each other. Formally, we are given k query points Q = q1, · · · , qk, and a compatibi...

The case of n unity-variance random variables x1, XZ,. * *, x, governed by the joint probability density w(xl, xz, * * * x,) is considered, where the density depends on the (normalized) cross-covariances pii = E[(xi jzi)(xi li)]. It is shown that the condition holds for an “arbitrary” function f(xl, x2, * * * , x,) of n variables if and only if the underlying density w(xl, XZ, * * * , x,) is th...

The k nearest neighbor classification (k-NN) is a very simple and popular method for classification. However, it suffers from a major drawback, it assumes constant local class posterior probability. It is also highly dependent on and sensitive to the choice of the number of neighbors k. In addition, it severely lacks the desired probabilistic formulation. In this article, we propose a Bayesian ...

Nearest neighbor (NN) methods include at least six different groups of statistical methods. All have in common the idea that some aspect of the similarity between a point and its NN can be used to make useful inferences. In some cases, the similarity is the distance between the point and its NN; in others, the appropriate similarity is based on other identifying characteristics of the points. I...

Preprocess: a set D of points in R d Query: given a new point q, report a point pD with the smallest distance to q q p Motivation