We explore the eeect of dimensionality on the \nearest neigh-bor" problem. We show that under a broad set of conditions (much broader than independent and identically distributed dimensions), as di-mensionality increases, the distance to the nearest data point approaches the distance to the farthest data point. To provide a practical perspective , we present empirical results on both real and s...

The 1-N-N classifier is one of the oldest methods known. The idea is extremely simple: to classify X find its closest neighbor among the training points (call it X ,) and assign to X the label of X .

A fundamental activity common to image processing, pattern recognition, and clustering algorithm involves searching set of n , k-dimensional data for one which is nearest to a given target data with respect to distance function . Our goal is to find search algorithms with are full search equivalent -which is resulting match as a good as we could obtain if we were to search the set exhausting. 1...

Definition 1.1. Nearest Neighbor Search: Given a set of points {x1, . . . , xn} ∈ R preprocess them into a data structure X of size poly(n, d) in time poly(n, d) such that nearest neighbor queries can be performed in logarithmic time. In other words, given a search point q a radius r and X one can return an xi such the ||q − xi|| ≤ r or nothing if no such point exists. The search for xi should ...

conclusions by comparing the results of classification using multiple classifier fusion with respect to using each classifier separately, it is found that the classifier fusion is more effective in enhancing the detection accuracy. objectives through the improvement of classification accuracy rate, this work aims to present a computer-assisted diagnosis system for malaria parasite. materials an...

In this paper, using high order perturbative series expansion method, the critical exponents of the order parameter and susceptibility in transition from ferromagnetic to disordered phases for 1D quantum Ising model in transverse field, with ferromagnetic nearest neighbor and anti-ferromagnetic next to nearest neighbor interactions, are calculated. It is found that for small value of the frustr...

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 ...