We consider approximate nearest neighbor searching in metric spaces of constant doubling dimension. More formally, we are given a set S of n points and an error bound ε > 0. The objective is to build a data structure so that given any query point q in the space, it is possible to efficiently determine a point of S whose distance from q is within a factor of (1 + ε) of the distance between q and...

This work deals with the problem of classifying uncertain data. With this aim the Uncertain Nearest Neighbor (UNN) rule is here introduced, which represents the generalization of the deterministic nearest neighbor rule to the case in which uncertain objects are available. The UNN rule relies on the concept of nearest neighbor class, rather than on that of nearest neighbor object. The nearest ne...

This paper concerns approximate nearest neighbor searching algorithms, which have become increasingly important, especially in high dimensional perception areas such as computer vision, with dozens of publications in recent years. Much of this enthusiasm is due to a successful new approximate nearest neighbor approach called Locality Sensitive Hashing (LSH). In this paper we ask the question: c...

A nearest neighbor representation of a Boolean function is set positive and negative prototypes in Rn such that the has value 1 on an input iff closest prototype positive. For k-nearest majority classification k considered. The complexity minimal number needed to represent function. We give several bounds for this measure. Separations are given between cases when can be real or required Boolean...