1/m. If m = ⌦ ✓ k log Lr ◆ , then for any x 2 S, if x0 = b x2G(M) kx b xk, we have kA(x x0)k = O( ) with probability 1 e ⌦(m). Note that for any given point x0 in S, if we try to find its nearest neighbor of that point in an -net on S, then the difference between the two is at most the . In words, this lemma says that even if we consider measurements made on these points, i.e. a linear projecti...

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

The kth-nearest neighbor rule is arguably the simplest and most intuitively appealing nonparametric classification procedure. However, application of this method is inhibited by lack of knowledge about its properties, in particular, about the manner in which it is influenced by the value of k; and by the absence of techniques for empirical choice of k. In the present paper we detail the way in ...